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Few is different: deciphering many-body dynamics in mesoscopic quantum gases
Authors:
Juergen Berges,
Sandra Brandstetter,
Jasmine Brewer,
Georg Bruun,
Tilman Enss,
Stefan Floerchinger,
Keisuke Fujii,
Maciej Galka,
Giuliano Giacalone,
Qingze Guan,
Carl Heintze,
Lars H. Heyen,
Ilya Selyuzhenkov,
Selim Jochim,
Jesper Levinsen,
Philipp Lunt,
Silvia Masciocchi,
Aleksas Mazeliauskas,
Nir Navon,
Alice Ohlson,
Meera Parish,
Stephanie M. Reimann,
Francesco Scazza,
Thomas Schaefer,
Derek Teaney
, et al. (5 additional authors not shown)
Abstract:
Emergent macroscopic descriptions of matter, such as hydrodynamics, are central to our description of complex physical systems across a wide spectrum of energy scales. The conventional understanding of these many-body phenomena has recently been shaken by a number of experimental findings. Collective behavior of matter has been observed in \emph{mesoscopic} systems, such as high-energy hadron-hadr…
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Emergent macroscopic descriptions of matter, such as hydrodynamics, are central to our description of complex physical systems across a wide spectrum of energy scales. The conventional understanding of these many-body phenomena has recently been shaken by a number of experimental findings. Collective behavior of matter has been observed in \emph{mesoscopic} systems, such as high-energy hadron-hadron collisions, or ultra-cold gases with only few strongly interacting fermions. In such systems, the separation of scales between macroscopic and microscopic dynamics (at the heart of any effective theory) is inapplicable. To address the conceptual challenges that arise from these observations and explore the universality of emergent descriptions of matter, the EMMI Rapid Reaction Task Force was assembled. This document summarizes the RRTF discussions on recent theoretical and experimental advances in this rapidly developing field. Leveraging technological breakthroughs in the control of quantum systems, we can now quantitatively explore what it means for a system to exhibit behavior beyond the sum of its individual parts. In particular, the report highlights how the (in)applicability of hydrodynamics and other effective theories can be probed across three principal frontiers: the size frontier, the equilibrium frontier, and the interaction frontier.
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Submitted 22 June, 2026; v1 submitted 5 September, 2025;
originally announced September 2025.
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Fate of an impurity strongly interacting with a thermal Bose gas
Authors:
Jiří Etrych,
Sebastian J. Morris,
Simon M. Fischer,
Gevorg Martirosyan,
Christopher J. Ho,
Moritz Drescher,
Manfred Salmhofer,
Zoran Hadzibabic,
Tilman Enss,
Christoph Eigen
Abstract:
We spectroscopically study mobile impurities immersed in a homogeneous bosonic bath (a box-trapped Bose gas), varying the bath temperature and the strength of impurity-bath interactions. We compare our results to those for a quasipure Bose-Einstein condensate (BEC), and find that for strong impurity-bath interactions, the spectra narrow with increasing temperature, while the impurity energy shift…
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We spectroscopically study mobile impurities immersed in a homogeneous bosonic bath (a box-trapped Bose gas), varying the bath temperature and the strength of impurity-bath interactions. We compare our results to those for a quasipure Bose-Einstein condensate (BEC), and find that for strong impurity-bath interactions, the spectra narrow with increasing temperature, while the impurity energy shift is suppressed. Near the critical temperature for condensation, many-body effects still play an important role, and only for a nondegenerate bath, the system approaches the classical Boltzmann-gas behavior. The key spectral features are reproduced within the theory of an ideal Bose polaron.
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Submitted 8 August, 2025;
originally announced August 2025.
