Showing 1–50 of 122 results for author: Busch, T

Ground state of the Hubbard model with spin-dependent linear potential

Authors: Jacek Dobrzyniecki, Thomas Busch

Abstract: We investigate the competition between attractive spin-spin interactions and spin-separating external forces in the ground state of a one-dimensional Fermi-Hubbard model. We consider a lattice with open boundary conditions, subject to a linear external potential whose gradient is opposite for the two spin components, so that each spin species sees a potential minimum at a different end of the latt… ▽ More We investigate the competition between attractive spin-spin interactions and spin-separating external forces in the ground state of a one-dimensional Fermi-Hubbard model. We consider a lattice with open boundary conditions, subject to a linear external potential whose gradient is opposite for the two spin components, so that each spin species sees a potential minimum at a different end of the lattice. Using density-matrix renormalization group (DMRG) simulations, we map the ground-state density distributions and the number of doubly occupied sites as a function of the potential gradient $β$ and interaction strength. We identify three distinct regimes separated by critical threshold gradients: (i) a small-$β$ regime where fermion pairing remains robust against the external potential; (ii) an intermediate-$β$ phase-separated regime characterized by a staircase-like decrease in the doublon number, corresponding to the successive, one-by-one breaking of bound pairs; and (iii) a large-$β$ regime where the two spin components are completely spatially separated. We complement the numerical results with a phenomenological model and a local-density approximation analysis, from which we derive closed-form analytical estimates for these critical threshold values. We also verify that the staircase structure persists under additional harmonic confinement. Our results are directly testable in cold-atom experiments, and demonstrate that a spin-dependent linear potential enables precise, integer-level control of the number of bound fermion pairs. △ Less

Submitted 27 April, 2026; originally announced April 2026.

Comments: 19 pages, 14 figures

Optical creation of dark-bright soliton lattices in multicomponent Bose-Einstein condensates

Authors: Y. Braver, D. Burba, Th. Busch, G. Juzeliūnas, P. G. Kevrekidis

Abstract: We present a widely accessible and experimentally realizable technique for the controlled creation of dark-bright solitons and soliton lattices in atomic Bose-Einstein condensates. The method is based on preparing the condensate in a dark state of a $Λ$-coupled three-level system. Numerical simulations reveal that individual dark-bright solitons created through this scheme can survive over experim… ▽ More We present a widely accessible and experimentally realizable technique for the controlled creation of dark-bright solitons and soliton lattices in atomic Bose-Einstein condensates. The method is based on preparing the condensate in a dark state of a $Λ$-coupled three-level system. Numerical simulations reveal that individual dark-bright solitons created through this scheme can survive over experimentally accessible timescales, even when the coupling laser fields are switched off. Meanwhile, the fate of soliton lattices upon the quench of the fields depends on the scattering lengths. When they are all equal, the lattice is found to persist on timescales comparable to the condensate lifetime, even though the analysis of dynamical stability reveals that they possess unstable modes. In this case the resulting destabilization is not found to be detrimental, as it leads to recurrent dynamics. On the other hand, for unequal scattering lengths the lattice structure gets destroyed once the instability sets in. △ Less

Submitted 30 March, 2026; originally announced March 2026.

Comments: 8 pages, 5 figures

Chiral and pair superfluidity in triangular ladder produced by state-dependent Kronig-Penney lattice

Authors: Domantas Burba, Giedrius Žlabys, Dzmitry Viarbitski, Thomas Busch, Gediminas Juzeliūnas

Abstract: We propose a concrete realization of a triangular ladder for ultracold atoms, which simultaneously hosts geometric frustration and unusual two-body interactions, and in particular controllable pair hopping and density-induced tunneling. This is done by means of a spin-dependent Kronig-Penney lattice created using a spatially-dependent tripod-type atom-light coupling. We apply density matrix renorm… ▽ More We propose a concrete realization of a triangular ladder for ultracold atoms, which simultaneously hosts geometric frustration and unusual two-body interactions, and in particular controllable pair hopping and density-induced tunneling. This is done by means of a spin-dependent Kronig-Penney lattice created using a spatially-dependent tripod-type atom-light coupling. We apply density matrix renormalization group (DMRG) calculations to derive the quantum phase diagram. We find that pair tunneling stabilizes a robust pair superfluid, characterized by power-law decay of pair correlations. Additionally, a chiral superfluid arises from frustration induced by competing nearest neighbor (NN) and next-nearest neighbor (NNN) tunnelings. Finally, in the high barrier regime, we map our system onto the XXZ spin model and find the exact phase transition points. △ Less

Submitted 4 March, 2026; originally announced March 2026.

Comments: 12 pages, 6 figures

Mobile impurity interacting with a Hubbard chain and the role of Friedel oscillations

Authors: Felipe Isaule, Abel Rojo-Francàs, Duc Tuan Hoang, Thomás Fogarty, Thomas Busch, Bruno Juliá-Díaz

Abstract: This work examines a mobile impurity interacting with a bath of a few spin-$\uparrow$ and spin-$\downarrow$ fermions in a small one-dimensional open lattice system. We study ground-state properties using the exact diagonalization method, where the system is modeled by a three-component Fermi Hubbard Hamiltonian. We find that in addition to the standard phase separation between a strongly repulsive… ▽ More This work examines a mobile impurity interacting with a bath of a few spin-$\uparrow$ and spin-$\downarrow$ fermions in a small one-dimensional open lattice system. We study ground-state properties using the exact diagonalization method, where the system is modeled by a three-component Fermi Hubbard Hamiltonian. We find that in addition to the standard phase separation between a strongly repulsive impurity and the bath, a strongly-attractive impurity also phase separates with the fermionic holes due to the particle-hole symmetry. Furthermore, we find that the impurity can show an oscillatory pattern in its density for intermediate attractive and repulsive bath-impurity interactions, which are induced by Friedel oscillations in the finite-size fermionic bath. This rich behavior of the impurity could be probed with fermionic ultracold mixtures in optical lattices. △ Less

Submitted 3 June, 2026; v1 submitted 5 February, 2026; originally announced February 2026.

Comments: Accepted version. 17 pages, 16 figures

Journal ref: Phys. Rev. B 113, 224303 (2026)

Emergent topological properties in spatially modulated sub-wavelength barrier lattices

Authors: Giedrius Žlabys, Wen-Bin He, Domantas Burba, Sarika Sasidharan Nair, Thomas Busch, Tomoki Ozawa

Abstract: We investigate topological phenomena in a spatially modulated Dirac-$δ$ lattice, where the scattering potential varies periodically in space. Changing the potential modulation frequency leads to Hofstadter's butterfly-like energy spectrum and enables the emergence of topological transport regimes characterized by non-trivial Chern numbers. We show how the considered modulated system is connected t… ▽ More We investigate topological phenomena in a spatially modulated Dirac-$δ$ lattice, where the scattering potential varies periodically in space. Changing the potential modulation frequency leads to Hofstadter's butterfly-like energy spectrum and enables the emergence of topological transport regimes characterized by non-trivial Chern numbers. We show how the considered modulated system is connected to the Hofstadter model via the Harper equation. By adiabatically varying spatial modulation parameters, we demonstrate controllable quantum transport and verify the topological nature of these effects through Wannier center displacement and bulk invariant calculations. We also propose an experimentally feasible realization of such a system using optically controlled three-level atoms. Our findings showcase spatially engineered Kronig-Penney-type systems as versatile platforms for investigating and exploiting different topological quantum transport regimes. △ Less

Submitted 18 December, 2025; originally announced December 2025.

Correlated decoherence and thermometry with mobile impurities in a 1D Fermi gas

Authors: Sindre Brattegard, Thomás Fogarty, Thomas Busch, Mark T. Mitchison

Abstract: We theoretically investigate the correlated decoherence dynamics of two mobile impurities trapped within a gas of ultracold fermionic atoms. We use a mean-field approximation to self-consistently describe the effect of impurity-gas collisions on impurity motion, while decoherence of the impurities' internal state is computed exactly within a functional determinant approach. At equilibrium, we find… ▽ More We theoretically investigate the correlated decoherence dynamics of two mobile impurities trapped within a gas of ultracold fermionic atoms. We use a mean-field approximation to self-consistently describe the effect of impurity-gas collisions on impurity motion, while decoherence of the impurities' internal state is computed exactly within a functional determinant approach. At equilibrium, we find that the impurities undergo bath-induced localisation as the impurity-gas interaction strength is increased. We then study the non-equilibrium dynamics induced by a sudden change of the impurities' internal state, which can be experimentally probed by Ramsey interferometry. Our theoretical approach allows us to investigate the effect of impurity motion on decoherence dynamics, finding strong deviations from the universal behaviour associated with Anderson's orthogonality catastrophe when the mass imbalance between impurity and gas atoms is small. Finally, we show that mobile impurities can be used as thermometers of their environment and that bath-mediated correlations can be beneficial for thermometric performance at low temperatures, even in the presence of non-trivial impurity motion. Our results showcase the interesting open quantum dynamics of mobile impurities dephasing in a common environment, and could help provide more precise temperature estimates of ultracold fermionic mixtures. △ Less

Submitted 2 September, 2025; v1 submitted 27 August, 2025; originally announced August 2025.

