Showing 1–50 of 94 results for author: Eckardt, A

Edge-state interferometry as a probe of local flux in isolated quantum Hall systems

Authors: Botao Wang, Nathan Goldman, André Eckardt

Abstract: Quantum point contacts (QPCs) are essential tools for transport experiments in solid-state systems, enabling the detection of fractional charges and anyonic braiding statistics. Realizing analogous transport setups in isolated quantum-simulation platforms, such as ultracold atoms, remains challenging, since it typically requires coupling to external reservoirs. Here we show that the scattering pro… ▽ More Quantum point contacts (QPCs) are essential tools for transport experiments in solid-state systems, enabling the detection of fractional charges and anyonic braiding statistics. Realizing analogous transport setups in isolated quantum-simulation platforms, such as ultracold atoms, remains challenging, since it typically requires coupling to external reservoirs. Here we show that the scattering properties of chiral edge states at a QPC can instead be extracted directly from the stationary edge currents of an isolated, reservoir-free lattice system. Exploiting the sensitivity of this scattering to Aharonov-Bohm-type phases, we propose an equilibrium protocol to detect local magnetic fluxes from ground-state edge currents. We further introduce a dynamical scheme, robust against finite temperature and particle-number fluctuations, based on the post-quench evolution following a sudden potential-bias removal. Since anyonic excitations are themselves associated with a local, quantized magnetic flux, our approach should extend to probing anyonic statistical phases in quantum-engineered platforms. △ Less

Submitted 12 July, 2026; originally announced July 2026.

Comments: 9 pages, 4+1 figures; comments are welcome

Quantum statistical enhancement of collective behaviour in a bosonic active Ising model

Authors: Kian L. Assent, Emil Strauch, Sabine H. L. Klapp, André Eckardt, Alexander Schnell

Abstract: Collective behaviour such as flocking (the collective motion of a spontaneously formed group along a common direction) or aster formation (the binding of opposing flocks, inhibiting each others motion) are intriguing emergent phenomena in active systems with local alignment rules. Until recently, their occurrence was mainly studied for classical systems, a prime example being the active Ising mode… ▽ More Collective behaviour such as flocking (the collective motion of a spontaneously formed group along a common direction) or aster formation (the binding of opposing flocks, inhibiting each others motion) are intriguing emergent phenomena in active systems with local alignment rules. Until recently, their occurrence was mainly studied for classical systems, a prime example being the active Ising model (AIM), which translates the main ingredients of flocking and aster formation (i.e., alignment and self-propulsion) to a lattice framework. Here we introduce and study a one-dimensional (1D) quantum lattice variant of the AIM, based on ideal bosons with a spin degree of freedom. We find that both the collective behaviours of the 1D classical model, flocking and aster formation, are markedly enhanced by the bosonic quantum statistics. This contrasts with a recent quantum generalization of the AIM based onto hard-core bosons [Khasseh et al., Phys. Rev. Lett. 135, 248302 (2025)], where flocking, but neither its quantum-statistical stabilization nor aster states were observed as a consequence of interactions. Moreover, we investigate the competition of this quantum statistical stabilization of collective phases with their suppression by the quantum fluctuations induced by a transverse external magnetic field. △ Less

Submitted 2 July, 2026; v1 submitted 16 June, 2026; originally announced June 2026.

Adiabatic realization of anomalous Floquet topological systems

Authors: Luca Asteria, Marcel N. Kosch, Henrik P. Zahn, Jonathan Bracker, André Eckardt, Klaus Sengstock, Christof Weitenberg

Abstract: Topology has emerged as a central concept for classifying phases of matter. The situation is especially rich in periodically driven systems, where anomalous Floquet topological phases break the usual bulk-boundary correspondence between Chern number and edges modes of two-dimensional systems. These phases were so far realized by periodic modulation of the tunneling elements at frequencies near-res… ▽ More Topology has emerged as a central concept for classifying phases of matter. The situation is especially rich in periodically driven systems, where anomalous Floquet topological phases break the usual bulk-boundary correspondence between Chern number and edges modes of two-dimensional systems. These phases were so far realized by periodic modulation of the tunneling elements at frequencies near-resonant with respect to the system's bandwidth, a regime where Floquet heating plays a significant role in interacting systems. Here we show that such anomalous Floquet topological phases can also be realized by means of an adiabatic protocol, where the system is always in the instantaneous ground state of the cyclic path in parameter space, like in a Thouless charge pump. We experimentally realize such a state using ultracold atoms in a hexagonal lattice where we adiabatically modulate the lattice geometry, including the sublattice offset. To infer the topology, we use the micromotion area in real-space, which was recently identified as a proxy for the winding number. This way of realizing anomalous phases avoids resonant Floquet heating and imperfect loading into the target state. We demonstrate the robustness of the adiabatic construction by observing the anomalous phase even in the presence of mean-field interactions of magnitude comparable to all other energy scales. These findings are promising for engineering novel topological states in a more robust way. △ Less

Submitted 15 June, 2026; originally announced June 2026.

Adiabatic preparation of a fractional quantum Hall fluid by coherently pumping atoms from a Bose-Einstein condensate

Authors: Alberto Tabarelli de Fatis, Christof Weitenberg, Alexander Schnell, André Eckardt, Iacopo Carusotto

Abstract: We propose a protocol to adiabatically prepare a many-particle fractional quantum Hall fluid of bosonic ultracold atoms exploiting a time-dependent coherent coupling of a strongly interacting atomic state with a large dilute Bose-Einstein condensate. Starting from an empty cloud, atoms with well-defined angular momentum are coherently pumped into the fluid by Raman beams with a Laguerre-Gauss prof… ▽ More We propose a protocol to adiabatically prepare a many-particle fractional quantum Hall fluid of bosonic ultracold atoms exploiting a time-dependent coherent coupling of a strongly interacting atomic state with a large dilute Bose-Einstein condensate. Starting from an empty cloud, atoms with well-defined angular momentum are coherently pumped into the fluid by Raman beams with a Laguerre-Gauss profile. Compared to number-conserving schemes which rely on finite-size-induced topological gaps, we identify an adiabatic path in the Fock space which avoids crossing topological phase transitions and thus maintains a sizable adiabatic gap open at all times. The efficiency of our preparation protocol is numerically assessed for typical experimental parameters up to particle numbers that largely exceed the experimental state-of-the-art. The crucial advantage of including an anharmonic confinement is finally highlighted. △ Less

Submitted 14 June, 2026; originally announced June 2026.

Comments: 10 pages, 10 figures

Dissipation-assisted preparation of Floquet-Laughlin states in superconducting circuits

Authors: Luis C. Steinfadt, André Eckardt, Francesco Petiziol

Abstract: Fractional Chern insulators (FCIs) are lattice analogs of fractional quantum Hall systems, where the interplay of strong interactions with a frustrated tunnelling kinetics leads to the emergence of a gapped ground state with long-range entanglement and anyonic excitations. The highly correlated nature of such systems makes their adiabatic preparation challenging already beyond the minimal system s… ▽ More Fractional Chern insulators (FCIs) are lattice analogs of fractional quantum Hall systems, where the interplay of strong interactions with a frustrated tunnelling kinetics leads to the emergence of a gapped ground state with long-range entanglement and anyonic excitations. The highly correlated nature of such systems makes their adiabatic preparation challenging already beyond the minimal system size of two particles. Considering Floquet implementations of the bosonic Harper-Hofstadter-Hubbard model of few photons in superconducting circuits, we design protocols for the driven-dissipative stabilization of its FCI ground state at half filling via quantum bath engineering. Dissipation control is achieved through the coupling to driven leaky cavity modes, which realize a tuneable artificial environment having the Floquet-FCI as its approximate fixed point. For systems of two, three and six particles, we show numerically how the flexibility of the control scheme further allows for the detection of fractional quantum Hall signatures in the stabilized steady states, including bulk incompressibility, Hall response and the trapping of fractional charges. Our results provide a concrete pathway to dissipation-assisted preparation of strongly correlated states in quantum simulators. △ Less

Submitted 26 May, 2026; v1 submitted 18 May, 2026; originally announced May 2026.

Comments: 5 + 2 + 2 pages, 2 + 0 + 0 figures, 0 + 0 + 3 tables

Dissipative Floquet engineering of gapped many-body phases using thermal baths

Authors: Lorenz Wanckel, André Eckardt

Abstract: Floquet engineering, the control of a quantum system by means of time-periodic driving, allows to modify the properties of the system so that it becomes described by an approximate effective time-independent Hamiltonian. However, in the presence of interactions the stabilization of interesting many-body ground states of such effective Hamiltonians is possible only on a certain time scale, beyond w… ▽ More Floquet engineering, the control of a quantum system by means of time-periodic driving, allows to modify the properties of the system so that it becomes described by an approximate effective time-independent Hamiltonian. However, in the presence of interactions the stabilization of interesting many-body ground states of such effective Hamiltonians is possible only on a certain time scale, beyond which Floquet heating sets in, as it results from unwanted driving induced resonant excitation. Moreover, already the preparation of such states is challenged by excitations due to imperfect adiabatic dynamics, especially when a phase transition has to be passed. Here, we propose a general dissipative strategy for the preparation and stabilization of effective ground states that are protected by an energy gap. Our approach relies on coupling the driven system to a thermal bath, the properties of which are chosen so that it both suppresses Floquet heating and guides the system into a non-equilibrium steady state with a large occupation of the effective ground-state, but generally non-thermal occupations of excited states of the effective Hamiltonian. We use the Floquet-Born-Markov master equation to verify the proposed strategy for the example of a strongly driven Bose-Hubbard chain with an effective gapped Mott-insulator ground state. △ Less

Submitted 1 April, 2026; originally announced April 2026.