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Observation of pattern stabilization in a driven superfluid
Authors:
Nikolas Liebster,
Marius Sparn,
Elinor Kath,
Jelte Duchene,
Keisuke Fujii,
Sarah L. Görlitz,
Tilman Enss,
Helmut Strobel,
Markus K. Oberthaler
Abstract:
The formation of patterns in driven systems has been studied extensively, and their emergence can be connected to a fine balance of instabilities and stabilization mechanisms. While the early phase of pattern formation can be understood on the basis of linear stability analyses, the long-time dynamics can only be described by accounting for the interactions between the excitations generated by the…
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The formation of patterns in driven systems has been studied extensively, and their emergence can be connected to a fine balance of instabilities and stabilization mechanisms. While the early phase of pattern formation can be understood on the basis of linear stability analyses, the long-time dynamics can only be described by accounting for the interactions between the excitations generated by the drive. Here, we observe the stabilization of square patterns in an interaction-driven, two-dimensional Bose-Einstein condensate. These patterns emerge due to inherent high-order processes that become relevant in the regime of large phonon occupations. Theoretically, this can be understood as the emergence of a stable fixed point of coupled nonlinear amplitude equations, which include phonon-phonon interactions. We experimentally probe the predicted flows towards such a stable fixed-point, as well as repulsion from a saddle fixed-point, using the experimental control unique to quantum gases.
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Submitted 10 December, 2024; v1 submitted 7 September, 2023;
originally announced September 2023.
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Complex scaling flows in the quench dynamics of interacting particles
Authors:
Tilman Enss,
Noel Cuadra Braatz,
Giacomo Gori
Abstract:
Many-body systems driven out of equilibrium can exhibit scaling flows of the quantum state. For a sudden quench to resonant interactions between particles we construct a new class of analytical scaling solutions for the time evolved wave function with a complex scale parameter. These solutions determine the exact dynamical scaling of observables such as the pair correlation function, the contact a…
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Many-body systems driven out of equilibrium can exhibit scaling flows of the quantum state. For a sudden quench to resonant interactions between particles we construct a new class of analytical scaling solutions for the time evolved wave function with a complex scale parameter. These solutions determine the exact dynamical scaling of observables such as the pair correlation function, the contact and the fidelity. We give explicit examples of the nonequilibrium dynamics for two trapped fermions or bosons quenched to unitarity, for ideal Bose polarons, and for resonantly interacting, Borromean three-body systems. These solutions reveal universal scaling properties of interacting many-body systems that arise from the buildup of correlations at short times after the quench.
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Submitted 29 August, 2022; v1 submitted 11 March, 2022;
originally announced March 2022.
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Universal scaling at a pre-thermal dark state
Authors:
Marvin Syed,
Tilman Enss,
Nicolò Defenu
Abstract:
Recent experimental and theoretical progress as well as the prospect of commercially viable quantum technologies have inspired great interest in the study of open quantum systems and their dynamics. Many open quantum systems are well described by an effective non-Hermitian Hamiltonian generating a time evolution that allows eigenstates to decay and dissipate to the environment. In this framework,…
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Recent experimental and theoretical progress as well as the prospect of commercially viable quantum technologies have inspired great interest in the study of open quantum systems and their dynamics. Many open quantum systems are well described by an effective non-Hermitian Hamiltonian generating a time evolution that allows eigenstates to decay and dissipate to the environment. In this framework, quantum coherent scaling is traditionally tied to the appearance of dark states, where the effect of dissipation becomes negligible. Here, we discuss the universal dynamical scaling after a sudden quench of the non-Hermitian $O(N)$ model Hamiltonian. While universality is generally spoiled by non-Hermiticity, we find that for a given set of internal parameters short-time scaling behaviour is restored with an initial slip exponent profoundly different from that of closed quantum systems. This result is tied to the compensation of dissipation by interaction effects at short times leading to a prethermal dark state, where coherent many-body dynamics can be still observed.
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Submitted 9 June, 2022; v1 submitted 28 December, 2021;
originally announced December 2021.
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Self-stabilized Bose polarons
Authors:
Richard Schmidt,
Tilman Enss
Abstract:
The mobile impurity in a Bose-Einstein condensate (BEC) is a paradigmatic many-body problem. For weak interaction between the impurity and the BEC, the impurity deforms the BEC only slightly and it is well described within the Fröhlich model and the Bogoliubov approximation. For strong local attraction this standard approach, however, fails to balance the local attraction with the weak repulsion b…
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The mobile impurity in a Bose-Einstein condensate (BEC) is a paradigmatic many-body problem. For weak interaction between the impurity and the BEC, the impurity deforms the BEC only slightly and it is well described within the Fröhlich model and the Bogoliubov approximation. For strong local attraction this standard approach, however, fails to balance the local attraction with the weak repulsion between the BEC particles and predicts an instability where an infinite number of bosons is attracted toward the impurity. Here we present a solution of the Bose polaron problem beyond the Bogoliubov approximation which includes the local repulsion between bosons and thereby stabilizes the Bose polaron even near and beyond the scattering resonance. We show that the Bose polaron energy remains bounded from below across the resonance and the size of the polaron dressing cloud stays finite. Our results demonstrate how the dressing cloud replaces the attractive impurity potential with an effective many-body potential that excludes binding. We find that at resonance, including the effects of boson repulsion, the polaron energy depends universally on the effective range. Moreover, while the impurity contact is strongly peaked at positive scattering length, it remains always finite. Our solution highlights how Bose polarons are self-stabilized by repulsion, providing a mechanism to understand quench dynamics and nonequilibrium time evolution at strong coupling.