Comments: V2: Added references. 15 pages, 11 figures, comments are welcome

Journal ref: Phys. Rev. A 113, 013302 (2026)

Quantum droplets in one-dimensional mixtures of quasi Bose-Einstein condensates and Tonks-Girardeau gases

Authors: Wen-Bin He, Su Yi, Thomas Busch

Abstract: While binary atomic Bose-Einstein condensates are typically prone to collapse under strong interspecies attraction, it has been shown that higher-order fluctuation corrections, known as Lee-Huang-Yang corrections, can stabilize the mixture. In this work, we demonstrate an alternative stabilization mechanism based on kinetic energy. Specifically, we consider a one-dimensional mixture of a quasi-BEC… ▽ More While binary atomic Bose-Einstein condensates are typically prone to collapse under strong interspecies attraction, it has been shown that higher-order fluctuation corrections, known as Lee-Huang-Yang corrections, can stabilize the mixture. In this work, we demonstrate an alternative stabilization mechanism based on kinetic energy. Specifically, we consider a one-dimensional mixture of a quasi-BEC and a Tonks-Girardeau gas, and show that the kinetic energy of the TG component can counteract the interspecies attraction, thereby preventing collapse. This balance leads to the formation of a self-bound quantum droplet, which exhibits two distinct regimes: a low-density and a high-density droplet. We argue that these regimes are smoothly connected by a crossover. Furthermore, an analysis of the derivatives of the ground state energy reveals that the transition from a miscible mixture to the droplet phase is of third order. Our findings extend the theoretical understanding of quantum droplets in low-dimensional quantum gases, and the proposed system is experimentally accessible within current ultracold atom platforms. △ Less

Submitted 22 August, 2025; originally announced August 2025.

Comments: 10 pages, 6 figures

Condensate-mediated dimerization of impurities in atomic BECs

Authors: Hoshu Hiyane, Thomás Fogarty, Jose Carlos Pelayo, Thomas Busch

Abstract: We show that strongly correlated impurities confined in an optical lattice can form localized, molecule-like dimer states in the presence of a Bose-Einstein condensate (BEC). By systematically studying the effect of the lattice potential on this mixture, we reveal the two roles of the condensate in assisting the formation of dimerized impurities: mediating the attractive interaction among impuriti… ▽ More We show that strongly correlated impurities confined in an optical lattice can form localized, molecule-like dimer states in the presence of a Bose-Einstein condensate (BEC). By systematically studying the effect of the lattice potential on this mixture, we reveal the two roles of the condensate in assisting the formation of dimerized impurities: mediating the attractive interaction among impurities and rescaling the lattice potential of impurities. At strong coupling between the impurities and the condensate, the two mechanisms cooperate to induce a structural transition, resulting in the rearrangement of dimers. We also show that the nonequilibrium dynamics of these states can be interpreted as a dimerized soliton train. △ Less

Submitted 29 July, 2025; originally announced July 2025.

Comments: 18 pages, 6 figures

Droplet-gas phases and their dynamical formation in particle imbalanced mixtures

Authors: Jose Carlos Pelayo, George A. Bougas, Thomás Fogarty, Thomas Busch, Simeon I. Mistakidis

Abstract: We explore the ground state phase diagram and nonequilibrium dynamics of genuine two-component particle-imbalanced droplets in both isotropic and anisotropic three-dimensional confinements. A gradual transition from mixed droplet-gas to gas configurations is revealed as the average intercomponent attraction decreases or the transverse confinement becomes tighter. Within the mixed structures, a spe… ▽ More We explore the ground state phase diagram and nonequilibrium dynamics of genuine two-component particle-imbalanced droplets in both isotropic and anisotropic three-dimensional confinements. A gradual transition from mixed droplet-gas to gas configurations is revealed as the average intercomponent attraction decreases or the transverse confinement becomes tighter. Within the mixed structures, a specific majority fragment binds to the minority droplet, satisfying the density ratio locking condition, while the remaining atoms are in a gas state. Our extended Gross-Pitaevskii numerical results are corroborated by a suitable variational approximation capturing the shape and characteristics of droplet-gas fragments. The tunability of the relatively low gas fraction is showcased through parametric variations of the atom number, the intercomponent imbalance, the trap aspect ratio, or the radius of a box potential. To validate the existence and probe the properties of these exotic phases, we simulate the standard time-of-flight and radio frequency experimental techniques. These allow to dynamically identify the resilience of the droplet fragment and the expansion of the gas fraction. Our results, amenable to current experimental cold atom settings, are expected to guide forthcoming investigations aiming to reveal unseen out-of-equilibrium droplet dynamics. △ Less

Submitted 4 December, 2025; v1 submitted 10 June, 2025; originally announced June 2025.

Light-induced localized vortices in multicomponent Bose-Einstein condensates

Authors: Y. Braver, D. Burba, S. S. Nair, G. Žlabys, E. Anisimovas, Th. Busch, G. Juzeliūnas

Abstract: We study continuous interaction of a trapped two-component Bose-Einstein condensate with light fields in a $Λ$-type configuration. Using light beams with orbital angular momentum, we theoretically show how to create a stable, pinned vortex configuration, where the rotating component is confined to the region surrounded by the second, non-rotating component. The atoms constituting this vortex can b… ▽ More We study continuous interaction of a trapped two-component Bose-Einstein condensate with light fields in a $Λ$-type configuration. Using light beams with orbital angular momentum, we theoretically show how to create a stable, pinned vortex configuration, where the rotating component is confined to the region surrounded by the second, non-rotating component. The atoms constituting this vortex can be localized in volumes much smaller than the volume occupied by the second component. We also show that the vortex position can be changed dynamically by moving the laser beams, provided the beams' movement speed remains below the speed of sound. This allows us to use the localized vortex to stir the second component, and to determine the superfluid flow's critical velocity. △ Less

Submitted 30 August, 2025; v1 submitted 10 June, 2025; originally announced June 2025.

Comments: 13 pages, 7 figures

Journal ref: Phys. Rev. A 112, 033301 (2025)

Two identical 1D anyons with zero-range interactions: Exchange statistics, scattering theory, and anyon-anyon mapping

Authors: Raúl Hidalgo-Sacoto, Thomas Busch, D. Blume

Abstract: While elementary particles obey either bosonic or fermionic exchange statistics, generalized exchange statistics that interpolate between bosons and fermions -- applicable to quasi-particles -- constitute an intriguing topic, both from the fundamental and practical points of view. This work develops a scattering framework for two identical 1D bosonic anyons and two identical 1D fermionic anyons wi… ▽ More While elementary particles obey either bosonic or fermionic exchange statistics, generalized exchange statistics that interpolate between bosons and fermions -- applicable to quasi-particles -- constitute an intriguing topic, both from the fundamental and practical points of view. This work develops a scattering framework for two identical 1D bosonic anyons and two identical 1D fermionic anyons with zero-range contact interactions. The two-body system with zero-range interactions, both in free space and under external confinement, is used to illustrate the recently proposed bosonic-anyon -- fermionic-anyon mapping~(R. Hidalgo-Sacoto {\em{et al.}}, arXiv:2505.17669), which connects the eigenstates of bosonic anyons to those of fermionic anyons and vice versa. Performing explicit calculations for two-particle systems, the momentum distributions and the off-diagonal correlations of the single-particle density matrix for bosonic anyons and fermionic anyons are confirmed to be distinct. We also confirm the previously derived asymptotic coefficients of the momentum distribution tail at orders $k^{-2}$ and $k^{-3}$ for two harmonically confined anyons. Non-universal contributions at order $k^{-4}$ are discussed. △ Less

Submitted 29 May, 2025; originally announced May 2025.

Comments: 17 pages, 4 figures

Universal momentum tail of identical one-dimensional anyons with two-body interactions

Authors: Raúl Hidalgo-Sacoto, Thomas Busch, D. Blume

Abstract: Non-relativistic anyons in 1D possess generalized exchange statistics in which the exchange of two identical anyons generates a non-local phase that is governed by the spatial ordering of the particles and the statistical parameter $α$. Working in the continuum, we demonstrate the existence of two distinct types of 1D anyons, namely bosonic anyons and fermionic anyons. We identify a many-body Hami… ▽ More Non-relativistic anyons in 1D possess generalized exchange statistics in which the exchange of two identical anyons generates a non-local phase that is governed by the spatial ordering of the particles and the statistical parameter $α$. Working in the continuum, we demonstrate the existence of two distinct types of 1D anyons, namely bosonic anyons and fermionic anyons. We identify a many-body Hamiltonian with additive two-body zero-range interactions that supports bosonic and fermionic anyon eigenstates, which are, for arbitrary interaction strength, related through a generalized bosonic-anyon--fermionic-anyon mapping, an extension of the celebrated Bose-Fermi mapping for zero-range interacting 1D systems. The momentum distributions of bosonic and fermionic anyons are distinct: while both feature $k^{-2}$ and $k^{-3}$ tails, the associated prefactors differ. Our work reveals intricate connections between the generalized exchange statistics, the universal two- and three-body Tan contacts of systems consisting of $N$ identical particles, and the emergence of statistics-induced chiral symmetry breaking. △ Less

Submitted 23 May, 2025; originally announced May 2025.

