Fig. 1: | Communications Physics

Fig. 1

From: Dynamical equilibration across a quenched phase transition in a trapped quantum gas

Fig. 1

Simulation of quench-induced dynamical equilibration. a Quench protocol: starting from a purely thermal state, with a given atom number, we linearly quench temperature to lower values and chemical potential to positive values over a ramp duration τR to mimic experimental conditions. b Dynamical response of an equilibrium thermal gas subjected to different cooling quench rates (τR = 1440, 144, 18 ms, from top to bottom), demonstrating the equilibration route towards a finite temperature phase-coherent condensate. The characteristic regions depicted here refer to density isosurfaces of the highest-populated mode, chosen such that n(t)/n(t → ∞) = 0.1% (yellow), or 3% (green), where n(t → ∞) describes the final equilibrated peak condensate density for N = 6.6 × 106 atoms. Different rows correspond to different durations of the constant applied external cooling ramps, from the very slow, quasi-adiabatic (top) to the very fast, nearly instantaneous ones (bottom), with the intermediate case representing typical quenches used in experimental studies of phase transitions. For rather slow ramps, most condensate formation happens during the external cooling. For shorter quench duration, the condensate appears around the end of the ramp, and there is a small number of spontaneously generated defects (vortex filaments), depicted in purple. In a fast quench, most condensate growth dynamics occurs after the end of the ramp, with the system at the end of the ramp being in a highly non-equilibrium state exhibiting large occupation of a handful of modes, and consisting of a dense random vortex tangle. Such a tangle unravels in time into a phase-fluctuating condensate, or quasi-condensate, with numerous well-formed interacting filaments, whose presence perturbs the phase and opposes the formation of long-range coherence; after further evolution, at most few long-living vortices may survive, and they are experimentally observed after expansion