Micromotion area as proxy for anomalous Floquet topological systems

Authors: Luca Asteria, Klaus Sengstock, André Eckardt, Christof Weitenberg

Abstract: Driven Floquet systems can realize topological phases with no static counterparts. These so-called anomalous Floquet topology breaks the bulk-boundary correspondence based on the Chern number. The number of edge modes in each band gap is instead determined by another integer index, a winding number, which is calculated from the time evolution operator of the bulk states within one driving period.… ▽ More Driven Floquet systems can realize topological phases with no static counterparts. These so-called anomalous Floquet topology breaks the bulk-boundary correspondence based on the Chern number. The number of edge modes in each band gap is instead determined by another integer index, a winding number, which is calculated from the time evolution operator of the bulk states within one driving period. While in the non-driven system, Chern markers provide a useful local proxy for the Chern number in the bulk, so far no such local bulk indicator is known for the winding number in Floquet systems. Here we consider two-band models and show that the area enclosed during a Floquet period by an initially localized particle signals the presence of an anomalous phase when it approaches half the unit cell area. In general, we show that at the fine-tuned point of dispersionless dynamics during the micromotion, the enclosed area is quantized and an exact proportionality relation exists between the area and the winding number. Direct detection of anomalous topology in real space could be realized in several quantum simulation platforms, and could be useful for systems with disorder or interactions. Building on the connection between area and winding number, we also show a way to realize arbitrarily high winding numbers. △ Less

Submitted 26 March, 2026; originally announced March 2026.

Comments: 7 pages, 3 figures

Revealing Pseudo-Fermionization and Chiral Binding of One-Dimensional Anyons using Adiabatic State Preparation

Authors: Brice Bakkali-Hassani, Joyce Kwan, Perrin Segura, Yanfei Li, Isaac Tesfaye, Gerard Valentí-Rojas, André Eckardt, Markus Greiner

Abstract: Fractional statistics give rise to quantum behaviors that differ fundamentally from those of bosons and fermions. While two-dimensional anyons play a major role in strongly correlated systems and topological quantum computing, the nature of their one-dimensional (1D) counterparts remains the subject of intense debate, with renewed interest fueled by recent experimental progress. Theoretically, 1D… ▽ More Fractional statistics give rise to quantum behaviors that differ fundamentally from those of bosons and fermions. While two-dimensional anyons play a major role in strongly correlated systems and topological quantum computing, the nature of their one-dimensional (1D) counterparts remains the subject of intense debate, with renewed interest fueled by recent experimental progress. Theoretically, 1D anyons are predicted to host exotic many-body phases and quantum phase transitions, yet experimental signatures have remained elusive. Using ultracold atoms in an optical lattice, we prepare two-body ground states of the 1D anyon-Hubbard model by combining Hamiltonian engineering via quasiperiodic drives and adiabatic state manipulation. We uncover the effects of statistical interactions that lead to pseudo-fermionization and to the formation of chiral bound states when particles remain close together. Our results establish a link between lattice and continuum realizations of anyon models, and mark important steps towards the precise control of 1D anyons in both equilibrium and out-of-equilibrium settings. △ Less

Submitted 23 February, 2026; originally announced February 2026.

Comments: 7 pages (4 figures) + 18 pages (11 figures)

Feedback cooling of fermionic atoms in optical lattices

Authors: Wenhua Zhao, Ling-Na Wu, Francesco Petiziol, André Eckardt

Abstract: We discuss the preparation of topological insulator states with fermionic ultracold atoms in optical lattices by means of measurement-based Markovian feedback control. The designed measurement and feedback operators induce an effective dissipative channel that stabilizes the desired insulator state, either in an exact way or approximately in the case where additional experimental constraints are a… ▽ More We discuss the preparation of topological insulator states with fermionic ultracold atoms in optical lattices by means of measurement-based Markovian feedback control. The designed measurement and feedback operators induce an effective dissipative channel that stabilizes the desired insulator state, either in an exact way or approximately in the case where additional experimental constraints are assumed. Successful state preparation is demonstrated in one-dimensional insulators as well as for Haldane's Chern insulator, by calculating the fidelity between the target ground state and the steady state of the feedback-modified master equation. The fidelity is obtained numerically through exact diagonalization or via time evolution of the system with moderate sizes. For larger 2D systems, we compare the mean occupation of the single-particle eigenstates for the ground and steady state computed through mean-field kinetic equations. △ Less

Submitted 21 July, 2025; v1 submitted 13 January, 2025; originally announced January 2025.

Comments: resubmission to SciPost

Journal ref: SciPost Phys. 19, 073 (2025)

Experimental protocol for observing single quantum many-body scars with transmon qubits

Authors: Peter Græns Larsen, Anne E. B. Nielsen, André Eckardt, Francesco Petiziol

Abstract: Quantum many-body scars are energy eigenstates which fail to reproduce thermal expectation values of local observables, in systems where the rest of the many-body spectrum fulfils eigenstate thermalization. Experimental observation of quantum many-body scars has so far been limited to models with multiple scar states evenly spaced in energy. It is thus an interesting question whether even single i… ▽ More Quantum many-body scars are energy eigenstates which fail to reproduce thermal expectation values of local observables, in systems where the rest of the many-body spectrum fulfils eigenstate thermalization. Experimental observation of quantum many-body scars has so far been limited to models with multiple scar states evenly spaced in energy. It is thus an interesting question whether even single isolated scars, which theoretically embody the weakest possibile violation of eigenstate thermalization and may be thought to have no detectable impact in experiments, can leave a trace in measurable quantities. Moreover, single scars offer an interesting scenario for exploring the connection between quantum many-body scars and the original notion of scarring in quantum dynamical systems theory. Here we propose protocols to observe single scars in architectures of fixed-frequency, fixed-coupling superconducting qubits. We first adapt known models possessing the desired features into a form particularly suited for the experimental platform. We develop protocols for the implementation of these models, through trotterized sequences of two-qubit cross-resonance interactions, and verify the existence of the approximate scar state in the stroboscopic effective Hamiltonian. Since a single scar cannot be detected from coherent revivals in the dynamics, differently from towers of scar states, we propose and numerically investigate alternative and experimentally-accessible signatures. These include the dynamical response of the scar to local state deformations, to controlled noise, and to the resolution of the Lie-Suzuki-Trotter digitization. △ Less

Submitted 11 August, 2025; v1 submitted 18 October, 2024; originally announced October 2024.

Comments: 17 pages, 7 figures

Journal ref: SciPost Phys. 20, 036 (2026)

Effective (Floquet) Lindblad generators from spectral unwinding

Authors: Görkem D. Dinc, André Eckardt, Alexander Schnell

Abstract: A mathematical description of the reduced dynamics of an open quantum system can often be given in terms of a completely positive and trace preserving (CPTP) map, also known as quantum channel. In a seminal work by Wolf et al. [Phys. Rev. Lett. 101, 150402 (2008)], it was shown that deciding whether a given quantum channel was generated from an underlying effective Markovian dynamics, with time-in… ▽ More A mathematical description of the reduced dynamics of an open quantum system can often be given in terms of a completely positive and trace preserving (CPTP) map, also known as quantum channel. In a seminal work by Wolf et al. [Phys. Rev. Lett. 101, 150402 (2008)], it was shown that deciding whether a given quantum channel was generated from an underlying effective Markovian dynamics, with time-independent generator of Lindblad form, is generally an NP-hard problem. The difficulty is related to the fact that one has to search through all possible branches of the operator logarithm of the map, in order to identify, if any of the resulting effective generators is of Lindblad form. In this work we show that in cases where one has access to the full reduced dynamics at all previous times (the dynamical map) one can significantly facilitate the search for an effective generator by making use of Floquet theory. By performing a spectral unwinding such that the effective micromotion is minimized, the effective Floquet generator is often an excellent candidate for an effective generator of Lindblad form. This significantly reduces the complexity of the search for an effective generator of Lindblad form in many (though not all) cases. Our results are relevant for engineering Floquet Lindbladians in complex many-body systems. △ Less

Submitted 3 June, 2025; v1 submitted 25 September, 2024; originally announced September 2024.

Journal ref: Physical Review A 111 (6), 062216 (2025)

Quantum geometry of bosonic Bogoliubov quasiparticles

Authors: Isaac Tesfaye, André Eckardt

Abstract: Bosonic Bogoliubov de Gennes (BBdG) Hamiltonians describe the excitations of weakly interacting Bose condensates as well as photonic systems under parametric driving. Their topological features have been studied mainly by utilizing a generalized symplectic version of the Berry curvature and related Chern numbers. However, a full characterization of geometrical features in BBdG systems is still lac… ▽ More Bosonic Bogoliubov de Gennes (BBdG) Hamiltonians describe the excitations of weakly interacting Bose condensates as well as photonic systems under parametric driving. Their topological features have been studied mainly by utilizing a generalized symplectic version of the Berry curvature and related Chern numbers. However, a full characterization of geometrical features in BBdG systems is still lacking. Here, we propose a symplectic quantum geometric tensor (SQGT), whose imaginary part leads to the previously studied symplectic Berry curvature, while the real part gives rise to a symplectic quantum metric, providing a natural distance measure in the space of bosonic Bogoliubov modes. The SQGT is directly related to observable properties of BBdG systems. We show how to measure all components of the SQGT by extracting excitation rates in response to periodic modulations of the systems' parameters. Moreover, we connect the symplectic Berry curvature to a generalized symplectic anomalous velocity term for Bogoliubov-Bloch wave packets. We test our results for a bosonic Bogoliubov-Haldane model. △ Less

Submitted 15 October, 2025; v1 submitted 18 June, 2024; originally announced June 2024.