Comments: 15 pages, 2 figures

Leveraging quantum statistics to enhance heat engines

Authors: Keerthy Menon, Thomas Busch, Thomás Fogarty

Abstract: A key focus of designing quantum thermal devices is the potential advantage that can be gleaned from genuine quantum effects when compared to classical devices. The recent experimental realization of the Pauli engine, where energy is extracted via changes in particle statistics as an alternative to conventional heat sources has opened new avenues of research where quantum statistics can be conside… ▽ More A key focus of designing quantum thermal devices is the potential advantage that can be gleaned from genuine quantum effects when compared to classical devices. The recent experimental realization of the Pauli engine, where energy is extracted via changes in particle statistics as an alternative to conventional heat sources has opened new avenues of research where quantum statistics can be considered as a thermodynamic resource. In this work we propose hybrid quantum heat engines which utilize additional strokes that change the single particle statistics between bosonic and fermionic descriptions during the cycle. To accomplish this we consider the 1D Lieb Liniger gas whereby the s wave interactions can be tuned between the non interacting and the hard core limit, which are described by bosonic and fermionic statistics respectively. We show that by suitably choosing where to implement these statistical strokes during an Otto like cycle, the efficiency and work output can be significantly enhanced when compared to fully bosonic or fully fermionic engines. Furthermore, in the degenerate regime our engine can operate at the Carnot efficiency, due to the interplay between the different contributions of heat and work induced by the statistical strokes. Finally, we highlight how our thermodynamic cycles can realize other thermal operations,such as refrigerators, promising similar statistical enhancements for a wide range of temperatures. △ Less

Submitted 25 March, 2025; originally announced March 2025.

Comments: 14 pages, 7 figures

Quantum correlations and spatial localization in trapped one-dimensional ultra-cold Bose-Bose-Bose mixtures

Authors: Tran Duong Anh-Tai, Miguel A. García-March, Thomas Busch, Thomás Fogarty

Abstract: We systematically investigate and illustrate the complete ground-state phase diagram for a one-dimensional, three-species mixture of a few repulsively interacting bosons trapped harmonically. To numerically obtain the solutions to the many-body Schrödinger equation, we employ the improved Exact Diagonalization method [T. D. Anh-Tai {\it et al.}, SciPost Physics 15, 048 (2023)], which is capable of… ▽ More We systematically investigate and illustrate the complete ground-state phase diagram for a one-dimensional, three-species mixture of a few repulsively interacting bosons trapped harmonically. To numerically obtain the solutions to the many-body Schrödinger equation, we employ the improved Exact Diagonalization method [T. D. Anh-Tai {\it et al.}, SciPost Physics 15, 048 (2023)], which is capable of treating strongly-correlated few-body systems from first principles in an efficiently truncated Hilbert space. We present our comprehensive results for all possible combinations of intra- and interspecies interactions in the extreme limits that are either the ideal limit ($g=0$) or close to the hard-core limit ($g\to\infty$). These results show the emergence of unique ground-state properties related to correlations, coherence and spatial localization stemming from strongly repulsive interactions. △ Less

Submitted 4 June, 2025; v1 submitted 25 January, 2025; originally announced January 2025.

Comments: 22 pages, 12 figures

Emergence of nonequilibrium Lieb excitations in periodically driven strongly interacting bosons

Authors: Hoshu Hiyane, Giedrius Žlabys, Thomas Busch, Shohei Watabe

Abstract: We study the exact nonequilibrium spectral function of a gas of strongly correlated Tonks-Girardeau bosons subjected to a strong periodic drive. Utilizing the theory of Floquet spectral function in conjunction with the Bose-Fermi mapping theorem, we show that nonequilibrium Lieb modes emerge if the underlying mapped fermions form a Floquet-Fermi sea. In the low-frequency regime, the exact analysis… ▽ More We study the exact nonequilibrium spectral function of a gas of strongly correlated Tonks-Girardeau bosons subjected to a strong periodic drive. Utilizing the theory of Floquet spectral function in conjunction with the Bose-Fermi mapping theorem, we show that nonequilibrium Lieb modes emerge if the underlying mapped fermions form a Floquet-Fermi sea. In the low-frequency regime, the exact analysis reveals the emergence of characteristic linear Lieb excitations for the bosonic system, while the underlying mapped fermions displays the wide Dirac-like linear dispersion. △ Less

Submitted 23 December, 2024; originally announced December 2024.

Comments: 5 pages, 4 figures

Quench dynamics in topologically non-trivial quantum many-body systems

Authors: Sarika Sasidharan Nair, Giedrius Žlabys, Wen-Bin He, Thomás Fogarty, Thomas Busch

Abstract: We investigate the nonequilibrium dynamics of a groundstate fermionic many body gas subjected to a quench between parameter regimes of a topologically nontrivial Hamiltonian. By focusing on the role of the chiral edge states inherent to the system, we calculate the many body overlap and show that the characteristic monotonic decay of the orthogonality catastrophe with increasing system size is not… ▽ More We investigate the nonequilibrium dynamics of a groundstate fermionic many body gas subjected to a quench between parameter regimes of a topologically nontrivial Hamiltonian. By focusing on the role of the chiral edge states inherent to the system, we calculate the many body overlap and show that the characteristic monotonic decay of the orthogonality catastrophe with increasing system size is notably altered. Specifically, we demonstrate that the dynamics are governed not solely by the total particle number but rather by the number of occupied single particle edge states. This behavior is further explained through an analysis of the full work probability distribution, providing a deeper understanding of the system's dynamics. △ Less

Submitted 2 December, 2024; originally announced December 2024.

Comments: 9 pages,7 figures

Shortcuts to Adiabaticity in Anisotropic Bose-Einstein Condensates

Authors: Chinmayee Mishra, Thomas Busch, Thomás Fogarty

Abstract: We propose shortcut to adiabaticity protocols for Bose-Einstein condensates trapped in generalized anisotropic harmonic traps in three dimensions. These protocols enable high-fidelity tuning of trap geometries on time scales much faster than those required for adiabatic processes and are robust across a wide range of interaction strengths, from weakly interacting regimes to the Thomas-Fermi limit.… ▽ More We propose shortcut to adiabaticity protocols for Bose-Einstein condensates trapped in generalized anisotropic harmonic traps in three dimensions. These protocols enable high-fidelity tuning of trap geometries on time scales much faster than those required for adiabatic processes and are robust across a wide range of interaction strengths, from weakly interacting regimes to the Thomas-Fermi limit. Using the same approach, we also design STA paths to rapidly drive interaction strengths in both isotropic and anisotropic traps. Comparisons with standard linear ramps of system parameters demonstrate significant improvements in performance. Finally, we apply these STA techniques to a unitary engine cycle with a BEC as the working medium. The STA methods significantly enhance the engine's power output without reducing efficiency and remain highly effective even after multiple consecutive cycles. △ Less

Submitted 27 November, 2024; originally announced November 2024.

Comments: 10 pages, 5 figures

The Lieb excitations and topological flat mode of spectral function of Tonks-Girardeau gas in Kronig-Penney potential

Authors: Wen-Bin He, Giedrius Žlabys, Hoshu Hiyane, Sarika Sasidharan Nair, Thomas Busch

Abstract: Lieb excitations are fundamental to the understanding of the low energy behaviour of many-body quantum gases. Here we study the spectral function of a Tonks-Girardeau gas in a finite sized Kronig-Penney potential and show that the Lieb-I and Lieb-II excitations can become gapped as a function of the barrier height. Moreover, we reveal the existence of a topological flat mode near the Fermi energy… ▽ More Lieb excitations are fundamental to the understanding of the low energy behaviour of many-body quantum gases. Here we study the spectral function of a Tonks-Girardeau gas in a finite sized Kronig-Penney potential and show that the Lieb-I and Lieb-II excitations can become gapped as a function of the barrier height. Moreover, we reveal the existence of a topological flat mode near the Fermi energy and at zero momentum and show that this is robust to perturbations in the system. Through a scaling analysis, we determine the divergent behaviour of the spectral function. Our results provide a significant reference for the observation and understanding of the gapped Lieb excitations and the topological flat mode of quantum gases in experimentally realistic subwavelength optical lattice potentials. △ Less

Submitted 17 October, 2024; originally announced October 2024.

