Fig. 6
From: Dynamical equilibration across a quenched phase transition in a trapped quantum gas
Decoupling of number and coherence growth. a Integrated first-order correlation function, \(g_{\mathrm{1}}^{{\mathrm{int}}}\left( {d_x} \right)\) (defined, at a general time, t, in Methods), for the initial equilibrium thermal state. b Dynamical evolution of \(g_{\mathrm{1}}^{{\mathrm{int}}}\left( {d_x} \right)\) (solid lines/bands) for fast (τR = 84 ms, left), intermediate (τR = 300 ms, middle) and slow (τR = 1440 ms, right) quench rates, depicted in terms of scaled time (t − tbec)/τG. Images also show the corresponding equilibrium values for the same (μ(t), T(t)) combinations (dashed lines). For our chosen parameters, the equilibrium system is already in the phase-coherent condensate regime, for which \(g_{\mathrm{1}}^{{\mathrm{int}}}\left( {d_x} \right)\approx \left( {1 - \left| {d_x} \right|{\mathrm{/}}L} \right)\), for all times t ≳ tbec, with the correlation function for slower ramps approaching the corresponding equilibrium ones faster than for fast ramps. c Growth of the coherence length in time: systems with more than two vortices on average exhibit coherence smaller than the system size, indicating that for the fastest ramps the system is still in the phase-fluctuating regime. d Condensate growth curves collapsing onto a single curve when time from the condensate onset is scaled to the intrinsic system growth timescale τG. Inset shows corresponding ratio, rPO, of most-populated to next-most-populated eigenmode of the one-body density matrix. e Corresponding scaled deviation, δlcoh(t), of dynamical to equilibrium coherence length [based on Eq. (1)]. At t = tbec, the slower ramps (600 ms, 1440 ms) are closer to equilibrium than the faster ones. Slower ramps, scaled to their respective τG, re-equilibrate faster to a phase-coherent BEC (for which δlcoh = 0), with faster ramps only reaching full system coherence asymptotically. Statistical errors are shown by coloured bands in (b) and vertical error bars in (c, e). Horizontal error bars in (c–e) arise from the combination of the uncertainty in identifying tbec and the fitting error for τG