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Submitted 29 June, 2022; v1 submitted 26 February, 2021;
originally announced February 2021.
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Dynamical quantum phase transition in a bosonic system with long-range interactions
Authors:
Marvin Syed,
Tilman Enss,
Nicolò Defenu
Abstract:
In this paper, we investigate the dynamical quantum phase transitions appearing in the Loschmidt echo and the time-dependent order parameter of a quantum system of harmonically coupled degenerate bosons as a function of the power-law decay $σ$ of long-range interactions. Following a sudden quench, the nonequilibrium dynamics of this system are governed by a set of nonlinear coupled Ermakov equatio…
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In this paper, we investigate the dynamical quantum phase transitions appearing in the Loschmidt echo and the time-dependent order parameter of a quantum system of harmonically coupled degenerate bosons as a function of the power-law decay $σ$ of long-range interactions. Following a sudden quench, the nonequilibrium dynamics of this system are governed by a set of nonlinear coupled Ermakov equations. To solve them, we develop an analytical approximation valid at late times. Based on this approximation, we show that the emergence of a dynamical quantum phase transition hinges on the generation of a finite mass gap following the quench, starting from a massless initial state. In general, we can define two distinct dynamical phases characterized by the finiteness of the post-quench mass gap. The Loschmidt echo exhibits periodical nonanalytic cusps whenever the initial state has a vanishing mass gap and the final state has a finite mass gap. These cusps are shown to coincide with the maxima of the time-dependent long-range correlations.
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Submitted 15 February, 2021; v1 submitted 11 November, 2020;
originally announced November 2020.
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Complex networks with tuneable dimensions as a universality playground
Authors:
Ana P. Millán,
Giacomo Gori,
Federico Battiston,
Tilman Enss,
Nicolò Defenu
Abstract:
Universality is one of the key concepts in understanding critical phenomena. However, for interacting inhomogeneous systems described by complex networks a clear understanding of the relevant parameters for universality is still missing. Here we discuss the role of a fundamental network parameter for universality, the spectral dimension. For this purpose, we construct a complex network model where…
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Universality is one of the key concepts in understanding critical phenomena. However, for interacting inhomogeneous systems described by complex networks a clear understanding of the relevant parameters for universality is still missing. Here we discuss the role of a fundamental network parameter for universality, the spectral dimension. For this purpose, we construct a complex network model where the probability of a bond between two nodes is proportional to a power law of the nodes' distances. By explicit computation we prove that the spectral dimension for this model can be tuned continuously from $1$ to infinity, and we discuss related network connectivity measures. We propose our model as a tool to probe universal behaviour on inhomogeneous structures and comment on the possibility that the universal behaviour of correlated models on such networks mimics the one of continuous field theories in fractional Euclidean dimensions.
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Submitted 21 April, 2021; v1 submitted 18 June, 2020;
originally announced June 2020.
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Theory of a resonantly interacting impurity in a Bose-Einstein condensate
Authors:
Moritz Drescher,
Manfred Salmhofer,
Tilman Enss
Abstract:
We investigate a Bose-Einstein condensate in strong interaction with a single impurity particle. While this situation has received considerable interest in recent years, the regime of strong coupling remained inaccessible to most approaches due to an instability in Bogoliubov theory arising near the resonance. We present a nonlocal extension of Gross-Pitaevskii theory that is free of such divergen…
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We investigate a Bose-Einstein condensate in strong interaction with a single impurity particle. While this situation has received considerable interest in recent years, the regime of strong coupling remained inaccessible to most approaches due to an instability in Bogoliubov theory arising near the resonance. We present a nonlocal extension of Gross-Pitaevskii theory that is free of such divergences and does not require the use of the Born approximation in any of the interaction potentials. We find a new dynamical transition regime between attractive and repulsive polarons, where an interaction quench results in a finite number of coherent oscillations in the density profiles of the medium and in the contact parameter before equilibrium is reached.