Report number: Phys. Rev. A 111, 013312(2025)

Journal ref: Phys. Rev. A 111, 013312(2025)

Bose-Fermi $N$-polaron state emergence from correlation-mediated blocking of phase separation

Authors: Felipe Gómez-Lozada, Hoshu Hiyane, Thomas Busch, Thomás Fogarty

Abstract: We study $N$ fermionic impurities in a one-dimensional lattice bosonic bath at unit filling. Using DMRG and mixed boundary conditions-periodic for bosons, open for fermions -- we find an $N$-polaron ground state replacing phase separation at high interspecies repulsion. This tightly bound state of clustered particles emerges due to strong impurity-bath correlations, which induce large impurity-imp… ▽ More We study $N$ fermionic impurities in a one-dimensional lattice bosonic bath at unit filling. Using DMRG and mixed boundary conditions-periodic for bosons, open for fermions -- we find an $N$-polaron ground state replacing phase separation at high interspecies repulsion. This tightly bound state of clustered particles emerges due to strong impurity-bath correlations, which induce large impurity-impurity correlations that we quantify via the von Neumann entropy and bipartite mutual information, respectively. This system also reveals a fermionic self-localization effect from a Mott insulator background due to local correlations between the impurities and the bath. The growth of long-range correlations breaks this Mott phase, resulting in the transition to impurity clusters delocalized along the system. Finally, we show that there is a critical impurity number, which depends on intraspecies bosonic interaction, beyond which phase separation is recovered. △ Less

Submitted 28 February, 2025; v1 submitted 20 September, 2024; originally announced September 2024.

Comments: 10 pages, 12 figures. Updated version with additional discussion on the multiple impurity case and system-size scaling

Phases and dynamics of quantum droplets in the crossover to two-dimensions

Authors: Jose Carlos Pelayo, George Bougas, Thomás Fogarty, Thomas Busch, Simeon I. Mistakidis

Abstract: We explore the ground states and dynamics of ultracold atomic droplets in the crossover region from three to two dimensions by solving the two-dimensional and the quasi two-dimensional extended Gross-Pitaevskii equations numerically and with a variational approach. By systematically comparing the droplet properties, we determine the validity regions of the pure two-dimensional description, and the… ▽ More We explore the ground states and dynamics of ultracold atomic droplets in the crossover region from three to two dimensions by solving the two-dimensional and the quasi two-dimensional extended Gross-Pitaevskii equations numerically and with a variational approach. By systematically comparing the droplet properties, we determine the validity regions of the pure two-dimensional description, and therefore the dominance of the logarithmic nonlinear coupling, as a function of the sign of the averaged mean-field interactions and the size of the transverse confinement. One of our main findings is that droplets become substantially extended upon transitioning from negative-to-positive averaged mean-field interactions. This is accompanied by a significant reduction of their binding energies which are approximately inversely proportional to the square of their size. To explore fundamental dynamical properties in the crossover region, we study interaction quenches and show that the droplets perform a periodic breathing motion for modest quench strengths, while larger quench amplitudes lead to continuous expansion exhibiting density ring structures. We also showcase that it is possible to form complex bulk and surface density patterns in anisotropic geometries following the quench. Since we are working with realistic parameters, our results can directly facilitate future experimental realizations. △ Less

Submitted 17 March, 2025; v1 submitted 23 July, 2024; originally announced July 2024.

Journal ref: SciPost Phys. 18, 129 (2025)

Engineering impurity Bell states through coupling with a quantum bath

Authors: Tran Duong Anh-Tai, Thomás Fogarty, Sergi de María-García, Thomas Busch, Miguel A. García-March

Abstract: We theoretically demonstrate the feasibility of creating Bell states in multi-component ultra-cold atomic gases by solely using the ability to control the inter-particle interactions via Feshbach resonances. For this we consider two distinguishable impurities immersed in an atomic background cloud of a few bosons, with the entire system being confined in a one-dimensional harmonic trap. By analyzi… ▽ More We theoretically demonstrate the feasibility of creating Bell states in multi-component ultra-cold atomic gases by solely using the ability to control the inter-particle interactions via Feshbach resonances. For this we consider two distinguishable impurities immersed in an atomic background cloud of a few bosons, with the entire system being confined in a one-dimensional harmonic trap. By analyzing the numerically obtained ground states we demonstrate that the two impurities can form spatially entangled bipolaron states due to mediated interactions from the bosonic bath. Our analysis is based on calculating the correlations between the two impurities in a two-mode basis, which is experimentally accessible by measuring the particles positions in the left or right sides of the trap. While interspecies interactions are crucial in order to create the strongly entangled impurity states, it can also inhibit correlations depending on the ordering of the impurities and three-body impurity-bath correlations. We show how these drawbacks can be mitigated by manipulating the properties of the bath, namely its size, mass and intraspecies interactions, allowing to create impurity Bell states over a wide range of impurity-impurity interactions. △ Less

Submitted 14 October, 2024; v1 submitted 11 June, 2024; originally announced June 2024.

Comments: 11 pages, 7 figures. To appear in Physical Review Research

Phases and dynamics of few fermionic impurities immersed in two-dimensional boson droplets

Authors: Jose Carlos Pelayo, Thomás Fogarty, Thomas Busch, Simeon I. Mistakidis

Abstract: We unravel the ground state properties and emergent non-equilibrium dynamics of a mixture consisting of a few spin-polarized fermions embedded in a two-dimensional bosonic quantum droplet. For an increasingly attractive droplet-fermion interaction we find a transition from a spatially delocalized fermion configuration to a state where the fermions are highly localized and isolated. This process is… ▽ More We unravel the ground state properties and emergent non-equilibrium dynamics of a mixture consisting of a few spin-polarized fermions embedded in a two-dimensional bosonic quantum droplet. For an increasingly attractive droplet-fermion interaction we find a transition from a spatially delocalized fermion configuration to a state where the fermions are highly localized and isolated. This process is accompanied by the rise of induced fermion-fermion interactions mediated by the droplet. Additionally, for increasing attractive droplet-fermion coupling, undulations in the droplet density occur in the vicinity of the fermions manifesting the back-action of the latter. Following interaction quenches from strong attractive to weaker droplet-fermion couplings reveals the spontaneous nucleation of complex excitation patterns in the fermion density such as ring and cross shaped structures. These stem from the enhanced interference of the fermions that remain trapped within the droplet, which emulates, to a good degree, an effective potential for the fermions. The non-negligible back-action of the droplet manifests itself in the fact that the effective potential predictions are less accurate at the level of the many-body wave function. Our results provide a paradigm for physics beyond the reduced single-component droplet model, unveiling the role of back-action in droplets and the effect of induced mediated interactions. △ Less

Submitted 20 May, 2024; originally announced May 2024.

Synthesis of layered gold tellurides AuSbTe and Au$_2$Te$_3$ and their semiconducting and metallic behavior

Authors: Emma A. Pappas, Rong Zhang, Cheng Peng, Robert T. Busch, Jian-Min Zuo, Thomas P. Devereaux, Daniel P. Shoemaker

Abstract: Previous studies on natural samples of pampaloite (AuSbTe) revealed the crystal structure of a potentially cleavable and/or exfoliable material, while studies on natural and synthetic montbrayite (Sb-containing Au$_2$Te$_3$) claimed various chemical compositions for this low symmetry compound. Few investigations of synthetic samples have been reported for both materials, leaving much of their chem… ▽ More Previous studies on natural samples of pampaloite (AuSbTe) revealed the crystal structure of a potentially cleavable and/or exfoliable material, while studies on natural and synthetic montbrayite (Sb-containing Au$_2$Te$_3$) claimed various chemical compositions for this low symmetry compound. Few investigations of synthetic samples have been reported for both materials, leaving much of their chemical, thermal and electronic characteristics unknown. Here, we investigate the stability, electronic properties and synthesis of the gold antimony tellurides AuSbTe and Au$_{1.9}$Sb$_{0.46}$Te$_{2.64}$ (montbrayite). Differential thermal analysis and $\textit{in situ}$ powder x-ray diffraction revealed that AuSbTe is incongruently melting, while Au$_{1.9}$Sb$_{0.46}$Te$_{2.64}$ is congruently melting. Calculations of the band structures and four-point resistivity measurements showed that AuSbTe is a semiconductor and Au$_{1.9}$Sb$_{0.46}$Te$_{2.64}$ a metal. Various synthesis attempts confirmed the limited stable chemical composition of Au$_{1.9}$Sb$_{0.46}$Te$_{2.64}$, identified successful methods to synthesize both compounds, and highlighted the challenges associated with single crystal synthesis of AuSbTe. △ Less

Submitted 3 February, 2025; v1 submitted 24 April, 2024; originally announced April 2024.

Comments: 12 pages, 13 figures

Journal ref: Inorganic Chemistry 2025 64 (4), 1613-1623

Thouless pumping and trapping of two-component gap solitons

Authors: Hao Lyu, Yongping Zhang, Thomas Busch

Abstract: We study Thouless pumping and arresting of gap solitons in a two-component Bose gas loaded into an optical superlattice. We show that, depending on the atomic interactions and chemical potentials, the two solitons can be simultaneously pumped or trapped, but we also identify regimes where one soliton is pumped and the other arrested. These behaviors can be understood by considering an effective mo… ▽ More We study Thouless pumping and arresting of gap solitons in a two-component Bose gas loaded into an optical superlattice. We show that, depending on the atomic interactions and chemical potentials, the two solitons can be simultaneously pumped or trapped, but we also identify regimes where one soliton is pumped and the other arrested. These behaviors can be understood by considering an effective model of the system based on a variational approach, which reveals that the soliton width is a suitable qualifier for the observed behaviours: solitons with a larger width get transported, while solitons with a smaller width get trapped. Since these width can be controlled by tuning interactions, it should be possible to observe all behaviours experimentally. △ Less

Submitted 10 October, 2024; v1 submitted 21 April, 2024; originally announced April 2024.

