Phase separation and pattern formation in a binary Bose-Einstein condensate

TL;DR

This paper proposes a novel method using coupling-induced pattern formation in binary Bose-Einstein condensates to experimentally test the Kibble-Zurek mechanism of topological defect formation during quantum phase transitions.

Contribution

It introduces a new scheme for testing the Kibble-Zurek mechanism via pattern formation in BECs, including analysis of different trap geometries and verification through simulations.

Findings

Pattern formation scales with quench rate as predicted by KZM in ring traps.

Different scaling laws are observed in elongated harmonic traps.

Simulation confirms the predicted scaling exponent.

Abstract

The miscibility-immiscibility phase transition in binary Bose-Einstein condensates (BECs) can be controlled by a coupling between the two components. Here we propose a new scheme that uses coupling-induced pattern formation to test the Kibble-Zurek mechanism (KZM) of topological-defect formation in a quantum phase transition. For a binary BEC in a ring trap we find that the number of domains forming the pattern scales with the coupling quench rate with an exponent as predicted by the KZM. For a binary BEC in an elongated harmonic trap we find a different scaling law due to the transition being spatially inhomogeneous. We perform a "simulation" of the harmonically trapped system in a ring trap to verify the scaling exponent.