Thermalization in a one-dimensional integrable system

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Abstract

We present numerical results demonstrating the possibility of thermalization of single-particle observables in a one-dimensional integrable system (a quasicondensate of ultra-cold, weakly-interacting bosonic atoms being studied as a definite example). These results may seem counterintuitive because the physical system is integrable in both the quantum and classical (mean-field) descriptions. However, we find a class of initial conditions that admits the relaxation of distributions of single-particle observables to the equilibrium state very close to the Bose-Einstein thermal distribution of Bogoliubov quasiparticles. Our numerical results allow us to explain experimentally observed thermalization in one-dimensional ultracold atomic gases on a short (~1 ms) time scale.

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Relaxation in a Completely Integrable Many-Body Quantum System: An Ab Initio Study of the Dynamics of the Highly Excited States of Lattice Hard-Core Bosons

Marcos Rigol, Vanja Dunjko, Maxim Olshanii … (2006)

In this Letter we pose the question of whether a many-body quantum system with a full set of conserved quantities can relax to an equilibrium state, and, if it can, what the properties of such state are. We confirm the relaxation hypothesis through a thorough ab initio numerical investigation of the dynamics of hard-core bosons on a one-dimensional lattice. Further, a natural extension of the Gibbs ensemble to integrable systems results in a theory that is able to predict the mean values of physical observables after relaxation. Finally, we show that our generalized equilibrium carries more memory of the initial conditions than the usual thermodynamic one. This effect may have many experimental consequences, some of which having already been observed in the recent experiment on the non-equilibrium dynamics of one-dimensional hard-core bosons in a harmonic potential [T. Kinoshita, T. Wenger, D. S. Weiss, Nature (London) 440, 900 (2006)].

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Non-equilibrium coherence dynamics in one-dimensional Bose gases

I Lesanovsky, J. Schmiedmayer, T. Schumm … (2007)

Low-dimensional systems are beautiful examples of many-body quantum physics. For one-dimensional systems the Luttinger liquid approach provides insight into universal properties. Much is known of the equilibrium state, both in the weakly and strongly interacting regime. However, it remains a challenge to probe the dynamics by which this equilibrium state is reached. Here we present a direct experimental study of the coherence dynamics in both isolated and coupled degenerate 1d Bose gases. Dynamic splitting is used to create two 1d systems in a phase coherent state. The time evolution of the coherence is revealed in local phase shifts of the subsequently observed interference patterns. Completely isolated 1d Bose gases are observed to exhibit a universal sub-exponential coherence decay in excellent agreement with recent predictions by Burkov et al. [Phys. Rev. Lett. 98, 200404 (2007)]. For two coupled 1d Bose gases the coherence factor is observed to approach a non-zero equilibrium value as predicted by a Bogoliubov approach. This coupled-system decay to finite coherence is the matter wave equivalent of phase locking two lasers by injection. The non-equilibrium dynamics of superfluids plays an important role in a wide range of physical systems, such as superconductors, quantum-Hall systems, superfluid Helium, and spin systems. Our experiments studying coherence dynamics show that 1d Bose gases are ideally suited for investigating this class of phenomena.

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Probing three-body correlations in a quantum gas using the measurement of the third moment of density fluctuations

Isabelle Bouchoule, Karen V. Kheruntsyan, Thibaut Jacqmin … (2010)

We perform measurements of the third moment of atom number fluctuations in small slices of a very elongated weakly interacting degenerate Bose gas. We find a positive skewness of the atom number distribution in the ideal gas regime and a reduced skewness compatible with zero in the quasi-condensate regime. For our parameters, the third moment is a thermodynamic quantity whose measurement constitutes a sensitive test of the equation of state and our results are in agreement with a modified Yang-Yang thermodynamic prediction. Moreover, we show that the measured skewness reveals the presence of true three body correlations in the system.