Comments: 7 pages, 3 figures

Journal ref: Phys. Rev. Res. 6, L042010 (2024)

Quantum soliton-trains of strongly correlated impurities in Bose-Einstein condensates

Authors: Hoshu Hiyane, Thomas Busch, Thomás Fogarty

Abstract: Strongly correlated impurities immersed in a Bose-Einstein condensate (BEC) can form a periodic structure of tightly localized single atoms due to competing inter- and intra-species interactions, leading to a self-organized pinned state. In this work, we show numerically that the impurities in the self-pinned state form a soliton-train, as a consequence of a BEC-mediated attractive self-interactio… ▽ More Strongly correlated impurities immersed in a Bose-Einstein condensate (BEC) can form a periodic structure of tightly localized single atoms due to competing inter- and intra-species interactions, leading to a self-organized pinned state. In this work, we show numerically that the impurities in the self-pinned state form a soliton-train, as a consequence of a BEC-mediated attractive self-interaction and ordering due to the exclusion principle. The dynamics of the impurities possess similar characteristics to bright matter-wave solitons as they appear in attractive BECs, however in the few impurities case, the detailed nature of collisions is determined by their quantum statistics. △ Less

Submitted 26 August, 2024; v1 submitted 18 February, 2024; originally announced February 2024.

Comments: 7 pages, 4 figures

Journal ref: Phys. Rev. Research 6, L032040 (2024)

High fidelity control of a many-body Tonks--Girardeau gas with an effective mean-field approach

Authors: Muhammad S. Hasan, Thomás Fogarty, Jing Li, Andreas Ruschhaupt, Thomas Busch

Abstract: Shortcuts to adiabaticity (STA) are powerful tools that can be used to control quantum systems with high fidelity. They work particularly well for single particle and non-interacting systems which can be described exactly and which possess invariant or self-similar dynamics. However, finding an exact STA for strongly correlated many-body systems can be difficult, as their complex dynamics may not… ▽ More Shortcuts to adiabaticity (STA) are powerful tools that can be used to control quantum systems with high fidelity. They work particularly well for single particle and non-interacting systems which can be described exactly and which possess invariant or self-similar dynamics. However, finding an exact STA for strongly correlated many-body systems can be difficult, as their complex dynamics may not be easily described, especially for larger systems that do not possess self-similar solutions. Here, we design STAs for one-dimensional bosonic gas in the Tonks--Girardeau limit by using a mean-field approach that succinctly captures the strong interaction effects through a quintic nonlinear term in the Schrödinger equation. We show that for the case of the harmonic oscillator with a time-dependent trap frequency the mean-field approach works exactly and recovers the well-known STA from literature. To highlight the robustness of our approach we also show that it works effectively for anharmonic potentials, achieving higher fidelities than other typical control techniques. △ Less

Submitted 3 April, 2024; v1 submitted 1 February, 2024; originally announced February 2024.

Comments: 8 pages, 5 figures

Dynamical invariant based shortcut to equilibration in open quantum systems

Authors: Mohamed Boubakour, Shimpei Endo, Thomás Fogarty, Thomas Busch

Abstract: We propose using the dynamical invariant also known as the Lewis-Riesenfeld invariant, to speed-up the equilibration of a driven open quantum system. This allows us to reverse engineer the time-dependent master equation that describes the dynamics of the open quantum system and systematically derive a protocol that realizes a shortcut to equilibration. The method does not require additional constr… ▽ More We propose using the dynamical invariant also known as the Lewis-Riesenfeld invariant, to speed-up the equilibration of a driven open quantum system. This allows us to reverse engineer the time-dependent master equation that describes the dynamics of the open quantum system and systematically derive a protocol that realizes a shortcut to equilibration. The method does not require additional constraints on the timescale of the dynamics beside the Born-Markov approximation and can be generically applied to boost single particle quantum engines significantly. We demonstrate it with the damped harmonic oscillator, and show that our protocol can achieve a high-fidelity control in shorter timescales than simple non-optimized protocols. We find that the system is heated during the dynamics to speed-up the equilibration, which can be considered as an analogue of the Mpemba effect in quantum control. △ Less

Submitted 14 February, 2025; v1 submitted 21 January, 2024; originally announced January 2024.

Comments: 6 pages, 1 figure and an appendix

Controlling dark solitons on the healing length scale

Authors: Ling-Zheng Meng, Li-Chen Zhao, Th. Busch, Yongping Zhang

Abstract: While usually the optical diffraction limit is setting a limit for the lengthscales on which a typical alkali Bose-Einstein condensate can be controlled, we show that in certain situations control via matter waves can achieve smaller resolutions. For this we consider a small number of impurity atoms which are trapped inside the density dip of a dark soliton state and show that any grey soliton can… ▽ More While usually the optical diffraction limit is setting a limit for the lengthscales on which a typical alkali Bose-Einstein condensate can be controlled, we show that in certain situations control via matter waves can achieve smaller resolutions. For this we consider a small number of impurity atoms which are trapped inside the density dip of a dark soliton state and show that any grey soliton can be obtained by just driving the impurity atoms. By controlling the driving force on the impurity, one can therefore fully control the position and velocity of the dark soliton, and also study controlled collisions between these non-linear objects. △ Less

Submitted 20 February, 2023; originally announced February 2023.

Comments: 7 pages, 6 figures

Fermionization of a Few-Body Bose System Immersed into a Bose-Einstein Condensate

Authors: Tim Keller, Thomás Fogarty, Thomas Busch

Abstract: We study the recently introduced self-pinning transition [Phys. Rev. Lett. 128, 053401 (2022)] in a quasi-one-dimensional two-component quantum gas in the case where the component immersed into the Bose-Einstein condensate has a finite intraspecies interaction strength. As a result of the matter-wave backaction, the fermionization in the limit of infinite intraspecies repulsion occurs via a first-… ▽ More We study the recently introduced self-pinning transition [Phys. Rev. Lett. 128, 053401 (2022)] in a quasi-one-dimensional two-component quantum gas in the case where the component immersed into the Bose-Einstein condensate has a finite intraspecies interaction strength. As a result of the matter-wave backaction, the fermionization in the limit of infinite intraspecies repulsion occurs via a first-order phase transition to the self-pinned state, which is in contrast to the asymptotic behavior in static trapping potentials. The system also exhibits an additional superfluid state for the immersed component if the interspecies interaction is able to overcome the intraspecies repulsion. We approximate the superfluid state in an analytical model and derive an expression for the phase transition line that coincides with well-known phase separation criteria in binary Bose systems. The full phase diagram of the system is mapped out numerically for the case of two and three atoms in the immersed component. △ Less

Submitted 30 June, 2023; v1 submitted 2 February, 2023; originally announced February 2023.

Comments: 17 pages, 4 figures

Journal ref: SciPost Phys. 15, 095 (2023)

Quantum chaos in interacting Bose-Bose mixtures

Authors: Tran Duong Anh-Tai, Mathias Mikkelsen, Thomas Busch, Thomás Fogarty

Abstract: The appearance of chaotic quantum dynamics significantly depends on the symmetry properties of the system, and in cold atomic systems many of these can be experimentally controlled. In this work, we systematically study the emergence of quantum chaos in a minimal system describing one-dimensional harmonically trapped Bose-Bose mixtures by tuning the particle-particle interactions. Using an advance… ▽ More The appearance of chaotic quantum dynamics significantly depends on the symmetry properties of the system, and in cold atomic systems many of these can be experimentally controlled. In this work, we systematically study the emergence of quantum chaos in a minimal system describing one-dimensional harmonically trapped Bose-Bose mixtures by tuning the particle-particle interactions. Using an advanced exact diagonalization scheme, we examine the transition from integrability to chaos when the inter-component interaction changes from weak to strong. Our study is based on the analysis of the level spacing distribution and the distribution of the matrix elements of observables in terms of the eigenstate thermalization hypothesis and their dynamics. We show that one can obtain strong signatures of chaos by increasing the inter-component interaction strength and breaking the symmetry of intra-component interactions. △ Less

Submitted 12 May, 2023; v1 submitted 12 January, 2023; originally announced January 2023.

