Behaviour of the energy gap in a model of Josephson coupled Bose–Einstein condensates

Abstract

In this work we investigate the energy gap between the ground state and the first excited state in a model of two single-mode Bose-Einstein condensates coupled via Josephson tunneling. The energy gap is never zero when the tunneling interaction is non-zero. The gap exhibits no local minimum below a threshold coupling which separates a delocalised phase from a self-trapping phase that occurs in the absence of the external potential. Above this threshold point one minimum occurs close to the Josephson regime, and a set of minima and maxima appear in the Fock regime. Expressions for the position of these minima and maxima are obtained. The connection between these minima and maxima and the dynamics for the expectation value of the relative number of particles is analysed in detail. We find that the dynamics of the system changes as the coupling crosses these points.

Properties of a coupled two-species atom–heteronuclear-molecule condensate

“…2(b). Similar semiclassicalquantum correspondence was observed in two-component condensates [45,46] and condensates in double-well potentials [47,48].…”

“…The basic assumption here is that the spatial wave functions for these modes are fixed so that we can associate each mode with an annihilation operatorâ i of a particle in mode i(= 1, 2 and m). Similar models have been extensively used in the studies of condensates in double-well potentials [34,47,48], coupled atom-molecule condensates [10,11,12,13,14,15,16,17,18,19], as well as spinor condensates [35].…”

Analytical results for Josephson dynamics of ultracold bosons

“…Furthermore, it is stated in [21,25] that the revival time grows linearly with the number of particles N. This is obviously true for those investigations with UN = const only, as can be seen from our expression (40). However, note that even only slightly away from the Rabi limit, when Λ approaches or becomes greater than one, the constants c 1 and c 2 and the parameter g become relevant.…”

Time-dependent semiclassics for ultracold bosons

“…The dynamics of the reduced quantities j and φ have been studied by several groups in this "classical picture" [31,36,37], in particular the differences between the classical and the quantum dynamics [38][39][40]. Though the purely classical description can clearly not describe the mentioned collapses and revivals of the population imbalance, it is able to give some indication of e.g.…”