Equilibrating dynamics in quenched Bose gases: Characterizing multiple time regimes

Abstract

We address the physics of equilibration in ultracold atomic gases following a quench of the interaction parameter. Our work is based on a bath model which generates damping of the bosonic excitations. We illustrate this dissipative behavior through the momentum distribution of the excitations, n k , observing that larger k modes have shorter relaxation times τ (k); they will equilibrate faster, as has been claimed in recent experimental work. We identify three time regimes. At short times n k exhibits oscillations; these are damped out at intermediate times where the system appears to be in a false or slowly converging equilibrium. Finally, at longer times, full equilibration occurs. This false-equilibrium is, importantly, associated with the k dependence in τ (k) and has implications for experiment.PACS numbers: 03.75. Kk, 47.37.+q, 43.20.Ks Introduction-Recent interaction quench experiments in cold bosonic gases are providing unique perspectives into the behavior of out-of-equilibrium dynamics of quantum systems [1][2][3][4][5]. These perspectives were hitherto not available in the quantum fluids of condensed matter. The extent to which equilibrium is accessible and the time constants for equilibration are all open questions. Equally of interest is the nature of metastable states, (often) so produced. Considerable theoretical attention has gone into this subject, albeit characterizing the post-quench physics entirely in terms of oscillatory behavior [4,6,7,[9][10][11].How long do these oscillations persist and how does ultimate equilibration proceed for different momentum states is a complicated problem that is the focus of the present paper. Here we discuss the different time scales associated with dissipation and equilibration in the context of the evolution of the momentum distribution n k for a three-dimensional Bose gas. While we use a specific bath model to derive detailed results for n k (t), our central results can almost be anticipated by making use of empirical observations in previous quench experiments [4,5]. As emphasized in both experiments, the equilibration dynamics is rather strongly dependent on the momentum of the state under consideration. An unpublished analysis [12] of the experiments in Ref. 4, led to the conclusion that damping at large momentum had to be included. Also notable is the claim that "it is perhaps not unexpected that higher momenta dynamics saturate faster" [5]. This demonstration that large momentum k, high energy, states equilibrate more rapidly than those at small k is the aim of this paper. It leads to a multistep equilibration process, assuming, as is reasonable, that the condensate also evolves in time as the system re-equilibrates.The important point at issue is that the relaxation times τ (k) disperse with k. At some intermediate time after the quench, there will always be higher energy k states which will be able to follow quasi-adiabatically the (necessarily) slower relaxation of the condensate. But lower energy states, as well as the condensate, will not

Bound-state signatures in quenched Bose-Einstein condensates

“…This 013616-2 equivalence between our variational calculation and the HFB formalism was suggested recently in Ref. [14], Our variational treatment thus suffers from the same low-momentum energy gap as found in the HFB formalism; however, because this unphysical gap should manifest itself at longer time and length scales, this should not hinder our study of short-time, short-distance behavior. This is a motivating reason why the HFB formalism was able to correctly simulate [25] the coherent atom-molecule oscillations observed a decade ago [17], the main results of which can be reproduced by our single-channel variational model [47], Our formalism also reduces to Bogoliubov theory once the usual approximations are made: replace the operators a0 and % by the constant ^/kq, neglect quartic interaction terms of noncondensed particles in Eq.…”

“…(2), as is typically required in mean-field theories at the Bogoliubov level, then we see from Eq. (3) that this implies a momentum cutoff A satisfying Aaf < 1 [41,48], There is no bound state in this limit and any important physics occurring uniquely on the time scale cog' and length scale a/ of the bound state is therefore absent in all variants of Bogoliubov theory [10][11][12]14], When the quench is adiabatic with respect to the bound state (cf. Ref.…”

“…We have been able to analytically evaluate the integrals in Eqs. (14) and (15) for the initial conditions …”

Nonequilibrium states of a quenched Bose gas

“…We note, in passing, that the short-time behavior of the condensate fraction and other higher-order correlation functions in quenched Bose gases have been the focus of several recent studies [44,45,[48][49][50].…”

Stability and anomalous compressibility of Bose gases near resonance: The scale-dependent interactions and thermal effects

“…Since the conventional perturbation theories are no longer valid for these strongly interacting systems, we are confronted with the theoretical challenge of unravelling the puzzle of large-scattering-length physics. Among the various applications of Feshbach resonance, what has attracted particular interest is the atomic Bose gas at large positive scattering lengths, known as the resonant Bose gas on the upper branch of a Feshbach resonance [6][7][8][9][10][11][12][13][14][15][16][17][18].For a dilute Bose gas where the scattering length is small and positive, the dominant contribution to its chemical potential is described by the Hartree-Fock mean-field value, µ HF = 4πan, with n the number density of the particles. The leading order correction to the mean-field result is proportional to a dimensionless parameter √ na 3 , and the dilute limit is hence defined as na 3 ≪ 1.…”