Abstract
We consider the non-equilibrium dynamics of a weakly interacting Bose gas tightly confined to a highly elongated double well potential. We use a self-consistent time-dependent Hartree--Fock approximation in combination with a projection of the full three-dimensional theory to several coupled one-dimensional channels. This allows us to model the time-dependent splitting and phase imprinting of a gas initially confined to a single quasi one-dimensional potential well and obtain a microscopic description of the ensuing damped Josephson oscillations.
Highlights
Over the last decade and a half quasi-one-dimensional Bose gases have provided a key platform for experimental studies of non-equilibrium evolution in isolated one-dimensional manyparticle quantum systems, see e.g. [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16]
In many works [44,75] it is assumed that the longitudinal expansion has little effect
The 1D boson density develops a central density peak which is underestimated by HF calculations. To make this precise we consider the simpler case of the Lieb–Liniger model in a harmonic trap V (x), where we can compare finite-temperature HF computations to results using Yang–Yang thermodynamics combined with the Local Density Approximation (YY+LDA)
Summary
Over the last decade and a half quasi-one-dimensional Bose gases have provided a key platform for experimental studies of non-equilibrium evolution in isolated one-dimensional manyparticle quantum systems, see e.g. [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16]. Taking into account Gaussian fluctuations on top of the solution of the classical field equations in a self-consistent way produces only very weakly damped Josephson-like oscillations [62,66] Given this state of affairs it is natural to question whether the experiments are in the right regime for a sine-Gordon based description to apply. An obvious question is how good the low-energy projection to two one-dimensional Bose gases is in the experimentally relevant parameter regime Another important issue is that the initial state that is prepared after splitting the gas and imprinting a phase difference is not known, as the splitting process has so far only been modelled in a qualitative phenomenological way [67,68], or via methods that rely on a two-mode approximation [69], a classical field approximation [70] or a restriction to the transverse direction only [69]. Density-phase oscillations are observed to be strongly damped over timescales that are comparable to those seen in the experiment
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