Box traps on an atom chip for one-dimensional quantum gases

Es, J.J.P. van; Wicke, P.; Amerongen, Aaldert H. van; Rétif, C.; Whitlock, S.; Druten, N. J. van

doi:10.1088/0953-4075/43/15/155002

Cited by 47 publications

(48 citation statements)

References 48 publications

(109 reference statements)

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“…As a proof of principle we computed the time evolution in the Lieb-Liniger model of the static density moment g 2 (x = 0, t) after a quench from the Bose-Einstein condensate. This represents a rare example of a full postquench time evolution of a truly interacting model and therefore it can be directly connected to experimental results in ring-like geometries [72], box-like potentials [73] or any other experimental realization of the onedimensional Bose gas where the confining trap influences time scales which are much larger than the relaxation time of one-point functions as g 2 (x = 0, t) [9,12]. The comparison between the finite size calculations and the thermodynamic limit in figure 1 shows indeed that for short times the relaxation processes are well approximated by N ∼ 10 particles.…”

mentioning

confidence: 75%

Relaxation dynamics of local observables in integrable systems

Nardis¹,

Piroli²,

Caux³

2015

J. Phys. A: Math. Theor.

113

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We show, using the quench action approach [1], that the whole post-quench time evolution of an integrable system in the thermodynamic limit can be computed with a minimal set of data which are encoded in what we denote the generalized single-particle overlap coefficient s Ψ 0 0 (λ). This function can be extracted from the thermodynamically leading part of the overlaps between the eigenstates of the model and the initial state. For a generic global quench the shape of s Ψ 0 0 (λ) in the low momentum limit directly gives the exponent for the power law decay to the effective steady state. As an example we compute the time evolution of the static density-density correlation in the interacting Lieb-Liniger gas after a quench from a Bose-Einstein condensate. This shows an approach to equilibrium with power law t −3 which turns out to be independent of the post-quench interaction and of the considered observable. Introduction. Understanding the non-equilibrium time evolution of a many-body interacting system is one of the main challenges in contemporary physics [2,3]. The study of systems with nontrivial interactions among their constituents is hard enough when the system is in its ground state; things however get even more complicated out of equilibrium, since most of the usual theoretical tools then become inapplicable. This is mainly due to the high energy regions of the spectrum which are probed by the time evolution, where the mean field approach and low energy approximations are not valid. Numerical simulations on the other hand are severely limited in the range of time or of system sizes [4]. Developing new methods able to predict the short-, intermediate-and long-time dynamics of an out-of-equilibrium system is thus an urgent priority, especially in view of the rapid progress achieved in experiments on ultracold atoms [5][6][7][8][9][10][11][12].Since the beginnings of quantum mechanics [13], much interest has been devoted to the fundamental problem of calculating the time dependence of physical observables in states which are not eigenstates of the Hamiltonian driving the time evolution. This situation has now come to be known as a quantum quench [2,14] and has been of major interest both from experimental and theoretical points of view. Most of the theoretical research focused so far on the expectation values of local observables at late times after the quench, when the system is in an effective steady state. In particular the Generalized Gibbs Ensemble (GGE) hypothesis [15,16] focuses on the possibility of reducing the huge complexity of the initial wave function to a reduced set of information, incorporated in the local conserved quantities of the system, which gives the expectation values of all physical observables in the steady state. However the question of how to perform an analogous simplification for the whole post-quench

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mentioning

confidence: 75%

Relaxation dynamics of local observables in integrable systems

Nardis¹,

Piroli²,

Caux³

2015

J. Phys. A: Math. Theor.

113

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“…This allows us in particular to access the physical properties of the nonthermal steady state at long times after the quench and is an example of a quench to a truly interacting system for which exact results are obtained in the thermodynamic limit. Our results would be applicable to experiments in ringlike geometries [14] or boxlike potentials [13]. The overall method we use, being quite generic, forms a blueprint for potentially treating many other quench situations.…”

Section: Introductionmentioning

confidence: 95%

“…Besides being of experimental interest [13][14][15], this case, surprisingly, cannot be treated theoretically using the standard GGE, due to creeping infinities in the expectation values of the conserved charges [12].…”

Section: Introductionmentioning

confidence: 99%

Solution for an interaction quench in the Lieb-Liniger Bose gas

et al. 2014

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Solution for an interaction quench in the Lieb-Liniger Bose gasDe Nardis, J.; Wouters, B.M.; Brockmann, M.; Caux, J.S. General rightsIt is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an open content license (like Creative Commons). Disclaimer/Complaints regulationsIf you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library: http://uba.uva.nl/en/contact, or a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible. We study a quench protocol where the ground state of a free many-particle bosonic theory in one dimension is let unitarily evolve in time under the integrable Lieb-Liniger Hamiltonian of δ-interacting repulsive bosons. By using a recently proposed variational method, we here obtain the exact nonthermal steady state of the system in the thermodynamic limit and discuss some of its main physical properties. Besides being a rare case of a thermodynamically exact solution to a truly interacting quench situation, this interestingly represents an example where a standard implementation of the generalized Gibbs ensemble fails.

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“…Although even box shaped potentials seem experimentally feasible [8][9][10], our observations should not qualitatively depend on the specific form of the trapping geometry. Hence, an experimental investigation of the few-body decay is realizable with state-of-the-art technologies.…”

Section: Summary and Discussionmentioning

confidence: 66%

Tunneling decay of two interacting bosons in an asymmetric double-well potential: A spectral approach

et al. 2013

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We study the full-fledged microscopic dynamics of two interacting, ultracold bosons in a onedimensional double-well potential, through the numerically exact diagonalization of the many-body Hamiltonian. With the particles initially prepared in the left well, we increase the width of the right well in subsequent trap realizations and witness how the tunneling oscillations evolve into particle loss. In this closed system, we analyze the spectral signatures of single-and two-particle tunneling for the entire range of repulsive interactions. We conclude that for comparable widths of the two wells, pair-wise tunneling of the bosons may be realized for specific system parameters. In contrast, the decay process (corresponding to a broad right well) is dominated by uncorrelated single-particle decay.

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Box traps on an atom chip for one-dimensional quantum gases

Cited by 47 publications

References 48 publications

Relaxation dynamics of local observables in integrable systems

Relaxation dynamics of local observables in integrable systems

Solution for an interaction quench in the Lieb-Liniger Bose gas

Tunneling decay of two interacting bosons in an asymmetric double-well potential: A spectral approach

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