Comments: 9+29 pages, 3+2 figures; v3 added discussion on PHS and comparison to QGT; v4 minor additions to SM

Journal ref: Phys. Rev. Res. 7, L042052 (2025)

Benchmarking quantum master equations beyond ultraweak coupling

Authors: C. S. Tello Breuer, T. Becker, A. Eckardt

Abstract: Recently, Nathan and Rudner derived a Gorini-Kossakowski-Sudarshan-Lindblad master equation from the Redfield equation. The claim is that the level of approximation is equal to that of the Redfield equation. Here we benchmark the Nathan-Rudner equation (NRE) against the exact solution of a damped harmonic oscillator and compare its performance to that of the time-dependent Redfield equation (RE).… ▽ More Recently, Nathan and Rudner derived a Gorini-Kossakowski-Sudarshan-Lindblad master equation from the Redfield equation. The claim is that the level of approximation is equal to that of the Redfield equation. Here we benchmark the Nathan-Rudner equation (NRE) against the exact solution of a damped harmonic oscillator and compare its performance to that of the time-dependent Redfield equation (RE). We find that which of the equations performs better depends on the regime considered. It turns out that the short-time dynamics is generally much better captured by the RE, whereas the NRE delivers results comparable to those of the rotating-wave approximation. For the steady state, in the high-temperature limit the RE again performs better and its solution approaches the exact result for ultrahigh temperatures. Nevertheless, here also the NR equation constitutes a good approximation. In the low-temperature limit, in turn, the NRE provides a better approximation than the RE. For too strong coupling, here the RE might even fail completely by predicting unphysical behaviour. △ Less

Submitted 23 July, 2024; v1 submitted 13 March, 2024; originally announced March 2024.

Optimal form of time-local non-Lindblad master equations

Authors: Tobias Becker, André Eckardt

Abstract: Time-local quantum master equations that describe open quantum systems beyond the limit of ultraweak system-bath coupling are often not of Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) form. Prominent examples are the Redfield equation approximating general open quantum systems and the Hu-Paz-Zhang equation exactly describing a damped harmonic oscillator. Here, we show that not only the former, but… ▽ More Time-local quantum master equations that describe open quantum systems beyond the limit of ultraweak system-bath coupling are often not of Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) form. Prominent examples are the Redfield equation approximating general open quantum systems and the Hu-Paz-Zhang equation exactly describing a damped harmonic oscillator. Here, we show that not only the former, but also the latter can be brought to pseudo-Lindblad form, with a dissipator that resembles that of a GKSL equation, except for the fact that some of the terms have negative weights. Moreover, we systematically investigate transformations that leave the dissipator of pseudo-Lindblad equations unchanged, while changing the relative weight between its positive and negative terms. These can be used to minimize the weights of the negative terms, which is optimal both for the convergence of a recently developed quantum-trajectory unraveling of pseudo-Lindblad equations as well as for the truncation of the negative terms to obtain a GKSL equation. △ Less

Submitted 19 July, 2024; v1 submitted 22 December, 2023; originally announced December 2023.

Reversible phasonic control of a quantum phase transition in a quasicrystal

Authors: Toshihiko Shimasaki, Yifei Bai, H. Esat Kondakci, Peter Dotti, Jared E. Pagett, Anna R. Dardia, Max Prichard, André Eckardt, David M. Weld

Abstract: Periodic driving can tune the quasistatic properties of quantum matter. A well-known example is the dynamical modification of tunneling by an oscillating electric field. Here we show experimentally that driving the phasonic degree of freedom of a cold-atom quasicrystal can continuously tune the effective quasi-disorder strength, reversibly toggling a localization-delocalization quantum phase trans… ▽ More Periodic driving can tune the quasistatic properties of quantum matter. A well-known example is the dynamical modification of tunneling by an oscillating electric field. Here we show experimentally that driving the phasonic degree of freedom of a cold-atom quasicrystal can continuously tune the effective quasi-disorder strength, reversibly toggling a localization-delocalization quantum phase transition. Measurements agree with fit-parameter-free theoretical predictions, and illuminate a fundamental connection between Aubry-André localization in one dimension and dynamic localization in the associated two-dimensional Harper-Hofstadter model. These results open up new experimental possibilities for dynamical coherent control of quantum phase transitions. △ Less

Submitted 1 December, 2023; originally announced December 2023.

Comments: 5 pages, 4 figures, Supplementary information

Controlling Nonequilibrium Bose-Einstein Condensation with Engineered Environments

Authors: Francesco Petiziol, André Eckardt

Abstract: Out of thermal equilibrium, bosonic quantum systems can Bose-condense away from the ground state, featuring a macroscopic occupation of an excited state or even of multiple states in the so-called Bose-selection scenario. In previous work, a theory was developed that predicts, in which states a driven-dissipative ideal Bose gas condenses. Here, we address the inverse problem: Given a target state… ▽ More Out of thermal equilibrium, bosonic quantum systems can Bose-condense away from the ground state, featuring a macroscopic occupation of an excited state or even of multiple states in the so-called Bose-selection scenario. In previous work, a theory was developed that predicts, in which states a driven-dissipative ideal Bose gas condenses. Here, we address the inverse problem: Given a target state with desired condensate fractions in certain single-particle states, how can this configuration be achieved by tuning available control parameters? Which type of experimental setup allows for flexible condensation control? We solve these problems, on the one hand, by proposing a Bose `condenser', experimentally implementable in a superconducting circuit, where targeted Bose condensation into eigenstates of a chain of resonators is driven through the coupling to artificial quantum baths, realized via auxiliary two-level systems. On the other, we develop a theory to solve the inverse problem based on linear programming methods. We further discuss the engineering of transition points between different Bose condensation configurations, which may find application for amplification, heat-flow control, and the design of highly-structured quantum baths. △ Less

Submitted 26 July, 2024; v1 submitted 3 November, 2023; originally announced November 2023.

Comments: 5 + 11 pages, 3 + 7 figures

Journal ref: Phys. Rev. A 110, L021701 (2024)

Beyond braid statistics: Constructing a lattice model for anyons with exchange statistics intrinsic to one dimension

Authors: Sebastian Nagies, Botao Wang, A. C. Knapp, André Eckardt, N. L. Harshman

Abstract: Anyons obeying fractional exchange statistics arise naturally in two dimensions: hard-core two-body constraints make the configuration space of particles not simply-connected. The braid group describes how topologically-inequivalent exchange paths can be associated to non-trivial geometric phases for abelian anyons. Braid-anyon exchange statistics can also be found in one dimension (1D), but this… ▽ More Anyons obeying fractional exchange statistics arise naturally in two dimensions: hard-core two-body constraints make the configuration space of particles not simply-connected. The braid group describes how topologically-inequivalent exchange paths can be associated to non-trivial geometric phases for abelian anyons. Braid-anyon exchange statistics can also be found in one dimension (1D), but this requires broken Galilean invariance to distinguish different ways for two anyons to exchange. However, recently it was shown that an alternative form of exchange statistics can occur in 1D because hard-core three-body constraints also make the configuration space not simply-connected. Instead of the braid group, the topology of exchange paths and their associated non-trivial geometric phases are described by the traid group. In this article we propose a first concrete model realizing this alternative form of anyonic exchange statistics. Starting from a bosonic lattice model that implements the desired geometric phases with number-dependent Peierls phases, we then define anyonic operators so that the kinetic energy term in the Hamiltonian becomes local and quadratic with respect to them. The ground-state of this traid-anyon-Hubbard model exhibits several indications of exchange statistics intermediate between bosons and fermions, as well as signs of emergent approximate Haldane exclusion statistics. The continuum limit results in a Galilean invariant Hamiltonian with eigenstates that correspond to previously constructed continuum wave functions for traid anyons. This provides not only an a-posteriori justification of our lattice model, but also shows that our construction serves as an intuitive approach to traid anyons, i.e. anyons intrinsic to 1D. △ Less

Submitted 14 January, 2024; v1 submitted 8 September, 2023; originally announced September 2023.

Comments: 43 pages, 15 figures

Journal ref: SciPost Phys. 16, 086 (2024)

A minimal quantum heat pump based on high-frequency driving and non-Markovianity

Authors: Manuel L. Alamo, Francesco Petiziol, André Eckardt

Abstract: We propose a minimal setup for a quantum heat pump, consisting of two tunnel-coupled quantum dots, each hosting a single level and each being coupled to a different fermionic reservoir. The working principle relies on both non-Markovian system-bath coupling and driving induced resonant coupling. We describe the system using a reaction-coordinate mapping in combination with Floquet-Born-Markov theo… ▽ More We propose a minimal setup for a quantum heat pump, consisting of two tunnel-coupled quantum dots, each hosting a single level and each being coupled to a different fermionic reservoir. The working principle relies on both non-Markovian system-bath coupling and driving induced resonant coupling. We describe the system using a reaction-coordinate mapping in combination with Floquet-Born-Markov theory and characterize its performance. △ Less

Submitted 19 June, 2024; v1 submitted 27 July, 2023; originally announced July 2023.