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Submitted 13 July, 2020; v1 submitted 4 March, 2020;
originally announced March 2020.
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Universal dynamical scaling of long-range topological superconductors
Authors:
Nicolò Defenu,
Giovanna Morigi,
Luca Dell'Anna,
Tilman Enss
Abstract:
We study the out-of-equilibrium dynamics of $p$-wave superconducting quantum wires with long-range interactions, when the chemical potential is linearly ramped across the topological phase transition. We show that the heat produced after the quench scales with the quench rate $δ$ according to the scaling law $δ^θ$, where the exponent $θ$ depends on the power law exponent of the long-range interact…
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We study the out-of-equilibrium dynamics of $p$-wave superconducting quantum wires with long-range interactions, when the chemical potential is linearly ramped across the topological phase transition. We show that the heat produced after the quench scales with the quench rate $δ$ according to the scaling law $δ^θ$, where the exponent $θ$ depends on the power law exponent of the long-range interactions. We identify the parameter regimes where this scaling can be cast in terms of the universal equilibrium critical exponents and can thus be understood within the Kibble-Zurek framework. When the electron hopping decays more slowly in space than pairing, it dominates the equilibrium scaling. Surprisingly, in this regime the dynamical critical behaviour arises only from paring and, thus, exhibits anomalous dynamical universality unrelated to equilibrium scaling. The discrepancy from the expected Kibble-Zurek scenario can be traced back to the presence of multiple universal terms in the equilibrium scaling functions of long-range interacting systems close to a second order critical point.
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Submitted 22 June, 2019;
originally announced June 2019.
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Coupled superfluidity of binary Bose mixtures in two dimensions
Authors:
Volker Karle,
Nicolo Defenu,
Tilman Enss
Abstract:
We consider a two-component Bose gas in two dimensions at low temperature with short-range repulsive interaction. In the coexistence phase where both components are superfluid, inter-species interactions induce a nondissipative drag between the two superfluid flows (Andreev-Bashkin effect). We show that this behavior leads to a modification of the usual Berezinskii-Kosterlitz-Thouless (BKT) transi…
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We consider a two-component Bose gas in two dimensions at low temperature with short-range repulsive interaction. In the coexistence phase where both components are superfluid, inter-species interactions induce a nondissipative drag between the two superfluid flows (Andreev-Bashkin effect). We show that this behavior leads to a modification of the usual Berezinskii-Kosterlitz-Thouless (BKT) transition in two dimensions. We extend the renormalization of the superfluid densities at finite temperature using the renormalization group approach and find that the vortices of one component have a large influence on the superfluid properties of the other, mediated by the nondissipative drag. The extended BKT flow equations indicate that the occurrence of the vortex unbinding transition in one of the components can induce the breakdown of superfluidity also in the other, leading to a locking phenomenon for the critical temperatures of the two gases.
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Submitted 9 July, 2019; v1 submitted 15 March, 2019;
originally announced March 2019.
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Dynamical criticality and domain-wall coupling in long-range Hamiltonians
Authors:
Nicolò Defenu,
Tilman Enss,
Jad C. Halimeh
Abstract:
Dynamical quantum phase transitions hold a deep connection to the underlying equilibrium physics of the quench Hamiltonian. In a recent study [J.~C.~Halimeh \textit{et al.}, arXiv:1810.07187], it has been numerically demonstrated that the appearance of anomalous cusps in the Loschmidt return rate coincides with the presence of bound domain walls in the spectrum of the quench Hamiltonian. Here, we…
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Dynamical quantum phase transitions hold a deep connection to the underlying equilibrium physics of the quench Hamiltonian. In a recent study [J.~C.~Halimeh \textit{et al.}, arXiv:1810.07187], it has been numerically demonstrated that the appearance of anomalous cusps in the Loschmidt return rate coincides with the presence of bound domain walls in the spectrum of the quench Hamiltonian. Here, we consider transverse-field Ising chains with power-law and exponentially decaying interactions, and show that by removing domain-wall coupling via a truncated Jordan-Wigner transformation onto a Kitaev chain with long-range hopping and pairing, anomalous dynamical criticality is no longer present. This indicates that bound domain walls are necessary for anomalous cusps to appear in the Loschmidt return rate. We also calculate the dynamical phase diagram of the Kitaev chain with long-range hopping and pairing, which in the case of power-law couplings is shown to exhibit rich dynamical criticality including a doubly critical dynamical phase.