Comments: 25 pages, 8 figures

Journal ref: SciPost Phys. 15, 048 (2023)

Interaction enhanced quantum heat engine

Authors: Mohamed Boubakour, Thomás Fogarty, Thomas Busch

Abstract: We study a minimal quantum Otto heat engine, where the working medium consists of an interacting few-body system in a harmonic trap. This allows us to consider the interaction strength as an additional tunable parameter during the work strokes. We calculate the figures of merit of this engine as a function of the temperature and show clearly in which parameter regimes the interactions assist in en… ▽ More We study a minimal quantum Otto heat engine, where the working medium consists of an interacting few-body system in a harmonic trap. This allows us to consider the interaction strength as an additional tunable parameter during the work strokes. We calculate the figures of merit of this engine as a function of the temperature and show clearly in which parameter regimes the interactions assist in engine performance. We also study the finite time dynamics and the subsequent trade-off between the efficiency and the power, comparing the interaction enhanced cycle with the case where the system remains scale-invariant. △ Less

Submitted 7 February, 2023; v1 submitted 7 November, 2022; originally announced November 2022.

Comments: 9 pages, 8 figures

Making statistics work: a quantum engine in the BEC-BCS crossover

Authors: Jennifer Koch, Keerthy Menon, Eloisa Cuestas, Sian Barbosa, Eric Lutz, Thomás Fogarty, Thomas Busch, Artur Widera

Abstract: Heat engines convert thermal energy into mechanical work both in the classical and quantum regimes. However, quantum theory offers genuine nonclassical forms of energy, different from heat, which so far have not been exploited in cyclic engines to produce useful work. We here experimentally realize a novel quantum many-body engine fuelled by the energy difference between fermionic and bosonic ense… ▽ More Heat engines convert thermal energy into mechanical work both in the classical and quantum regimes. However, quantum theory offers genuine nonclassical forms of energy, different from heat, which so far have not been exploited in cyclic engines to produce useful work. We here experimentally realize a novel quantum many-body engine fuelled by the energy difference between fermionic and bosonic ensembles of ultracold particles that follows from the Pauli exclusion principle. We employ a harmonically trapped superfluid gas of $^6$Li atoms close to a magnetic Feshbach resonance which allows us to effectively change the quantum statistics from Bose-Einstein to Fermi-Dirac. We replace the traditional heating and cooling strokes of a quantum Otto cycle by tuning the gas between a Bose- Einstein condensate of bosonic molecules and a unitary Fermi gas (and back) through a magnetic field. The quantum nature of such a Pauli engine is revealed by contrasting it to a classical thermal engine and to a purely interaction-driven device. We obtain a work output of several $10^6$ vibrational quanta per cycle with an efficiency of up to $25\%$. Our findings establish quantum statistics as a useful thermodynamic resource for work production, shifting the paradigm of energy-conversion devices to a new class of emergent quantum engines. △ Less

Submitted 28 September, 2022; originally announced September 2022.

Comments: 13 pages, 10 figures

Journal ref: Nature 621, 723 (2023)

Quantum control and quantum speed limits in supersymmetric potentials

Authors: Christopher Campbell, Jing Li, Thomas Busch, Thomás Fogarty

Abstract: Supersymmetry allows one to build a hierarchy of Hamiltonians that share the same spectral properties and which are pairwise connected through common superpotentials. The iso-spectral properties of these Hamiltonians imply that the dynamics and therefore control of different eigenstates are connected through supersymmetric intertwining relations. In this work we explore how this enables one to stu… ▽ More Supersymmetry allows one to build a hierarchy of Hamiltonians that share the same spectral properties and which are pairwise connected through common superpotentials. The iso-spectral properties of these Hamiltonians imply that the dynamics and therefore control of different eigenstates are connected through supersymmetric intertwining relations. In this work we explore how this enables one to study general dynamics, shortcuts to adiabaticity (STA) and quantum speed limits for distinct states of different supersymmetric partner potentials by using the infinite box as an example. △ Less

Submitted 26 June, 2022; originally announced June 2022.

Comments: 13 pages, 3 figures

Detection of roton and phonon excitations in a spin-orbit coupled Bose-Einstein condensate with a moving barrier

Authors: Hao Lyu, Yongping Zhang, Thomas Busch

Abstract: We propose to detect phonon and roton excitations in a two-dimensional Bose-Einstein condensate with Raman-induced spin-orbit coupling by perturbing the atomic cloud with a weak barrier. The two excitation modes can be observed by moving the barrier along different directions in appropriate parameter regimes. Phonon excitations are identified by the appearance of solitary waves, while roton excita… ▽ More We propose to detect phonon and roton excitations in a two-dimensional Bose-Einstein condensate with Raman-induced spin-orbit coupling by perturbing the atomic cloud with a weak barrier. The two excitation modes can be observed by moving the barrier along different directions in appropriate parameter regimes. Phonon excitations are identified by the appearance of solitary waves, while roton excitations lead to distinctive spatial density modulations. We show that this method can also be used to determine the anisotropic critical velocities of superfluid. △ Less

Submitted 5 July, 2022; v1 submitted 20 April, 2022; originally announced April 2022.

Comments: 7 pages, 5 figures

Journal ref: Phys. Rev A 106, 013302 (2022)

Few-body Bose gases in low dimensions -- a laboratory for quantum dynamics

Authors: S. I. Mistakidis, A. G. Volosniev, R. E. Barfknecht, T. Fogarty, Th. Busch, A. Foerster, P. Schmelcher, N. T. Zinner

Abstract: Cold atomic gases have become a paradigmatic system for exploring fundamental physics, which at the same time allows for applications in quantum technologies. The accelerating developments in the field have led to a highly advanced set of engineering techniques that, for example, can tune interactions, shape the external geometry, select among a large set of atomic species with different propertie… ▽ More Cold atomic gases have become a paradigmatic system for exploring fundamental physics, which at the same time allows for applications in quantum technologies. The accelerating developments in the field have led to a highly advanced set of engineering techniques that, for example, can tune interactions, shape the external geometry, select among a large set of atomic species with different properties, or control the number of atoms. In particular, it is possible to operate in lower dimensions and drive atomic systems into the strongly correlated regime. In this review, we discuss recent advances in few-body cold atom systems confined in low dimensions from a theoretical viewpoint. We mainly focus on bosonic systems in one dimension and provide an introduction to the static properties before we review the state-of-the-art research into quantum dynamical processes stimulated by the presence of correlations. Besides discussing the fundamental physical phenomena arising in these systems, we also provide an overview of the calculational and numerical tools and methods that are commonly used, thus delivering a balanced and comprehensive overview of the field. We conclude by giving an outlook on possible future directions that are interesting to explore in these correlated systems. △ Less

Submitted 2 November, 2023; v1 submitted 22 February, 2022; originally announced February 2022.

Comments: 175 pages, 49 figures

Journal ref: Physics Reports 1042, 1 (2023)

Bloch oscillations in supersolids

Authors: Muhammad S. Hasan, J. Polo, J. C. Pelayo, Th. Busch

Abstract: We show that the motion of an accelerated atomic impurity immersed in a spin-orbit coupled Bose-Einstein condensate in the supersolid stripe phase undergoes oscillations, similar to the well-known phenomenon of Bloch oscillations in solids. While the back-action of the oscillatory movement onto the condensate excites phonon modes inside the supersolid, it does not affect the position of the roton… ▽ More We show that the motion of an accelerated atomic impurity immersed in a spin-orbit coupled Bose-Einstein condensate in the supersolid stripe phase undergoes oscillations, similar to the well-known phenomenon of Bloch oscillations in solids. While the back-action of the oscillatory movement onto the condensate excites phonon modes inside the supersolid, it does not affect the position of the roton minimum and therefore not the periodicity of the matter wave lattice. The ultimate decay of the oscillations is mostly due to the dispersion of the wavepacket and we show that this can be counteracted to a large extent by assuming that the impurity is a bright soliton. △ Less

Submitted 21 April, 2022; v1 submitted 1 December, 2021; originally announced December 2021.

Comments: 10 pages, 5 figures

Self-Pinning Transition of a Tonks-Girardeau Gas in a Bose-Einstein Condensate

Authors: Tim Keller, Thomás Fogarty, Thomas Busch

Abstract: We show that a Tonks-Girardeau (TG) gas that is immersed in a Bose-Einstein condensate can undergo a transition to a crystal-like Mott state with regular spacing between the atoms without any externally imposed lattice potential. We characterize this phase transition as a function of the interspecies interaction and temperature of the TG gas, and show how it can be measured via accessible observab… ▽ More We show that a Tonks-Girardeau (TG) gas that is immersed in a Bose-Einstein condensate can undergo a transition to a crystal-like Mott state with regular spacing between the atoms without any externally imposed lattice potential. We characterize this phase transition as a function of the interspecies interaction and temperature of the TG gas, and show how it can be measured via accessible observables in cold atom experiments. We also develop an effective model that accurately describes the system in the pinned insulator state and which allows us to derive the critical temperature of the transition. △ Less

Submitted 1 February, 2022; v1 submitted 2 September, 2021; originally announced September 2021.