Comments: 9 pages, 5 Figures

Journal ref: Phys. Rev. E 109, 064121 (2024)

Dissipative preparation of a Floquet topological insulator in an optical lattice via bath engineering

Authors: Alexander Schnell, Christof Weitenberg, André Eckardt

Abstract: Floquet engineering is an important tool for realizing topologically nontrivial band structures for charge-neutral atoms in optical lattices. However, the preparation of a topological-band-insulator-type state of fermions, with one nontrivial quasi-energy band filled completely and the others empty, is challenging as a result of both driving induced heating as well as imperfect adiabatic state pre… ▽ More Floquet engineering is an important tool for realizing topologically nontrivial band structures for charge-neutral atoms in optical lattices. However, the preparation of a topological-band-insulator-type state of fermions, with one nontrivial quasi-energy band filled completely and the others empty, is challenging as a result of both driving induced heating as well as imperfect adiabatic state preparation (with the latter induced by the unavoidable gap closing when passing the topological transition). An alternative procedure that has been proposed is to prepare such states dissipatively, i.e. as a steady state that emerges when coupling the system to reservoirs. Here we discuss a concrete scheme that couples the system to a weakly interacting Bose condensate given by second atomic species acting as a heat bath. Our strategy relies on the engineering of the potential for the bath particles, so that they occupy weakly coupled tubes perpendicular to the two-dimensional system. Using Floquet-Born-Markov theory, we show that the resulting nonequilibrium steady state of the driven-dissipative system approximates a topological insulator. We even find indications for the approximate stabilization of an anomalous Floquet topological insulator, a state that is impossible to realize in equilibrium. △ Less

Submitted 5 June, 2024; v1 submitted 7 July, 2023; originally announced July 2023.

Journal ref: SciPost Phys. 17, 052 (2024)

The cold-atom elevator: From edge-state injection to the preparation of fractional Chern insulators

Authors: Botao Wang, Monika Aidelsburger, Jean Dalibard, André Eckardt, Nathan Goldman

Abstract: Optical box traps for cold atoms offer new possibilities for quantum-gas experiments. Building on their exquisite spatial and temporal control, we propose to engineer system-reservoir configurations using box traps, in view of preparing and manipulating topological atomic states in optical lattices. First, we consider the injection of particles from the reservoir to the system: this scenario is sh… ▽ More Optical box traps for cold atoms offer new possibilities for quantum-gas experiments. Building on their exquisite spatial and temporal control, we propose to engineer system-reservoir configurations using box traps, in view of preparing and manipulating topological atomic states in optical lattices. First, we consider the injection of particles from the reservoir to the system: this scenario is shown to be particularly well suited to activate energy-selective chiral edge currents, but also, to prepare fractional Chern insulating ground states. Then, we devise a practical evaporative-cooling scheme to effectively cool down atomic gases into topological ground states. Our open-system approach to optical-lattice settings provides a new path for the investigation of ultracold quantum matter, including strongly-correlated and topological phases. △ Less

Submitted 27 June, 2023; originally announced June 2023.

Comments: 15 pages, 11 figures including Supplementary material

Quantum trajectories for time-local non-Lindblad master equations

Authors: Tobias Becker, Ché Netzer, André Eckardt

Abstract: For the efficient simulation of open quantum systems we often use quantum jump trajectories given by pure states that evolve stochastically to unravel the dynamics of the underlying master equation. In the Markovian regime, when the dynamics is described by a Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) master equation, this procedure is known as Monte-Carlo wavefunction (MCWF) approach . However,… ▽ More For the efficient simulation of open quantum systems we often use quantum jump trajectories given by pure states that evolve stochastically to unravel the dynamics of the underlying master equation. In the Markovian regime, when the dynamics is described by a Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) master equation, this procedure is known as Monte-Carlo wavefunction (MCWF) approach . However, beyond ultraweak system-bath coupling, the dynamics of the system is not described by an equation of GKSL type, but rather by the Redfield equation, which can be brought into pseudo-Lindblad form. Here negative dissipation strengths prohibit the conventional approach. To overcome this problem, we propose a pseudo-Lindblad quantum trajectory (PLQT) unraveling. It does not require an effective extension of the state space, like other approaches, except for the addition of a single classical bit. We test the PLQT for the eternal non-Markovian master equation for a single qubit and an interacting Fermi Hubbard chain coupled to a thermal bath and discuss its computational effort compared to solving the full master equation. △ Less

Submitted 22 September, 2023; v1 submitted 26 June, 2023; originally announced June 2023.

Realization of 1D Anyons with Arbitrary Statistical Phase

Authors: Joyce Kwan, Perrin Segura, Yanfei Li, Sooshin Kim, Alexey V. Gorshkov, André Eckardt, Brice Bakkali-Hassani, Markus Greiner

Abstract: Low-dimensional quantum systems can host anyons, particles with exchange statistics that are neither bosonic nor fermionic. Despite indications of a wealth of exotic phenomena, the physics of anyons in one dimension (1D) remains largely unexplored. Here, we realize Abelian anyons in 1D with arbitrary exchange statistics using ultracold atoms in an optical lattice, where we engineer the statistical… ▽ More Low-dimensional quantum systems can host anyons, particles with exchange statistics that are neither bosonic nor fermionic. Despite indications of a wealth of exotic phenomena, the physics of anyons in one dimension (1D) remains largely unexplored. Here, we realize Abelian anyons in 1D with arbitrary exchange statistics using ultracold atoms in an optical lattice, where we engineer the statistical phase via a density-dependent Peierls phase. We explore the dynamical behavior of two anyons undergoing quantum walks, and observe the anyonic Hanbury Brown-Twiss effect, as well as the formation of bound states without on-site interactions. Once interactions are introduced, we observe spatially asymmetric transport in contrast to the symmetric dynamics of bosons and fermions. Our work forms the foundation for exploring the many-body behavior of 1D anyons. △ Less

Submitted 2 June, 2023; originally announced June 2023.

Comments: 8+10 pages, 5 figures

Non-perturbative Floquet engineering of the toric-code Hamiltonian and its ground state

Authors: Francesco Petiziol, Sandro Wimberger, André Eckardt, Florian Mintert

Abstract: We theoretically propose a quantum simulation scheme for the toric-code Hamiltonian, the paradigmatic model of a quantum spin liquid, based on time-periodic driving. We develop a hybrid continuous-digital strategy that exploits the commutativity of different terms in the target Hamiltonian. It allows one to realize the required four-body interactions in a nonperturbative way, attaining strong coup… ▽ More We theoretically propose a quantum simulation scheme for the toric-code Hamiltonian, the paradigmatic model of a quantum spin liquid, based on time-periodic driving. We develop a hybrid continuous-digital strategy that exploits the commutativity of different terms in the target Hamiltonian. It allows one to realize the required four-body interactions in a nonperturbative way, attaining strong coupling and the suppression of undesired processes. In addition, we design an optimal protocol for preparing the topologically ordered ground states with high fidelity. A proof-of-principle implementation of a topological device and its use to simulate the topological phase transition are also discussed. The proposed scheme finds natural implementation in architectures of superconducting qubits with tuneable couplings. △ Less

Submitted 1 June, 2023; v1 submitted 17 November, 2022; originally announced November 2022.

Comments: 21 pages, 9 figures

Journal ref: Phys. Rev. B 109, 075126 (2024)

Indication of critical scaling in time during the relaxation of an open quantum system

Authors: Ling-Na Wu, Jens Nettersheim, Julian Feß, Alexander Schnell, Sabrina Burgardt, Silvia Hiebel, Daniel Adam, André Eckardt, Artur Widera

Abstract: Phase transitions correspond to the singular behavior of physical systems in response to continuous control parameters like temperature or external fields. Near continuous phase transitions, associated with the divergence of a correlation length, universal power-law scaling behavior with critical exponents independent of microscopic system details is found. Recently, dynamical quantum phase transi… ▽ More Phase transitions correspond to the singular behavior of physical systems in response to continuous control parameters like temperature or external fields. Near continuous phase transitions, associated with the divergence of a correlation length, universal power-law scaling behavior with critical exponents independent of microscopic system details is found. Recently, dynamical quantum phase transitions and universal scaling have been predicted and also observed in the non-equilibrium dynamics of isolated quantum systems after a quench, with time playing the role of the control parameter. However, signatures of such critical phenomena in time in open systems, whose dynamics is driven by the dissipative contact to an environment, were so far elusive. Here, we present results indicating that critical scaling with respect to time can also occur during the relaxation dynamics of an open quantum system described by mixed states. We experimentally measure the relaxation dynamics of the large atomic spin of individual Caesium atoms induced by the dissipative coupling via spin-exchange processes to an ultracold Bose gas of Rubidium atoms. For initial states far from equilibrium, the entropy of the spin state is found to peak in time, transiently approaching its maximum possible value, before eventually relaxing to its lower equilibrium value. Moreover, a finite-size scaling analysis based on numerical simulations shows that it corresponds to a critical point with respect to time of the dissipative system in the limit of large system sizes. It is signalled by the divergence of a characteristic length at a critical time, characterized by critical exponents that are found to be independent of system details. △ Less

Submitted 30 October, 2023; v1 submitted 10 August, 2022; originally announced August 2022.

Journal ref: Nat Commun 15, 1714 (2024)

Heat transport in an optical lattice via Markovian feedback control

Authors: Ling-Na Wu, André Eckardt

Abstract: Ultracold atoms offer a unique opportunity to study many-body physics in a clean and well-controlled environment. However, the isolated nature of quantum gases makes it difficult to study transport properties of the system, which are among the key observables in condensed matter physics. In this work, we employ Markovian feedback control to synthesize two effective thermal baths that couple to the… ▽ More Ultracold atoms offer a unique opportunity to study many-body physics in a clean and well-controlled environment. However, the isolated nature of quantum gases makes it difficult to study transport properties of the system, which are among the key observables in condensed matter physics. In this work, we employ Markovian feedback control to synthesize two effective thermal baths that couple to the boundaries of a one-dimensional Bose-Hubbard chain. This allows for the realization of a heat-current-carrying state. We investigate the steady-state heat current, including its scaling with system size and its response to disorder. In order to study large systems, we use semi-classical Monte-Carlo simulation and kinetic theory. The numerical results from both approaches show, as expected, that for non- and weakly interacting systems with and without disorder one finds the same scaling of the heat current with respect to the system size as it is found for systems coupled to thermal baths. Finally, we propose and test a scheme for measuring the energy flow. Thus, we provide a route for the quantum simulation of heat-current-carrying steady states of matter in atomic quantum gases. △ Less

Submitted 27 July, 2022; originally announced July 2022.