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Submitted 22 February, 2019;
originally announced February 2019.
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Quantum scale anomaly and spatial coherence in a 2D Fermi superfluid
Authors:
Puneet A. Murthy,
Nicolò Defenu,
Luca Bayha,
Marvin Holten,
Philipp M. Preiss,
Tilman Enss,
Selim Jochim
Abstract:
Quantum anomalies are violations of classical scaling symmetries caused by quantum fluctuations. Although they appear prominently in quantum field theory to regularize divergent physical quantities, their influence on experimental observables is difficult to discern. Here, we discovered a striking manifestation of a quantum anomaly in the momentum-space dynamics of a 2D Fermi superfluid of ultraco…
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Quantum anomalies are violations of classical scaling symmetries caused by quantum fluctuations. Although they appear prominently in quantum field theory to regularize divergent physical quantities, their influence on experimental observables is difficult to discern. Here, we discovered a striking manifestation of a quantum anomaly in the momentum-space dynamics of a 2D Fermi superfluid of ultracold atoms. We measured the position and pair momentum distribution of the superfluid during a breathing mode cycle for different interaction strengths across the BEC-BCS crossover. Whereas the system exhibits self-similar evolution in the weakly interacting BEC and BCS limits, we found a violation in the strongly interacting regime. The signature of scale-invariance breaking is enhanced in the first-order coherence function. In particular, the power-law exponents that characterize long-range phase correlations in the system are modified due to this effect, indicating that the quantum anomaly has a significant influence on the critical properties of 2D superfluids.
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Submitted 12 May, 2018;
originally announced May 2018.
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Dynamical critical scaling of long-range interacting quantum magnets
Authors:
Nicolo Defenu,
Tilman Enss,
Michael Kastner,
Giovanna Morigi
Abstract:
Slow variations (quenches) of the magnetic field across the paramagnetic-ferromagnetic phase transition of spin systems produce heat. In systems with short-range interactions the heat exhibits universal power-law scaling as a function of the quench rate, known as Kibble-Zurek scaling. In this work we analyze slow quenches of the magnetic field in the Lipkin-Meshkov-Glick (LMG) model, which describ…
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Slow variations (quenches) of the magnetic field across the paramagnetic-ferromagnetic phase transition of spin systems produce heat. In systems with short-range interactions the heat exhibits universal power-law scaling as a function of the quench rate, known as Kibble-Zurek scaling. In this work we analyze slow quenches of the magnetic field in the Lipkin-Meshkov-Glick (LMG) model, which describes fully connected quantum spins. We analytically determine the quantum contribution to the residual heat as a function of the quench rate $δ$ by means of a Holstein-Primakoff expansion about the mean-field value. Unlike in the case of short-range interactions, scaling laws in the LMG model are only found for a ramp ending at the critical point. If instead the ramp is symmetric, as in the typical Kibble-Zurek scenario, after crossing the critical point the system tends to reabsorb the defects formed during the first part of the ramp: the number of excitations exhibits a crossover behavior as a function of $δ$ and tends to a constant in the thermodynamic limit. Previous, and seemingly contradictory, theoretical studies are identified as specific limits of this dynamics. Our results can be tested on several experimental platforms, including quantum gases and trapped ions.
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Submitted 14 September, 2018; v1 submitted 30 April, 2018;
originally announced May 2018.
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Nonlinear spin diffusion and spin rotation in a trapped Fermi gas
Authors:
Tilman Enss
Abstract:
Transverse spin diffusion in a polarized, interacting Fermi gas leads to the Leggett-Rice effect, where the spin current precesses around the local magnetization. With a spin-echo sequence both the transverse diffusivity and the spin-rotation parameter $γ$ are obtained; the sign of $γ$ reveals the repulsive or attractive character of the effective interaction. In a trapped Fermi gas the spin diffu…
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Transverse spin diffusion in a polarized, interacting Fermi gas leads to the Leggett-Rice effect, where the spin current precesses around the local magnetization. With a spin-echo sequence both the transverse diffusivity and the spin-rotation parameter $γ$ are obtained; the sign of $γ$ reveals the repulsive or attractive character of the effective interaction. In a trapped Fermi gas the spin diffusion equations become nonlinear, and their numerical solution exhibits an inhomogeneous spin state even at the spin echo time. While the microscopic diffusivity and $γ$ increase at weak coupling, their apparent values inferred from the trap-averaged magnetization saturate in agreement with a recent experiment for a dilute ultracold Fermi gas.