Comments: 5 pages, 3 figures; 5 supplementary pages, 3 supplementary figures

Journal ref: Phys. Rev. Lett. 128, 053401 (2022)

Deep learning based quantum vortex detection in atomic Bose-Einstein condensates

Authors: Friederike Metz, Juan Polo, Natalya Weber, Thomas Busch

Abstract: Quantum vortices naturally emerge in rotating Bose-Einstein condensates (BECs) and, similarly to their classical counterparts, allow the study of a range of interesting out-of-equilibrium phenomena like turbulence and chaos. However, the study of such phenomena requires to determine the precise location of each vortex within a BEC, which becomes challenging when either only the condensate density… ▽ More Quantum vortices naturally emerge in rotating Bose-Einstein condensates (BECs) and, similarly to their classical counterparts, allow the study of a range of interesting out-of-equilibrium phenomena like turbulence and chaos. However, the study of such phenomena requires to determine the precise location of each vortex within a BEC, which becomes challenging when either only the condensate density is available or sources of noise are present, as is typically the case in experimental settings. Here, we introduce a machine learning based vortex detector motivated by state-of-the-art object detection methods that can accurately locate vortices in simulated BEC density images. Our model allows for robust and real-time detection in noisy and non-equilibrium configurations. Furthermore, the network can distinguish between vortices and anti-vortices if the condensate phase profile is also available. We anticipate that our vortex detector will be advantageous both for experimental and theoretical studies of the static and dynamical properties of vortex configurations in BECs. △ Less

Submitted 13 April, 2021; v1 submitted 23 December, 2020; originally announced December 2020.

Comments: 13+8 pages, 5+4 figures

Journal ref: Mach. Learn.: Sci. Technol. 2 035019 (2021)

Connecting scrambling and work statistics for short-range interactions in the harmonic oscillator

Authors: Mathias Mikkelsen, Thomás Fogarty, Thomas Busch

Abstract: We investigate the relationship between information scrambling and work statistics after a quench for the paradigmatic example of short-range interacting particles in a one-dimensional harmonic trap, considering up to five particles numerically. In particular, we find that scrambling requires finite interactions, in the presence of which the long-time average of the squared commutator for the indi… ▽ More We investigate the relationship between information scrambling and work statistics after a quench for the paradigmatic example of short-range interacting particles in a one-dimensional harmonic trap, considering up to five particles numerically. In particular, we find that scrambling requires finite interactions, in the presence of which the long-time average of the squared commutator for the individual canonical operators is directly proportional to the variance of the work probability distribution. In addition to the numerical results, we outline the mathematical structure of the N-body system which leads to this outcome. We thereby establish a connection between the scrambling properties and the induced work fluctuations, with the latter being an experimental observable that is directly accessible in modern cold atom experiments. △ Less

Submitted 20 February, 2022; v1 submitted 30 September, 2020; originally announced September 2020.

Comments: 6 pages, 2 figures (Supplemental Material: 7 pages, 2 figures). Minor revisions, corresponding to the published version, including an updated abstract

Journal ref: Physical Review Letters 128, 070605 (2022)

Cavity-enhanced magnetometer with a spinor Bose-Einstein condensate

Authors: Karol Gietka, Farokh Mivehvar, Thomas Busch

Abstract: We propose a novel type of composite light-matter magnetometer based on a transversely driven multi-component Bose-Einstein condensate coupled to two distinct electromagnetic modes of a linear cavity. Above the critical pump strength, the change of the population imbalance of the condensate caused by an external magnetic field entails the change of relative photon number of the two cavity modes. M… ▽ More We propose a novel type of composite light-matter magnetometer based on a transversely driven multi-component Bose-Einstein condensate coupled to two distinct electromagnetic modes of a linear cavity. Above the critical pump strength, the change of the population imbalance of the condensate caused by an external magnetic field entails the change of relative photon number of the two cavity modes. Monitoring the cavity output fields thus allows for nondestructive measurement of the magnetic field in real time. We show that the sensitivity of the proposed magnetometer exhibits Heisenberg-like scaling with respect to the atom number. For state-of-the-art experimental parameters, we calculate the lower bound on the sensitivity of such a magnetometer to be of the order of fT/$\sqrt{\mathrm{Hz}}$--pT/$\sqrt{\mathrm{Hz}}$ for a condensate of $10^4$ atoms with coherence times of the order of several ms. △ Less

Submitted 6 April, 2021; v1 submitted 17 August, 2020; originally announced August 2020.

Comments: 18 pages, 3 figures

Symmetry breaking in binary Bose-Einstein condensates in the presence of an inhomogeneous artificial gauge field

Authors: S. Sahar S. Hejazi, Juan Polo, Rashi Sachdeva, Thomas Busch

Abstract: We study a two component Bose-Einstein condensate in the presence of an inhomogeneous artificial gauge field. In response to this field, the condensate forms a localised vortex lattice structure that leads to a non-trivial symmetry breaking in the phase separated regime. The underlying physical mechanism can be understood by considering the energy landscape and we present a simplified model that i… ▽ More We study a two component Bose-Einstein condensate in the presence of an inhomogeneous artificial gauge field. In response to this field, the condensate forms a localised vortex lattice structure that leads to a non-trivial symmetry breaking in the phase separated regime. The underlying physical mechanism can be understood by considering the energy landscape and we present a simplified model that is capable of reproducing the main features of the phase separation transition. The intuition gained by numerically solving this simplified model is then corroborated using the analytical Thomas-Fermi model. △ Less

Submitted 5 August, 2020; originally announced August 2020.

Journal ref: Phys. Rev. A 102, 053309 (2020)

A many-body heat engine at criticality

Authors: Thomás Fogarty, Thomas Busch

Abstract: We show that a quantum Otto cycle in which the medium, an interacting ultracold gas, is driven between a superfluid and an insulating phase can outperform similar single particle cycles. The presence of an energy gap between the two phases can be used to improve performance, while the interplay between lattice forces and the particle distribution can lead to a many-body cooperative effect. Since f… ▽ More We show that a quantum Otto cycle in which the medium, an interacting ultracold gas, is driven between a superfluid and an insulating phase can outperform similar single particle cycles. The presence of an energy gap between the two phases can be used to improve performance, while the interplay between lattice forces and the particle distribution can lead to a many-body cooperative effect. Since finite time driving of this cycle can create unwanted non-equilibrium dynamics which can significantly impair the performance of the engine cycle, we also design an approximate shortcut to adiabaticity for the many-body state that can be used to achieve an efficient Otto cycle around a critical point. △ Less

Submitted 30 November, 2020; v1 submitted 1 June, 2020; originally announced June 2020.

Comments: Includes Supplementary Materials

Journal ref: Quantum Sci. Technol. 6 015003 (2020)

In situ thermometry of a cold Fermi gas via dephasing impurities

Authors: Mark T. Mitchison, Thomàs Fogarty, Giacomo Guarnieri, Steve Campbell, Thomas Busch, John Goold

Abstract: The precise measurement of low temperatures is a challenging, important and fundamental task for quantum science. In particular, in-situ thermometry is highly desirable for cold atomic systems due to their potential for quantum simulation. Here we demonstrate that the temperature of a non-interacting Fermi gas can be accurately inferred from the non-equilibrium dynamics of impurities immersed with… ▽ More The precise measurement of low temperatures is a challenging, important and fundamental task for quantum science. In particular, in-situ thermometry is highly desirable for cold atomic systems due to their potential for quantum simulation. Here we demonstrate that the temperature of a non-interacting Fermi gas can be accurately inferred from the non-equilibrium dynamics of impurities immersed within it, using an interferometric protocol and established experimental methods. Adopting tools from the theory of quantum parameter estimation, we show that our proposed scheme achieves optimal precision in the relevant temperature regime for degenerate Fermi gases in current experiments. We also discover an intriguing trade-off between measurement time and thermometric precision that is controlled by the impurity-gas coupling, with weak coupling leading to the greatest sensitivities. This is explained as a consequence of the slow decoherence associated with the onset of the Anderson orthogonality catastrophe, which dominates the gas dynamics following its local interaction with the immersed impurity. △ Less

Submitted 19 August, 2020; v1 submitted 6 April, 2020; originally announced April 2020.

Comments: 6+5 pages, 4+4 figures. Final author version

Journal ref: Phys. Rev. Lett. 125, 080402 (2020)

Pump Probe Spectroscopy of Bose Polarons: Dynamical Formation and Coherence

Authors: S. I. Mistakidis, G. C. Katsimiga, G. M. Koutentakis, Th. Busch, P. Schmelcher

Abstract: We propose and investigate a pump-probe spectroscopy scheme to unveil the time-resolved dynamics of fermionic or bosonic impurities immersed in a harmonically trapped Bose-Einstein condensate. In this scheme a pump pulse initially transfers the impurities from a noninteracting to a resonantly interacting spin-state and, after a finite time in which the system evolves freely, the probe pulse revers… ▽ More We propose and investigate a pump-probe spectroscopy scheme to unveil the time-resolved dynamics of fermionic or bosonic impurities immersed in a harmonically trapped Bose-Einstein condensate. In this scheme a pump pulse initially transfers the impurities from a noninteracting to a resonantly interacting spin-state and, after a finite time in which the system evolves freely, the probe pulse reverses this transition. This directly allows to monitor the nonequilibrium dynamics of the impurities as the dynamical formation of coherent attractive or repulsive Bose polarons and signatures of their induced-interactions are imprinted in the probe spectra. We show that for interspecies repulsions exceeding the intraspecies ones a temporal orthogonality catastrophe occurs, followed by enhanced energy redistribution processes, independently of the impurity's flavor. This phenomenon takes place over the characteristic trap timescales. For much longer timescales a steady state is reached characterized by substantial losses of coherence of the impurities. This steady state is related to eigenstate thermalization and it is demonstrated to be independent of the system's characteristics. △ Less

Submitted 4 August, 2020; v1 submitted 1 January, 2020; originally announced January 2020.

