# Universal dynamics of zero-momentum to plane-wave transition in spin-orbit coupled Bose-Einstein condensates

## TL;DR

This paper studies the universal dynamics during the phase transition in spin-orbit coupled Bose-Einstein condensates, revealing critical exponents and domain formation consistent with the Kibble-Zurek mechanism.

## Contribution

It provides a numerical and analytical analysis of the critical exponents and domain formation during the phase transition in spin-orbit coupled BECs.

## Key findings

- Critical velocity vanishes at the transition point.
- Correlation length diverges at the critical point.
- Numerical critical exponents match analytical predictions.

## Abstract

We investigate the universal spatiotemporal dynamics in spin-orbit coupled Bose-Einstein condensates which are driven from the zero-momentum phase to the plane-wave phase. The excitation spectrum reveals that, at the critical point, the Landau critical velocity vanishes and the correlation length diverges. Therefore, according to the Kibble-Zurek mechanism, spatial domains will spontaneously appear in such a quench through the critical point. By simulating the real-time dynamics, we numerically extract the static correlation length critical exponent v and the dynamic critical exponent z from the scalings of the temporal bifurcation delay and the spatial domain number. The numerical scalings consist well with the analytical ones obtained by analyzing the excitation spectrum.