Cavity-based reservoir engineering for Floquet-engineered superconducting circuits

Authors: Francesco Petiziol, André Eckardt

Abstract: Considering the example of superconducting circuits, we show how Floquet engineering can be combined with reservoir engineering for the controlled preparation of target states. Floquet engineering refers to the control of a quantum system by means of time-periodic forcing, typically in the high-frequency regime, so that the system is governed effectively by a time-independent Floquet Hamiltonian w… ▽ More Considering the example of superconducting circuits, we show how Floquet engineering can be combined with reservoir engineering for the controlled preparation of target states. Floquet engineering refers to the control of a quantum system by means of time-periodic forcing, typically in the high-frequency regime, so that the system is governed effectively by a time-independent Floquet Hamiltonian with novel interesting properties. Reservoir engineering, on the other hand, can be achieved in superconducting circuits by coupling a system of artificial atoms (or qubits) dispersively to pumped leaky cavities, so that the induced dissipation guides the system into a desired target state. It is not obvious that the two approaches can be combined, since reaching the dispersive regime, in which system and cavities exchange excitations only virtually, can be spoiled by driving-induced resonant transitions. However, working in the extended Floquet space and treating both system-cavity coupling as well as driving-induced excitation processes on the same footing perturbatively, we identify regimes, where reservoir engineering of targeted Floquet states is possible and accurately described by an effective time-independent master equation. We successfully benchmark our approach for the preparation of the ground state in a system of interacting bosons subjected to Floquet engineered magnetic fields in different lattice geometries. △ Less

Submitted 30 November, 2022; v1 submitted 31 May, 2022; originally announced May 2022.

Comments: 5 + 15 pages

Journal ref: Phys. Rev. Lett. 129, 233601 (2022)

Floquet-heating-induced Bose condensation in a scar-like mode of an open driven optical-lattice system

Authors: Alexander Schnell, Ling-Na Wu, Artur Widera, André Eckardt

Abstract: Periodically driven quantum systems suffer from heating via resonant excitation. While such Floquet heating guides a generic isolated system towards the infinite-temperature state, a driven open system, coupled to a thermal bath, will approach a non-equilibrium steady state. We show that the interplay of bath-induced dissipation and controlled Floquet heating can give rise to non-equilibrium Bose… ▽ More Periodically driven quantum systems suffer from heating via resonant excitation. While such Floquet heating guides a generic isolated system towards the infinite-temperature state, a driven open system, coupled to a thermal bath, will approach a non-equilibrium steady state. We show that the interplay of bath-induced dissipation and controlled Floquet heating can give rise to non-equilibrium Bose condensation in a mode protected from Floquet heating. In particular, we consider a one-dimensional (1D) Bose gas in an optical lattice of finite extent, which is coupled weakly to a three-dimensional thermal bath given by a second atomic species. The bath temperature $T$ lies well above the crossover temperature, below which the majority of the system's particles form a (finite-size) Bose condensate in the ground state. However, when a strong local potential modulation is switched on, which resonantly excites the system, a non-equilibrium Bose condensate is formed in a state that decouples from the drive. Our predictions, which are based on a microscopic model that is solved using kinetic equations of motion derived from Floquet-Born-Markov theory, can be probed under realistic experimental conditions. △ Less

Submitted 5 August, 2022; v1 submitted 14 April, 2022; originally announced April 2022.

Journal ref: Phys. Rev. A 107, L021301 (2023)

Quantum engineering of a synthetic thermal bath for bosonic atoms in a one-dimensional optical lattice via Markovian feedback control

Authors: Ling-Na Wu, André Eckardt

Abstract: We propose and investigate a scheme for engineering a synthetic thermal bath for a bosonic quantum gas in a one-dimensional optical lattice based on Markovian feedback control. The performance of our scheme is quantified by the fidelity between the steady state of the system and the effective thermal state. For double-well and triple-well systems with non-interacting particles, the steady state is… ▽ More We propose and investigate a scheme for engineering a synthetic thermal bath for a bosonic quantum gas in a one-dimensional optical lattice based on Markovian feedback control. The performance of our scheme is quantified by the fidelity between the steady state of the system and the effective thermal state. For double-well and triple-well systems with non-interacting particles, the steady state is found to be an exact thermal state, which is attributed to the fact that the transfer rates between all pairs of coupled eigenstates satisfy detailed balance condition. The scenario changes when there are more lattice sites, where the detailed balance condition does not hold any more, but remains an accurate approximation. Remarkably, our scheme performs very well at low and high temperature regimes, with the fidelity close to one. The performance at the intermediate temperature regime (where a crossover into a Bose condensed regime occurs) is slightly worse, and the fidelity shows a gentle decrease with increasing system size. We also discuss the interacting cases. In contrast to the non-interacting cases, the scheme is found to perform better at a higher temperature. Another difference is that the minimal temperature that can be engineered is nonzero and increases with the interaction strength. △ Less

Submitted 12 May, 2022; v1 submitted 29 March, 2022; originally announced March 2022.

Journal ref: SciPost Phys. 13, 059 (2022)

Measurable signatures of bosonic fractional Chern insulator states and their fractional excitations in a quantum-gas microscope

Authors: Botao Wang, Xiao-Yu Dong, André Eckardt

Abstract: The recent progress in engineering topological band structures in optical-lattice systems makes it promising to study fractional Chern insulator states in these systems. Here we consider a realistic finite system of a few repulsively interacting bosons on a square lattice with magnetic flux and sharp edges, as it can be realized in quantum-gas microscopes. We investigate under which conditions a f… ▽ More The recent progress in engineering topological band structures in optical-lattice systems makes it promising to study fractional Chern insulator states in these systems. Here we consider a realistic finite system of a few repulsively interacting bosons on a square lattice with magnetic flux and sharp edges, as it can be realized in quantum-gas microscopes. We investigate under which conditions a fractional Chern insulator state corresponding to the Laughlin-like state at filling $ν=1/2$ can be stabilized and its fractional excitations probed. Using numerical simulations, we find an incompressible bulk density at the expected filling for systems, whose linear extent is as small as 6-8 sites. This is a promising result, since such small systems are favorable with respect to the required adiabatic state preparation. Moreover, we also see very clear signatures of excitations with fractional charge in response both to static pinning potentials and dynamical flux insertion. Since the compressible edges, which are found to feature chiral currents, can serve as a reservoir, these observations are robust against changes in the total particle number. Our results suggest that signatures of both a fractional Chern insulator state and its fractional excitations can be found under realistic experimental conditions. △ Less

Submitted 6 January, 2022; v1 submitted 1 November, 2021; originally announced November 2021.

Comments: 23 pages, 8 figures; minor revision; resubmit to SciPost Physics

Journal ref: SciPost Phys. 12, 095 (2022)

Non-equilibrium mode competition in a pumped dye-filled cavity

Authors: Martina Vlaho, André Eckardt

Abstract: We consider a homogeneously pumped photon gas coupled to a dye medium and investigate how its steady state is effected when varying the pump power, the photon cavity lifetime and the cutoff frequency. We study how the interplay between pumping, loss, and dye-induced thermalization influences the selection of the cavity modes that acquire large occupation. Depending on the parameter regime, the lat… ▽ More We consider a homogeneously pumped photon gas coupled to a dye medium and investigate how its steady state is effected when varying the pump power, the photon cavity lifetime and the cutoff frequency. We study how the interplay between pumping, loss, and dye-induced thermalization influences the selection of the cavity modes that acquire large occupation. Depending on the parameter regime, the latter can be related either to lasing of (typically multiple) modes or to equilibrium-like photon condensation in the ground mode. We calculate and explain the phase diagram of the system, with a particular emphasis on the role played by a mode repulsion that occurs in the regime of weak cavity loss. △ Less

Submitted 9 September, 2021; v1 submitted 7 September, 2021; originally announced September 2021.

Journal ref: Phys. Rev. A 104, 063709 (2021)

High-frequency expansions for time-periodic Lindblad generators

Authors: Alexander Schnell, Sergey Denisov, André Eckardt

Abstract: Floquet engineering of isolated systems is often based on the concept of the effective time-independent Floquet Hamiltonian, which describes the stroboscopic evolution of a periodically driven quantum system in steps of the driving period and which is routinely obtained analytically using high-frequency expansions. The generalization of these concepts to open quantum systems described by a Markovi… ▽ More Floquet engineering of isolated systems is often based on the concept of the effective time-independent Floquet Hamiltonian, which describes the stroboscopic evolution of a periodically driven quantum system in steps of the driving period and which is routinely obtained analytically using high-frequency expansions. The generalization of these concepts to open quantum systems described by a Markovian master equation of Lindblad type turns out to be non-trivial: On the one hand, already for a two-level system two different phases can be distinguished, where the effective time-independent Floquet generator (describing the stroboscopic evolution) is either again Markovian and of Lindblad type or not. On the other hand, even though in the high-frequency regime a Lindbladian Floquet generator (Floquet Linbladian) is numerically found to exist, this behaviour is, curiously, not correctly reproduced within analytical high-frequency expansions. Here, we demonstrate that a proper Floquet Lindbladian can still be obtained from a high-frequency expansion, when treating the problem in a suitably chosen rotating frame. Within this approach, we can then also describe the transition to a phase at lower driving frequencies, where no Floquet Lindbladian exists, and show that the emerging non-Markovianity of the Floquet generator can entirely be attributed to the micromotion of the open driven system. △ Less

Submitted 20 October, 2021; v1 submitted 21 July, 2021; originally announced July 2021.

