Kibble-Zurek dynamics in an array of coupled binary Bose condensates

TL;DR

This paper investigates the universal dynamics of symmetry breaking in coupled binary Bose-Einstein condensates, demonstrating the applicability of the Kibble-Zurek mechanism and extracting critical exponents through numerical and analytical methods.

Contribution

It introduces a novel approach to determine static and dynamic critical exponents in Bose condensates undergoing symmetry breaking.

Findings

Kibble-Zurek scaling laws are confirmed in the system.

Critical exponents ν and z are extracted from bifurcation delay and domain formation.

The method allows simultaneous determination of critical exponents for phase transitions.

Abstract

Universal dynamics of spontaneous symmetry breaking is central to understanding the universal behavior of spontaneous defect formation in various system from the early universe, condensed-matter systems to ultracold atomic systems. We explore the universal real-time dynamics in an array of coupled binary atomic Bose-Einstein condensates in optical lattices, which undergo a spontaneous symmetry breaking from the symmetric Rabi oscillation to the broken-symmetry self-trapping. In addition to Goldstone modes, there exist gapped Higgs mode whose excitation gap vanishes at the critical point. In the slow passage through the critical point, we analytically find that the symmetry-breaking dynamics obeys the Kibble-Zurek mechanism. From the scalings of bifurcation delay and domain formation, we numerically extract two Kibble-Zurek exponents $b_{1}=\nu/(1+\nu z)$ and $b_{2}=1/(1+\nu z)$, which give the static correlation-length critical exponent $\nu$ and the dynamic critical exponent $z$. Our approach provides an efficient way to simultaneous determination of the critical exponents $\nu$ and $z$ for a continuous phase transition.