Comments: 17 pages, 8 figures

Journal ref: Phys. Rev. Research 2, 033380 (2020)

Many-body quantum dynamics and induced correlations of Bose polarons

Authors: S. I. Mistakidis, G. M. Koutentakis, G. C. Katsimiga, Th. Busch, P. Schmelcher

Abstract: We study the ground state properties and nonequilibrium dynamics of two spinor bosonic impurities immersed in a one-dimensional bosonic gas upon applying an interspecies interaction quench. For the ground state of two non-interacting impurities we reveal signatures of attractive induced interactions in both cases of attractive or repulsive interspecies interactions, while a weak impurity-impurity… ▽ More We study the ground state properties and nonequilibrium dynamics of two spinor bosonic impurities immersed in a one-dimensional bosonic gas upon applying an interspecies interaction quench. For the ground state of two non-interacting impurities we reveal signatures of attractive induced interactions in both cases of attractive or repulsive interspecies interactions, while a weak impurity-impurity repulsion forces the impurities to stay apart. Turning to the quench dynamics we inspect the time-evolution of the contrast unveiling the existence, dynamical deformation and the orthogonality catastrophe of Bose polarons. We find that for an increasing postquench repulsion the impurities reside in a superposition of two distinct two-body configurations while at strong repulsions their corresponding two-body correlation patterns show a spatially delocalized behavior evincing the involvement of higher excited states. For attractive interspecies couplings, the impurities exhibit a tendency to localize at the origin and remarkably for strong attractions they experience a mutual attraction on the two-body level that is imprinted as a density hump on the bosonic bath. △ Less

Submitted 24 April, 2020; v1 submitted 5 November, 2019; originally announced November 2019.

Comments: 25 pages, 12 figures

Orthogonality Catastrophe as a Consequence of the Quantum Speed Limit

Authors: Thomás Fogarty, Sebastian Deffner, Thomas Busch, Steve Campbell

Abstract: A remarkable feature of quantum many-body systems is the orthogonality catastrophe which describes their extensively growing sensitivity to local perturbations and plays an important role in condensed matter physics. Here we show that the dynamics of the orthogonality catastrophe can be fully characterized by the quantum speed limit and, more specifically, that any quenched quantum many-body syste… ▽ More A remarkable feature of quantum many-body systems is the orthogonality catastrophe which describes their extensively growing sensitivity to local perturbations and plays an important role in condensed matter physics. Here we show that the dynamics of the orthogonality catastrophe can be fully characterized by the quantum speed limit and, more specifically, that any quenched quantum many-body system whose variance in ground state energy scales with the system size exhibits the orthogonality catastrophe. Our rigorous findings are demonstrated by two paradigmatic classes of many-body systems -- the trapped Fermi gas and the long-range interacting Lipkin-Meshkov-Glick spin model. △ Less

Submitted 16 March, 2020; v1 submitted 23 October, 2019; originally announced October 2019.

Comments: 4.5+1 pages. 3+1 figures. Close to published version

Journal ref: Phys. Rev. Lett. 124, 110601 (2020)

Effects of coherence on quantum speed limits and shortcuts to adiabaticity in many-particle systems

Authors: Tian-Niu Xu, Jing Li, Thomas Busch, Xi Chen, Thomás Fogarty

Abstract: We discuss the effects of many-body coherence on the speed of evolution of ultracold atomic gases and the relation to quantum speed limits. Our approach is focused on two related systems, spinless fermions and the bosonic Tonks-Girardeau gas, which possess equivalent density dynamics but very different coherence properties. To illustrate the effect of the coherence on the dynamics we consider sque… ▽ More We discuss the effects of many-body coherence on the speed of evolution of ultracold atomic gases and the relation to quantum speed limits. Our approach is focused on two related systems, spinless fermions and the bosonic Tonks-Girardeau gas, which possess equivalent density dynamics but very different coherence properties. To illustrate the effect of the coherence on the dynamics we consider squeezing an anharmonic potential which confines the particles and find that the speed of the evolution exhibits subtle, but fundamental differences between the two systems. Furthermore, we explore the difference in the driven dynamics by implementing a shortcut to adiabaticity designed to reduce spurious excitations. We show that collisions between the strongly interacting bosons can lead to changes in the coherence which results in different evolution speeds and therefore different fidelities of the final states. △ Less

Submitted 8 April, 2020; v1 submitted 15 October, 2019; originally announced October 2019.

Comments: 12 pages, 8 figures

Report number: 2, 023125 (2020)

Journal ref: Physical Review RESEARCH (2020)

Spin-orbit coupling in the presence of strong atomic correlations

Authors: Ayaka Usui, Thomás Fogarty, Steve Campbell, Simon A. Gardiner, Thomas Busch

Abstract: We explore the influence of contact interactions on a synthetically spin-orbit coupled system of two ultracold trapped atoms. Even though the system we consider is bosonic, we show that a regime exists in which the competition between the contact and spin-orbit interactions results in the emergence of a ground state that contains a significant contribution from the anti-symmetric spin state. This… ▽ More We explore the influence of contact interactions on a synthetically spin-orbit coupled system of two ultracold trapped atoms. Even though the system we consider is bosonic, we show that a regime exists in which the competition between the contact and spin-orbit interactions results in the emergence of a ground state that contains a significant contribution from the anti-symmetric spin state. This ground state is unique to few-particle systems and does not exist in the mean-field regime. The transition to this state is signalled by an inversion in the average momentum from being dominated by centre-of-mass momentum to relative momentum and also affects the global entanglement shared between the real- and pseudo-spin spaces. Indeed, competition between the interactions can also result in avoided crossings in the groundstate which further enhances these correlations. However, we find that correlations shared between the pseudo-spin states are strongly depressed due to the spin-orbit coupling and therefore the system does not contain spin-spin entanglement. △ Less

Submitted 31 January, 2020; v1 submitted 6 October, 2019; originally announced October 2019.

Comments: 21 pages, 9 figures

Journal ref: New J. Phys. 22 013050 (2020)

Controlled creation of three-dimensional vortex structures in Bose--Einstein condensates using artificial magnetic fields

Authors: James Schloss, Peter Barnett, Rashi Sachdeva, Thomas Busch

Abstract: The physics of quantized vortex excitations in atomic Bose-Einstein condensates has been extensively studied in recent years.Although simple vortex lines are relatively easy to create, control, and measure in experiments, it is a lot more difficult to do the same for vortex ring structures.Here we suggest and explore a method for generating and controlling superfluid vortex rings, vortex ring latt… ▽ More The physics of quantized vortex excitations in atomic Bose-Einstein condensates has been extensively studied in recent years.Although simple vortex lines are relatively easy to create, control, and measure in experiments, it is a lot more difficult to do the same for vortex ring structures.Here we suggest and explore a method for generating and controlling superfluid vortex rings, vortex ring lattices, and other three dimensional vortex structures in toroidally-trapped superfluid Bose--Einstein condensates by using the artificial magnetic field produced by an optical nanofiber.The presence of the fiber also necessitates a multiply-connected geometry and we show that in this situation the presence of these vortex structures can be deduced from exciting the scissors mode of the condensate. △ Less

Submitted 6 October, 2019; originally announced October 2019.

Comments: 8 pages, 6 figures

Journal ref: Phys. Rev. A 102, 043325 (2020)

Driving interactions efficiently in a composite few-body system

Authors: Alan Kahan, Thomás Fogarty, Jing Li, Thomas Busch

Abstract: We study how to efficiently control an interacting few-body system consisting of three harmonically trapped bosons. Specifically we investigate the process of modulating the interparticle interactions to drive an initially non-interacting state to a strongly interacting one, which is an eigenstate of a chosen Hamiltonian. We also show that for unbalanced subsystems, where one can individually cont… ▽ More We study how to efficiently control an interacting few-body system consisting of three harmonically trapped bosons. Specifically we investigate the process of modulating the interparticle interactions to drive an initially non-interacting state to a strongly interacting one, which is an eigenstate of a chosen Hamiltonian. We also show that for unbalanced subsystems, where one can individually control the different inter- and intra-species interactions, complex dynamics originates when the symmetry of the ground state is broken by phase separation. However, as driving the dynamics too quickly can result in unwanted excitations of the final state, we optimize the driven processes using shortcuts to adiabaticity, which are designed to reduce these excitations at the end of the interaction ramp ensuring that the target eigenstate is reached. △ Less

Submitted 30 August, 2019; originally announced August 2019.

Comments: 17 pages, 11 figures