Open Quantum Dynamics of Mesoscopic Bose-Einstein ... - Physics

2. Properties of an atomic Bose condensate in a double-well potentialFigure 2.15: Condensate fraction versus temperature (scaled by Ω/k B )forN = 400 and differentvalues of the atom-interaction strength. In (a) Θ=0and in (b) Θ = 100.10.8(a)10.8(b)N 0/N0.60.4ExactApproximateN 0/N0.60.40.2T c= 80.60.2T c= 228200 50 100 150Temperature T00 1000 2000 3000 4000Temperature Thigh-temperature tail to the graph, with the critical point corresponding to a condensatefraction of N 0 /N ≃ 0.25. Because the analytic calculation of condensate fraction in Fig.2.14(a) assumes that N 0 /N → 0atT = T c , it makes a poor fit to the exact result for thissmall number of atoms. For very large self-interactions (Figs. 2.14(e&f)), N 0 /N decreasesat a slower rate (when the temperature axis has been scaled by T c ), making the value ofN 0 /N at T c even larger.For the larger condensate (Fig. 2.15), the high temperature tail is smaller, and so theapproximate calculation provides a better fit, except near the critical region. Once again,strong atom interactions decrease the rate at which this tail falls away, perhaps becausethe more strongly interacting atoms have a thermalising effect that aids the growth of thecondensate at higher temperatures. However, we should keep in mind that, for stronglyinteracting atoms, the validity of the Bose-Einstein distribution function (Eq. (2.63)) isnot guaranteed.2.3.3 Coherence properties of the ground stateThe ‘density function’ of the ground state of the condensate affords some insight intofirst-order coherence effects, and is defined in terms of the many-body boson operators asρ(x, t) =〈 ˆψ† (x, t) ˆψ(x, t)〉. (2.70)49