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Submitted 26 February, 2015; v1 submitted 12 January, 2015;
originally announced January 2015.
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Universal equation of state and pseudogap in the two-dimensional Fermi gas
Authors:
Marianne Bauer,
Meera M. Parish,
Tilman Enss
Abstract:
We determine the thermodynamic properties and the spectral function for a homogeneous two-dimensional Fermi gas in the normal state using the Luttinger-Ward, or self-consistent T-matrix, approach. The density equation of state deviates strongly from that of the ideal Fermi gas even for moderate interactions, and our calculations suggest that temperature has a pronounced effect on the pressure in t…
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We determine the thermodynamic properties and the spectral function for a homogeneous two-dimensional Fermi gas in the normal state using the Luttinger-Ward, or self-consistent T-matrix, approach. The density equation of state deviates strongly from that of the ideal Fermi gas even for moderate interactions, and our calculations suggest that temperature has a pronounced effect on the pressure in the crossover from weak to strong coupling, consistent with recent experiments. We also compute the superfluid transition temperature for a finite system in the crossover region. There is a pronounced pseudogap regime above the transition temperature: the spectral function shows a Bogoliubov-like dispersion with back-bending, and the density of states is significantly suppressed near the chemical potential. The contact density at low temperatures increases with interaction and compares well with both experiment and zero-temperature Monte Carlo results.
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Submitted 17 February, 2014; v1 submitted 5 November, 2013;
originally announced November 2013.
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Transverse spin diffusion in strongly interacting Fermi gases
Authors:
Tilman Enss
Abstract:
We compute spin diffusion in a dilute Fermi gas at arbitrary temperature, polarization and strong interaction in the normal phase using kinetic theory. While the longitudinal spin diffusivity depends weakly on polarization and diverges for small temperatures, the transverse spin diffusivity D_\perp has a strong polarization dependence and approaches a finite value for T->0 in the Fermi liquid phas…
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We compute spin diffusion in a dilute Fermi gas at arbitrary temperature, polarization and strong interaction in the normal phase using kinetic theory. While the longitudinal spin diffusivity depends weakly on polarization and diverges for small temperatures, the transverse spin diffusivity D_\perp has a strong polarization dependence and approaches a finite value for T->0 in the Fermi liquid phase. For a 3D unitary Fermi gas at infinite scattering length the diffusivities reach a minimum near the quantum limit of diffusion \hbar/m in the quantum degenerate regime and are strongly suppressed by medium scattering, and we discuss the importance of the spin-rotation effect. In two dimensions, D_\perp attains a minimum at strong coupling -1 < ln(kFa2D) < 1 and reaches D_\perp~0.2...0.3\hbar/m at large polarization. These values are consistent with recent measurements of two-dimensional ultracold atomic gases in the strong coupling regime.
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Submitted 27 September, 2013; v1 submitted 19 July, 2013;
originally announced July 2013.
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Shear viscosity and spin sum rules in strongly interacting Fermi gases
Authors:
Tilman Enss
Abstract:
Fermi gases with short-range interactions are ubiquitous in ultracold atomic systems. In the absence of spin-flipping processes the number of atoms in each spin species is conserved separately, and we discuss the associated Ward identities. For contact interactions the spin conductivity spectral function sigma_s(omega) has universal power-law tails at high frequency. We derive the spin f-sum rule…
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Fermi gases with short-range interactions are ubiquitous in ultracold atomic systems. In the absence of spin-flipping processes the number of atoms in each spin species is conserved separately, and we discuss the associated Ward identities. For contact interactions the spin conductivity spectral function sigma_s(omega) has universal power-law tails at high frequency. We derive the spin f-sum rule and show that it is not affected by these tails in d<4 dimensions. Likewise the shear viscosity spectral function eta(omega) has universal tails; in contrast they modify the viscosity sum rule in a characteristic way.