Journal ref: Phys. Rev. B 104, 165414 (2021)

Cooling and state preparation in an optical lattice via Markovian feedback control

Authors: Ling-Na Wu, André Eckardt

Abstract: We propose and investigate a scheme based on Markovian feedback control that allows for the preparation of single targeted eigenstates of a system of bosonic atoms in a one-dimensional optical lattice with high fidelity. It can be used for in-situ cooling the interacting system without particle loss, both for weak and strong interactions, and for experimentally preparing and probing individual exc… ▽ More We propose and investigate a scheme based on Markovian feedback control that allows for the preparation of single targeted eigenstates of a system of bosonic atoms in a one-dimensional optical lattice with high fidelity. It can be used for in-situ cooling the interacting system without particle loss, both for weak and strong interactions, and for experimentally preparing and probing individual excited eigenstates. For that purpose the system is assumed to be probed weakly via homodyne detection of photons that are scattered off-resonantly by the atoms from a structured probe beam into a cavity mode. By applying an inertial force to the system that is proportional to the measured signal, the system is then guided into a pure target state. The scheme is found to be robust against reduced measurement efficiencies. △ Less

Submitted 2 October, 2021; v1 submitted 7 June, 2021; originally announced June 2021.

Journal ref: Phys. Rev. Research 4, L022045 (2022)

Floquet chiral hinge modes and their interplay with Weyl physics in a three-dimensional lattice

Authors: Biao Huang, Viktor Novičenko, André Eckardt, Gediminas Juzeliūnas

Abstract: We demonstrate that a three dimensional time-periodically driven (Floquet) lattice can exhibit chiral hinge states and describe their interplay with Weyl physics. A peculiar type of the hinge states are enforced by the repeated boundary reflections with lateral Goos-Hänchen like shifts occurring at the second-order boundaries of our system. Such chiral hinge modes coexist in a wide range of parame… ▽ More We demonstrate that a three dimensional time-periodically driven (Floquet) lattice can exhibit chiral hinge states and describe their interplay with Weyl physics. A peculiar type of the hinge states are enforced by the repeated boundary reflections with lateral Goos-Hänchen like shifts occurring at the second-order boundaries of our system. Such chiral hinge modes coexist in a wide range of parameters regimes with Fermi arc surface states connecting a pair of Weyl points in a two-band model. We find numerically that these modes still preserve their locality along the hinge and their chiral nature in the presence of local defects and other parameter changes. We trace the robustness of such chiral hinge modes to special band structure unique in a Floquet system allowing all the eigenstates to be localized in quasi-one-dimensional regions parallel to each other when open hinge boundaries are introduced. The implementation of a model featuring both the second-order Floquet skin effect and the Weyl physics is straightforward with ultracold atoms in optical superlattices. △ Less

Submitted 11 October, 2021; v1 submitted 20 January, 2021; originally announced January 2021.

Comments: Published version, open access article, 17 pages, 13 figures, 74 references

Journal ref: Phys. Rev. B 104, 104312 (2021)

Lindbladian approximation beyond ultra-weak coupling

Authors: Tobias Becker, Ling-Na Wu, André Eckardt

Abstract: Away from equilibrium, the properties of open quantum systems depend on the details of their environment. A microscopic derivation of a master equation (ME) is therefore crucial. Of particular interest are Lindblad-type equations, not only because they provide the most general class of Markovian MEs, but also since they are the starting point for efficient quantum trajectory simulations. Lindblad-… ▽ More Away from equilibrium, the properties of open quantum systems depend on the details of their environment. A microscopic derivation of a master equation (ME) is therefore crucial. Of particular interest are Lindblad-type equations, not only because they provide the most general class of Markovian MEs, but also since they are the starting point for efficient quantum trajectory simulations. Lindblad-type MEs are commonly derived from the Born-Markov-Redfield equation via a rotating-wave approximation (RWA). However the RWA is valid only for ultra-weak system bath coupling and often fails to accurately describe nonequilibrium processes. Here we derive an alternative Lindbladian approximation to the Redfield equation, which does not rely on ultra-weak system-bath coupling. Applying it to an extended Hubbard model coupled to Ohmic baths, we show that, especially away from equilibrium, it provides a good approximation in large parameter regimes where the RWA fails. △ Less

Submitted 10 June, 2021; v1 submitted 28 December, 2020; originally announced December 2020.

Journal ref: Phys. Rev. E 104, 014110 (2021)

Robust and Ultrafast State Preparation by Ramping Artificial Gauge Potentials

Authors: Botao Wang, Xiao-Yu Dong, F. Nur Ünal, André Eckardt

Abstract: The implementation of static artificial magnetic fields in ultracold atomic systems has become a powerful tool, e.g. for simulating quantum-Hall physics with charge-neutral atoms. Taking an interacting bosonic flux ladder as a minimal model, we investigate protocols for adiabatic state preparation via magnetic flux ramps. Considering the fact that it is actually the artificial vector potential (in… ▽ More The implementation of static artificial magnetic fields in ultracold atomic systems has become a powerful tool, e.g. for simulating quantum-Hall physics with charge-neutral atoms. Taking an interacting bosonic flux ladder as a minimal model, we investigate protocols for adiabatic state preparation via magnetic flux ramps. Considering the fact that it is actually the artificial vector potential (in the form of Peierls phases) that can be experimentally engineered in optical lattices, rather than the magnetic field, we find that the time required for adiabatic state preparation dramatically depends on which pattern of Peierls phases is used. This can be understood intuitively by noting that different patterns of time-dependent Peierls phases that all give rise to the same magnetic field ramp, generally lead to different artificial electric fields during the ramp. Remarkably, we find that an optimal choice allows for preparing the ground state almost instantaneously. We relate this observation to shortcuts to adiabaticity via counterdiabatic driving. Our findings open new possibilities for robust state preparation in atomic quantum simulators. △ Less

Submitted 14 May, 2021; v1 submitted 1 September, 2020; originally announced September 2020.

Comments: Accepted in New Journal of Physics

Realization of an anomalous Floquet topological system with ultracold atoms

Authors: Karen Wintersperger, Christoph Braun, F. Nur Ünal, André Eckardt, Marco Di Liberto, Nathan Goldman, Immanuel Bloch, Monika Aidelsburger

Abstract: Coherent control via periodic modulation, also known as Floquet engineering, has emerged as a powerful experimental method for the realization of novel quantum systems with exotic properties. In particular, it has been employed to study topological phenomena in a variety of different platforms. In driven systems, the topological properties of the quasienergy bands can often be determined by standa… ▽ More Coherent control via periodic modulation, also known as Floquet engineering, has emerged as a powerful experimental method for the realization of novel quantum systems with exotic properties. In particular, it has been employed to study topological phenomena in a variety of different platforms. In driven systems, the topological properties of the quasienergy bands can often be determined by standard topological invariants, such as Chern numbers, which are commonly used in static systems. However, due to the periodic nature of the quasienergy spectrum, this topological description is incomplete and new invariants are required to fully capture the topological properties of these driven settings. Most prominently, there exist two-dimensional anomalous Floquet systems that exhibit robust chiral edge modes, despite all Chern numbers are equal to zero. Here, we realize such a system with bosonic atoms in a periodically-driven honeycomb lattice and infer the complete set of topological invariants from energy gap measurements and local Hall deflections. △ Less

Submitted 23 October, 2020; v1 submitted 23 February, 2020; originally announced February 2020.

Journal ref: Nature Physics 16, 1058-1063 (2020)

Design and characterization of a quantum heat pump in a driven quantum gas

Authors: Arko Roy, André Eckardt

Abstract: We propose the implementation of a quantum heat pump with ultracold atoms. It is based on two periodically driven coherently coupled quantum dots using ultracold atoms. Each dot possesses two relevant quantum states and is coupled to a fermionic reservoir. The working principle is based on energy-selective driving-induced resonant tunneling processes, where a particle that tunnels from one dot to… ▽ More We propose the implementation of a quantum heat pump with ultracold atoms. It is based on two periodically driven coherently coupled quantum dots using ultracold atoms. Each dot possesses two relevant quantum states and is coupled to a fermionic reservoir. The working principle is based on energy-selective driving-induced resonant tunneling processes, where a particle that tunnels from one dot to the other either absorbs or emits the energy quantum $\hbarω$ associated with the driving frequency, depending on its energy. We characterize the device using Floquet theory and compare simple analytical estimates to numerical simulations based on the Floquet-Born-Markov formalism. In particular, we show that driving-induced heating is directly linked to the micromotion of the Floquet states of the system. △ Less

Submitted 10 March, 2020; v1 submitted 16 December, 2019; originally announced December 2019.

Comments: 6 pages, 5 figures

Journal ref: Phys. Rev. E 101, 042109 (2020)

Prethermal memory loss in interacting quantum systems coupled to thermal baths

Authors: Ling-Na Wu, André Eckardt

Abstract: We study the relaxation dynamics of an extended Fermi-Hubbard chain with a strong Wannier-Stark potential tilt coupled to a bath. When the system is subjected to dephasing noise, starting from a pure initial state the system's total von Neumann entropy is found to grow monotonously. The scenario becomes rather different when the system is coupled to a thermal bath of finite temperature. Here, for… ▽ More We study the relaxation dynamics of an extended Fermi-Hubbard chain with a strong Wannier-Stark potential tilt coupled to a bath. When the system is subjected to dephasing noise, starting from a pure initial state the system's total von Neumann entropy is found to grow monotonously. The scenario becomes rather different when the system is coupled to a thermal bath of finite temperature. Here, for sufficiently large field gradients and initial energies, the entropy peaks in time and almost reaches its largest possible value (corresponding to the maximally mixed state), long before the system relaxes to thermal equilibrium. This entropy peak signals a prethermal memory loss and, relative to the time where it occurs, the system is found to exhibit a simple scaling behavior in space and time. By comparing the system's dynamics to that of a simplified model, the underlying mechanism is found to be related to the localization property of the Wannier-Stark system, which favors dissipative coupling between eigenstates that are close in energy. △ Less

Submitted 25 March, 2020; v1 submitted 23 November, 2019; originally announced November 2019.

