Probing the Excitations of a Lieb-Liniger Gas from Weak to Strong Coupling

Meinert, Florian; Panfil, Miłosz; Mark, Manfred J.; Lauber, Katharina; Caux, Jean-Sébastien; Nägerl, Hanns‐Christoph

doi:10.1103/physrevlett.115.085301

Cited by 132 publications

(163 citation statements)

References 32 publications

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“…In Bragg experiments, the detected Bragg signal is directly proportional to the Fourier transform of the two-point density-density correlation function [321][322][323][324] or dynamical structure factor S q,t,ω = dδdxe i(qx−ωδ) {n(t + δ/2, x), n(t−δ/2, 0)} . In the Luttinger framework in the Keldysh formalism this translates into S q,t,ω = − ρ c (−q, t, −ω)ρ c (q, t, ω) .…”

Section: Observabilitymentioning

confidence: 99%

Keldysh field theory for driven open quantum systems

2016

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Recent experimental developments in diverse areas -ranging from cold atomic gases to light-driven semiconductors to microcavity arrays -move systems into the focus which are located on the interface of quantum optics, many-body physics and statistical mechanics. They share in common that coherent and driven-dissipative quantum dynamics occur on an equal footing, creating genuine non-equilibrium scenarios without immediate counterpart in equilibrium condensed matter physics. This concerns both their non-thermal stationary states, as well as their many-body time evolution. It is a challenge to theory to identify novel instances of universal emergent macroscopic phenomena, which are tied unambiguously and in an observable way to the microscopic drive conditions. In this review, we discuss some recent results in this direction. Moreover, we provide a systematic introduction to the open system Keldysh functional integral approach, which is the proper technical tool to accomplish a merger of quantum optics and many-body physics, and leverages the power of modern quantum field theory to driven open quantum systems. CONTENTS

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Section: Observabilitymentioning

confidence: 99%

Keldysh field theory for driven open quantum systems

2016

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“…(40), yield g 3 (γ) in close agreement with accurate approximate expressions obtained in [23] by fitting on the numerical solution of Eqs. (7), (8), (9) and (40), as illustrated in Appendix C. Having performed all these verifications, we plot in Fig. 3 the coefficient c 4 as a function of γ from numerical calculations and the conjectures on e 2 and e 4 .…”

Section: B Conjecture In the Strongly-interacting Regimementioning

confidence: 99%

“…The one-dimensional Bose gas with contact interactions, known as the Lieb-Liniger model, is the paradigm of such systems [1]. This model well describes experiments with ultracold atoms in tight waveguides and some of its correlation functions have been experimentally probed in all interaction regimes [2][3][4][5][6][7][8][9]. From a theoretical point of view, since the model is integrable, its k-body correlations can in principle be obtained explicitly at all orders k, since they are linked to the (infinite) set of integrals of motion.…”

Section: Introductionmentioning

confidence: 99%

Connection between nonlocal one-body and local three-body correlations of the Lieb-Liniger model

et al. 2017

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We derive a connection between the fourth coefficient of the short-distance Taylor expansion of the one-body correlation function, and the local three-body correlation function of the LiebLiniger model of δ-interacting spinless bosons in one dimension. This connection, valid at arbitrary interaction strength, involves the fourth moment of the density of quasi-momenta. Generalizing recent conjectures, we propose approximate analytical expressions for the fourth coefficient covering the whole range of repulsive interactions, validated by comparison with accurate numerics. In particular, we find that the fourth coefficient changes sign at interaction strength γc 3.816, while the first three coefficients of the Taylor expansion of the one-body correlation function retain the same sign throughout the whole range of interaction strengths.

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“…Experiments with ultracold quantum gases are able to realize effectively one-dimensional systems by tightly confining the gas in two of the three spatial dimensions, either using optical lattice potentials or atom-chip traps [2,39,95,96,179,247,247,248,[276][277][278][279][280][281][282][283][284]. These experiments are now probing the predictions of the Lieb-Liniger model.…”

Section: Introductionmentioning

confidence: 99%

“…Bragg spectroscopy [247,248], and the contributions of the Type II branch to the dynamical structure factor, which does not have a counterpart in higher dimensions, has been revealed by comparing to numerical predictions obtained with algebraic Bethe ansatz based methods.…”

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confidence: 99%

Nonequilibrium dynamics of a one-dimensional Bose gas via the coordinate Bethe ansatz

Zill¹

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This thesis is concerned with non-equilibrium phenomena in interacting quantum manybody systems. Specifically, we investigate the time-evolution and relaxation dynamics of Bose gases in a highly restricted geometry, which constrains the dynamics to one spatial dimension. This leads to a description of the system in terms of a simple model Hamiltonian which permits exact many-body quantum mechanical solutions due to its integrability.In the first part of this thesis, a computational method is developed to obtain experimentally relevant correlation functions in the framework of the coordinate Bethe ansatz.We employ this method to compute exact ground-state correlation functions of the LiebLiniger gas for up to seven particles covering the whole regime of repulsive interactions. We also investigate the dynamics of the system after an instantaneous change of the interaction strength. This quantum quench deposits large amounts of energy that cannot be dissipated due to the system being closed, and so the dynamics far from equilibrium are probed. We prepare the system in two different initial states, and quench to the same final interaction strength. The latter is determined in such a way that the added energy due to the quench is the same for both scenarios. Conventional statistical mechanics predicts the same relaxed state, but due to the integrability of the system all considered correlation functions of the relaxed states differ from each other and also from the thermal ones.We then investigate the dynamics and relaxed state for a quench from zero to repulsive interactions in more detail, focussing on the mechanism of relaxation and the involved time-scales. We find that local correlation functions relax on time-scales determined by the interaction strength, in contrast to non-local correlation functions, whose relaxation time-scale is proportional to the system size.Next, we employ the same methodology to study the one-dimensional Bose gas with attractive interactions. In this case many-body bound states are permissible solutions of the Lieb-Liniger model. We compare exact ground-state correlation functions of up to seven particles to their corresponding mean-field solution. The latter displays a quantum phase transition at a critical interaction strength, marking the transition from a uniformdensity state to a localized bright soliton. Our exact results agree remarkably well with the corresponding mean-field solution past the critical point. We also investigate the dynamics following an interaction strength quench, starting again from the non-interacting ground state. Bound states strongly influence correlation functions for all post-quench interaction strengths, and local correlation functions are largely increased compared to their initial value.In the last part of this thesis, we investigate the behavior of the one-dimensional Bose gas under periodic driving of the interaction strength. To this end, we extend the coordinate Bethe-ansatz formalism by employing Floquet theory to obtain solutions for the...

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Probing the Excitations of a Lieb-Liniger Gas from Weak to Strong Coupling

Cited by 132 publications

References 32 publications

Keldysh field theory for driven open quantum systems

Keldysh field theory for driven open quantum systems

Connection between nonlocal one-body and local three-body correlations of the Lieb-Liniger model

Nonequilibrium dynamics of a one-dimensional Bose gas via the coordinate Bethe ansatz

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