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Submitted 5 February, 2013; v1 submitted 14 September, 2012;
originally announced September 2012.
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Fermi polarons in two dimensions
Authors:
Richard Schmidt,
Tilman Enss,
Ville Pietilä,
Eugene Demler
Abstract:
We theoretically analyze inverse radiofrequency (rf) spectroscopy experiments in two-component Fermi gases. We consider a small number of impurity atoms interacting strongly with a bath of majority atoms. In two-dimensional geometries we find that the main features of the rf spectrum correspond to an attractive polaron and a metastable repulsive polaron. Our results suggest that the attractive pol…
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We theoretically analyze inverse radiofrequency (rf) spectroscopy experiments in two-component Fermi gases. We consider a small number of impurity atoms interacting strongly with a bath of majority atoms. In two-dimensional geometries we find that the main features of the rf spectrum correspond to an attractive polaron and a metastable repulsive polaron. Our results suggest that the attractive polaron has been observed in a recent experiment [Phys. Rev. Lett. 106, 105301 (2011)].
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Submitted 7 February, 2012; v1 submitted 7 October, 2011;
originally announced October 2011.
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Lightcone renormalization and quantum quenches in one-dimensional Hubbard models
Authors:
Tilman Enss,
Jesko Sirker
Abstract:
The Lieb-Robinson bound implies that the unitary time evolution of an operator can be restricted to an effective light cone for any Hamiltonian with short-range interactions. Here we present a very efficient renormalization group algorithm based on this light cone structure to study the time evolution of prepared initial states in the thermodynamic limit in one-dimensional quantum systems. The alg…
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The Lieb-Robinson bound implies that the unitary time evolution of an operator can be restricted to an effective light cone for any Hamiltonian with short-range interactions. Here we present a very efficient renormalization group algorithm based on this light cone structure to study the time evolution of prepared initial states in the thermodynamic limit in one-dimensional quantum systems. The algorithm does not require translational invariance and allows for an easy implementation of local conservation laws. We use the algorithm to investigate the relaxation dynamics of double occupancies in fermionic Hubbard models as well as a possible thermalization. For the integrable Hubbard model we find a pure power-law decay of the number of doubly occupied sites towards the value in the long-time limit while the decay becomes exponential when adding a nearest neighbor interaction. In accordance with the eigenstate thermalization hypothesis, the long-time limit is reasonably well described by a thermal average. We point out though that such a description naturally requires the use of negative temperatures. Finally, we study a doublon impurity in a Néel background and find that the excess charge and spin spread at different velocities, providing an example of spin-charge separation in a highly excited state.
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Submitted 3 February, 2012; v1 submitted 8 April, 2011;
originally announced April 2011.
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Viscosity and scale invariance in the unitary Fermi gas
Authors:
Tilman Enss,
Rudolf Haussmann,
Wilhelm Zwerger
Abstract:
We compute the shear viscosity of the unitary Fermi gas above the superfluid transition temperature, using a diagrammatic technique that starts from the exact Kubo formula. The formalism obeys a Ward identity associated with scale invariance which guarantees that the bulk viscosity vanishes identically. For the shear viscosity, vertex corrections and the associated Aslamazov-Larkin contributions a…
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We compute the shear viscosity of the unitary Fermi gas above the superfluid transition temperature, using a diagrammatic technique that starts from the exact Kubo formula. The formalism obeys a Ward identity associated with scale invariance which guarantees that the bulk viscosity vanishes identically. For the shear viscosity, vertex corrections and the associated Aslamazov-Larkin contributions are shown to be crucial to reproduce the full Boltzmann equation result in the high-temperature, low fugacity limit. The frequency dependent shear viscosity $η(ω)$ exhibits a Drude-like transport peak and a power-law tail at large frequencies which is proportional to the Tan contact. The weight in the transport peak is given by the equilibrium pressure, in agreement with a sum rule due to Taylor and Randeria. Near the superfluid transition the peak width is of the order of $0.5 T_F$, thus invalidating a quasiparticle description. The ratio $η/s$ between the static shear viscosity and the entropy density exhibits a minimum near the superfluid transition temperature whose value is larger than the string theory bound $\hbar/(4πk_B)$ by a factor of about seven.
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Submitted 12 October, 2010; v1 submitted 30 July, 2010;
originally announced August 2010.