Journal ref: Phys. Rev. B 101, 220302 (2020)

Phasonic Spectroscopy of a Quantum Gas in a Quasicrystalline Lattice

Authors: Shankari V. Rajagopal, Toshihiko Shimasaki, Peter Dotti, Mantas Račiūnas, Ruwan Senaratne, Egidijus Anisimovas, André Eckardt, David M. Weld

Abstract: Phasonic degrees of freedom are unique to quasiperiodic structures, and play a central role in poorly-understood properties of quasicrystals from excitation spectra to wavefunction statistics to electronic transport. However, phasons are challenging to access dynamically in the solid state due to their complex long-range character and the effects of disorder and strain. We report phasonic spectros… ▽ More Phasonic degrees of freedom are unique to quasiperiodic structures, and play a central role in poorly-understood properties of quasicrystals from excitation spectra to wavefunction statistics to electronic transport. However, phasons are challenging to access dynamically in the solid state due to their complex long-range character and the effects of disorder and strain. We report phasonic spectroscopy of a quantum gas in a one-dimensional quasicrystalline optical lattice. We observe that strong phasonic driving produces a nonperturbative high-harmonic plateau strikingly different from the effects of standard dipolar driving. Tuning the potential from crystalline to quasicrystalline, we identify spectroscopic signatures of quasiperiodicity and interactions and map the emergence of a multifractal energy spectrum, opening a path to direct imaging of the Hofstadter butterfly. △ Less

Submitted 28 October, 2019; v1 submitted 11 September, 2019; originally announced September 2019.

Comments: 4 figures, 8 pages, supplemental materials included

Journal ref: Phys. Rev. Lett. 123, 223201 (2019)

Hopf characterization of two-dimensional Floquet topological insulators

Authors: F. Nur Ünal, André Eckardt, Robert-Jan Slager

Abstract: We present a topological characterization of time-periodically driven two-band models in 2+1 dimensions as Hopf insulators. The intrinsic periodicity of the Floquet system with respect to both time and the underlying two-dimensional momentum space constitutes a map from a three dimensional torus to the Bloch sphere. As a result, we find that the driven system can be understood by appealing to a Ho… ▽ More We present a topological characterization of time-periodically driven two-band models in 2+1 dimensions as Hopf insulators. The intrinsic periodicity of the Floquet system with respect to both time and the underlying two-dimensional momentum space constitutes a map from a three dimensional torus to the Bloch sphere. As a result, we find that the driven system can be understood by appealing to a Hopf map that is directly constructed from the micromotion of the drive. Previously found winding numbers are shown to correspond to Hopf invariants, which are associated with linking numbers describing the topology of knots in three dimensions. Moreover, after being cast as a Hopf insulator, not only the Chern numbers, but also the winding numbers of the Floquet topological insulator become accessible in experiments as linking numbers. We exploit this description to propose a feasible scheme for measuring the complete set of their Floquet topological invariants in optical lattices. △ Less

Submitted 12 September, 2019; v1 submitted 5 April, 2019; originally announced April 2019.

Comments: 6 pages, 3 figures + 2 pages, 1 figure supplementary

Journal ref: Phys. Rev. Research 1, 022003(R) (2019)

Bath-induced decay of Stark many-body localization

Authors: Ling-Na Wu, André Eckardt

Abstract: We investigate the relaxation dynamics of an interacting Stark-localized system coupled to a dephasing bath, and compare its behavior to the conventional disorder-induced many body localized system. Specifically, we study the dynamics of population imbalance between even and odd sites, and the growth of the von Neumann entropy. For a large potential gradient, the imbalance is found to decay on a t… ▽ More We investigate the relaxation dynamics of an interacting Stark-localized system coupled to a dephasing bath, and compare its behavior to the conventional disorder-induced many body localized system. Specifically, we study the dynamics of population imbalance between even and odd sites, and the growth of the von Neumann entropy. For a large potential gradient, the imbalance is found to decay on a time scale that grows quadratically with the Wannier-Stark tilt. For the non-interacting system, it shows an exponential decay, which becomes a stretched exponential decay in the presence of finite interactions. This is different from a system with disorder-induced localization, where the imbalance exhibits a stretched exponential decay also for vanishing interactions. As another clear qualitative difference, we do not find a logarithmically slow growth of the von-Neumann entropy as it is found for the disordered system. Our findings can immediately be tested experimentally with ultracold atoms in optical lattices. △ Less

Submitted 31 May, 2019; v1 submitted 18 March, 2019; originally announced March 2019.

Journal ref: Phys. Rev. Lett. 123, 030602 (2019)

How to Directly Measure Floquet Topological Invariants in Optical Lattices

Authors: F. Nur Ünal, Babak Seradjeh, André Eckardt

Abstract: The classification of topological Floquet systems with time-periodic Hamiltonians transcends that of static systems. For example, spinless fermions in periodically driven two-dimensional lattices are not completely characterized by the Chern numbers of the quasienergy bands, but rather by a set of winding numbers associated with the quasienergy gaps. We propose a scheme for measuring these winding… ▽ More The classification of topological Floquet systems with time-periodic Hamiltonians transcends that of static systems. For example, spinless fermions in periodically driven two-dimensional lattices are not completely characterized by the Chern numbers of the quasienergy bands, but rather by a set of winding numbers associated with the quasienergy gaps. We propose a scheme for measuring these winding numbers in a system of fermionic cold atoms in a periodically driven optical lattice efficiently and directly. It is based on the construction of a one-parameter family of experimentally feasible drives, continuously connecting the Floquet system of interest to a trivial reference system. The winding numbers are then determined by the identification and the tomography of the band-touching singularities occurring on the way. As a byproduct, we also propose a method for probing spectral properties of time evolution operators via a time analog of crystallography. △ Less

Submitted 30 June, 2019; v1 submitted 11 December, 2018; originally announced December 2018.

Comments: 6 pages, 5 figures

Journal ref: Phys. Rev. Lett. 122, 253601 (2019)

Describing many-body localized systems in thermal environments

Authors: Ling-Na Wu, Alexander Schnell, Giuseppe De Tomasi, Markus Heyl, André Eckardt

Abstract: In this work we formulate an efficient method for the description of many-body localized systems in weak contact with thermal environments at temperature $T$. For this purpose we exploit the representation of the system in terms of quasi-local integrals of motion ($l$-bits) to derive a quantum master equation using Born-Markov approximations. We show how this equation can be treated by using quant… ▽ More In this work we formulate an efficient method for the description of many-body localized systems in weak contact with thermal environments at temperature $T$. For this purpose we exploit the representation of the system in terms of quasi-local integrals of motion ($l$-bits) to derive a quantum master equation using Born-Markov approximations. We show how this equation can be treated by using quantum-jump Monte-Carlo techniques as well as by deriving approximate kinetic equations of motion. As an example, we consider the one-dimensional Anderson model for spinless fermions including also nearest-neighbor interactions, which we diagonalize approximately by employing a recently proposed method valid in the limit of strong disorder and weak interactions. Coupling the system to a global thermal bath, we study the transport between two leads with different chemical potentials at both of its ends. We find that the temperature-dependent current is captured by an interaction-dependent version of Mott's law for variable range hopping, where transport is enhanced/lowered depending on whether the interactions are attractive or repulsive, respectively. We interpret these results in terms of spatio-energetic correlations between the $l$-bits. △ Less

Submitted 14 November, 2018; originally announced November 2018.

Journal ref: New J. Phys. 21, 063026 (2019)

Is there a Floquet Lindbladian?

Authors: Alexander Schnell, André Eckardt, Sergey Denisov

Abstract: The stroboscopic evolution of a time-periodically driven isolated quantum system can always be described by an effective time-independent Hamiltonian. Whether this concept can be generalized to open Floquet systems, described by a Markovian master equation with time-periodic Lindbladian generator, remains an open question. By using a two level system as a model, we explicitly show the existence of… ▽ More The stroboscopic evolution of a time-periodically driven isolated quantum system can always be described by an effective time-independent Hamiltonian. Whether this concept can be generalized to open Floquet systems, described by a Markovian master equation with time-periodic Lindbladian generator, remains an open question. By using a two level system as a model, we explicitly show the existence of two well-defined parameter regions. In one region the stroboscopic evolution can be described by a Markovian master equation with a time-independent Floquet Lindbladian. In the other it cannot; but here the one-cycle evolution operator can be reproduced with an effective non-Markovian master equation that is homogeneous but non-local in time. Interestingly, we find that the boundary between the phases depends on when the evolution is stroboscopically monitored. This reveals the non-trivial role played by the micromotion in the dynamics of open Floquet systems. △ Less

Submitted 12 October, 2019; v1 submitted 28 September, 2018; originally announced September 2018.

