Reservoir interactions during Bose-Einstein condensation: modified critical scaling in the Kibble-Zurek mechanism of defect formation

TL;DR

This study investigates how energy-damping reservoir interactions influence the critical scaling and defect formation during Bose-Einstein condensation, revealing modifications to the dynamical critical exponent while maintaining core Kibble-Zurek scaling.

Contribution

It demonstrates that energy-damping reservoir interactions modify the dynamical critical exponent in the Kibble-Zurek mechanism during Bose-Einstein condensation.

Findings

Energy damping alters the scaling of winding number distribution.

Energy damping significantly modifies the dynamical critical exponent.

Correlation functions show the impact of energy damping on correlation length.

Abstract

As a test of the Kibble-Zurek mechanism (KZM) of defect formation, we simulate the Bose-Einstein condensation transition in a toroidally confined Bose gas using the stochastic projected Gross-Pitaevskii equation (SPGPE), with and without the energy-damping reservoir interaction. Energy-damping alters the scaling of the winding number distribution with the quench time - a departure from the universal KZM theory that relies on equilibrium critical exponents. Numerical values are obtained for the correlation-length critical exponent $\nu$ and the dynamical critical exponent $z$ for each variant of reservoir interaction theory. The energy-damping reservoir interactions cause significant modification of the dynamical critical exponent of the phase transition, whilst preserving the essential KZM critical scaling behavior. Comparison of numerical and analytical two-point correlation functions further illustrates the effect of energy damping on the correlation length during freeze out.