Journal ref: Phys. Rev. B 101, 100301 (2020)

Quantifying and controlling prethermal nonergodicity in interacting Floquet matter

Authors: Kevin Singh, Cora J. Fujiwara, Zachary A. Geiger, Ethan Q. Simmons, Mikhail Lipatov, Alec Cao, Peter Dotti, Shankari V. Rajagopal, Ruwan Senaratne, Toshihiko Shimasaki, Markus Heyl, André Eckardt, David M. Weld

Abstract: The use of periodic driving for synthesizing many-body quantum states depends crucially on the existence of a prethermal regime, which exhibits drive-tunable properties while forestalling the effects of heating. This motivates the search for direct experimental probes of the underlying localized nonergodic nature of the wave function in this metastable regime. We report experiments on a many-body… ▽ More The use of periodic driving for synthesizing many-body quantum states depends crucially on the existence of a prethermal regime, which exhibits drive-tunable properties while forestalling the effects of heating. This motivates the search for direct experimental probes of the underlying localized nonergodic nature of the wave function in this metastable regime. We report experiments on a many-body Floquet system consisting of atoms in an optical lattice subjected to ultrastrong sign-changing amplitude modulation. Using a double-quench protocol we measure an inverse participation ratio quantifying the degree of prethermal localization as a function of tunable drive parameters and interactions. We obtain a complete prethermal map of the drive-dependent properties of Floquet matter spanning four square decades of parameter space. Following the full time evolution, we observe sequential formation of two prethermal plateaux, interaction-driven ergodicity, and strongly frequency-dependent dynamics of long-time thermalization. The quantitative characterization of the prethermal Floquet matter realized in these experiments, along with the demonstration of control of its properties by variation of drive parameters and interactions, opens a new frontier for probing far-from-equilibrium quantum statistical mechanics and new possibilities for dynamical quantum engineering. △ Less

Submitted 27 August, 2019; v1 submitted 14 September, 2018; originally announced September 2018.

Comments: 9 pages, 5 figures

Journal ref: Phys. Rev. X 9, 041021 (2019)

Measuring the single-particle density matrix for fermions and hard-core bosons in an optical lattice

Authors: Luis A. Peña Ardila, Markus Heyl, André Eckardt

Abstract: Ultracold atoms in optical lattices provide clean, tunable, and well-isolated realizations of paradigmatic quantum lattice models. With the recent advent of quantum-gas microscopes, they now also offer the possibility to measure the occupations of individual lattice sites. What, however, has not yet been achieved is to measure those elements of the single-particle density matrix, which are off-dia… ▽ More Ultracold atoms in optical lattices provide clean, tunable, and well-isolated realizations of paradigmatic quantum lattice models. With the recent advent of quantum-gas microscopes, they now also offer the possibility to measure the occupations of individual lattice sites. What, however, has not yet been achieved is to measure those elements of the single-particle density matrix, which are off-diagonal in the occupation basis. Here, we propose a scheme to access these basic quantities both for fermions as well as hard-core bosons and investigate its accuracy and feasibility. The scheme relies on the engineering of a large effective tunnel coupling between distant lattice sites and a protocol that is based on measuring site occupations after two subsequent quenches. △ Less

Submitted 8 January, 2019; v1 submitted 21 June, 2018; originally announced June 2018.

Comments: 5 pages, 3 figures

Journal ref: Phys. Rev. Lett. 121, 260401 (2018)

The optimal frequency window for Floquet engineering in optical lattices

Authors: Gaoyong Sun, André Eckardt

Abstract: The concept of Floquet engineering is to subject a quantum system to time-periodic driving in such a way that it acquires interesting novel properties. It has been employed, for instance, for the realization of artificial magnetic fluxes in optical lattices and, typically, it is based on two approximations. First, the driving frequency is assumed to be low enough to suppress resonant excitations t… ▽ More The concept of Floquet engineering is to subject a quantum system to time-periodic driving in such a way that it acquires interesting novel properties. It has been employed, for instance, for the realization of artificial magnetic fluxes in optical lattices and, typically, it is based on two approximations. First, the driving frequency is assumed to be low enough to suppress resonant excitations to high-lying states above some energy gap separating a low energy subspace from excited states. Second, the driving frequency is still assumed to be large compared to the energy scales of the low-energy subspace, so that also resonant excitations within this space are negligible. Eventually, however, deviations from both approximations will lead to unwanted heating on a time scale $τ$. Using the example of a one-dimensional system of repulsively interacting bosons in a shaken optical lattice, we investigate the optimal frequency (window) that maximizes $τ$. As a main result, we find that, when increasing the lattice depth, $τ$ increases faster than the experimentally relevant time scale given by the tunneling time $\hbar/J$, so that Floquet heating becomes suppressed. △ Less

Submitted 24 January, 2020; v1 submitted 7 May, 2018; originally announced May 2018.

Comments: 11 pages, 8 figures

Journal ref: Phys. Rev. Research 2, 013241 (2020)

Charge density wave and charge pump of interacting fermions in circularly shaken hexagonal optical lattices

Authors: Tao Qin, Alexander Schnell, Klaus Sengstock, Christof Weitenberg, André Eckardt, Walter Hofstetter

Abstract: We analyze strong correlation effects and topological properties of interacting fermions with a Falicov-Kimball type interaction in circularly shaken hexagonal optical lattices, which can be effectively described by the Haldane-Falicov-Kimball model, using the real-space Floquet dynamical mean-field theory (DMFT). The Haldane model, a paradigmatic model of the Chern insulator, is experimentally re… ▽ More We analyze strong correlation effects and topological properties of interacting fermions with a Falicov-Kimball type interaction in circularly shaken hexagonal optical lattices, which can be effectively described by the Haldane-Falicov-Kimball model, using the real-space Floquet dynamical mean-field theory (DMFT). The Haldane model, a paradigmatic model of the Chern insulator, is experimentally relevant, because it has been realized using circularly shaken hexagonal optical lattices. We show that in the presence of staggering a charge density wave emerges, which is affected by interactions and resonant tunneling. We demonstrate that interactions smear out the edge states by introducing a finite life time of quasiparticles. Even though a general method for calculating the topological invariant of a nonequilibrium steady state is lacking, we extract the topological invariant using a Laughlin charge pump set-up. We find and attribute to the dissipations into the bath connected to every lattice site, which is intrinsic to real-space Floquet DMFT methods, that the pumped charge is not an integer even for the non-interacting case at very low reservoir temperatures. Furthermore, using the rate equation based on the Floquet-Born-Markov approximation, we calculate the charge pump from the rate equations for the non-interacting case to identify the role of the spectral properties of the bath. Starting from this approach we propose an experimental protocol for measuring quantized charge pumping. △ Less

Submitted 2 November, 2018; v1 submitted 9 April, 2018; originally announced April 2018.

Comments: 13 pages, 12 figures, published version

Journal ref: Phys. Rev. A 98, 033601 (2018)

Creating, probing, and manipulating fractionally charged excitations of fractional Chern insulators in optical lattices

Authors: Mantas Račiūnas, F. Nur Ünal, Egidijus Anisimovas, André Eckardt

Abstract: We propose a set of schemes to create and probe fractionally charged excitations of a fractional Chern insulator state in an optical lattice. This includes the creation of localized quasiparticles and quasiholes using both static local defects and the dynamical local insertion of synthetic flux quanta. Simulations of repulsively interacting bosons on a finite square lattice with experimentally rel… ▽ More We propose a set of schemes to create and probe fractionally charged excitations of a fractional Chern insulator state in an optical lattice. This includes the creation of localized quasiparticles and quasiholes using both static local defects and the dynamical local insertion of synthetic flux quanta. Simulations of repulsively interacting bosons on a finite square lattice with experimentally relevant open boundary conditions show that already a four-particle system exhibits signatures of charge fractionalization in the quantum-Hall-like state at the filling fraction of $1/2$ particle per flux quantum. This result is favorable for the prospects of adiabatic preparation of fractional Chern insulators. Our work is inspired by recent experimental breakthroughs in atomic quantum gases: the realization of strong artificial magnetic fields in optical lattices, the ability of single-site addressing in quantum gas microscopes, and the preparation of low-entropy insulating states by engineering an entropy-absorbing metallic reservoir. △ Less

Submitted 1 January, 2019; v1 submitted 5 April, 2018; originally announced April 2018.

Comments: 7 pages,3 figures

Journal ref: Phys. Rev. A 98, 063621 (2018)

A unified theory for excited-state, fragmented, and equilibrium-like Bose condensation in pumped photonic many-body systems

Authors: Daniel Vorberg, Roland Ketzmerick, André Eckardt

Abstract: We derive a theory for Bose condensation in nonequilibrium steady states of bosonic quantum gases that are coupled both to a thermal heat bath and to a pumped reservoir (or gain medium), while suffering from loss. Such a scenario describes photonic many-body systems such as exciton-polariton gases. Our analysis is based on a set of kinetic equations for a gas of noninteracting bosons. By identifyi… ▽ More We derive a theory for Bose condensation in nonequilibrium steady states of bosonic quantum gases that are coupled both to a thermal heat bath and to a pumped reservoir (or gain medium), while suffering from loss. Such a scenario describes photonic many-body systems such as exciton-polariton gases. Our analysis is based on a set of kinetic equations for a gas of noninteracting bosons. By identifying a dimensionless scaling parameter controlling the boson density, we derive a sharp criterion for which system states become selected to host a macroscopic occupation. We show that with increasing pump power, the system generically undergoes a sequence of nonequilibrum phase transitions. At each transition a state either becomes or ceases to be Bose selected (i.e. to host a condensate): The state which first acquires a condensate when the pumping exceeds a threshold is the one with the largest ratio of pumping to loss. This intuitive behavior resembles simple lasing. In the limit of strong pumping, the coupling to the heat bath becomes dominant so that eventually the ground state is selected, corresponding to equilibrium(-like) Bose condensation. For intermediate pumping strengths, several states become selected giving rise to fragmented nonequilibrium Bose condensation. We compare these predictions to experimental results obtained for excitons polaritons in a double-pillar structure [Phys. Rev. Lett. 108, 126403 (2012)] and find good agreement. Our theory, moreover, predicts that the reservoir occupation is clamped at a constant value whenever the system hosts an odd number of Bose condensates. △ Less

Submitted 23 March, 2018; originally announced March 2018.

Journal ref: Phys. Rev. A 97, 063621 (2018)