Causality and defect formation in the dynamics of an engineered quantum phase transition in a coupled binary Bose-Einstein condensate

TL;DR

This paper investigates how quantum phase transitions in a binary Bose-Einstein condensate lead to defect formation, confirming Kibble-Zurek predictions and exploring effects of inhomogeneity and causality on defect density.

Contribution

It extends previous studies by analyzing defect formation during engineered quantum phase transitions in BECs, including effects of inhomogeneity and causality on KZ scaling.

Findings

Number of domains scales with quench rate as predicted by KZ theory.

Density inhomogeneity modifies the dynamics and scaling law of defect formation.

Causality influences the propagation of the phase transition front and defect density.

Abstract

Continuous phase transitions occur in a wide range of physical systems, and provide a context for the study of non-equilibrium dynamics and the formation of topological defects. The Kibble-Zurek (KZ) mechanism predicts the scaling of the resulting density of defects as a function of the quench rate through a critical point, and this can provide an estimate of the critical exponents of a phase transition. In this work we extend our previous study of the miscible-immiscible phase transition of a binary Bose-Einstein condensate (BEC) composed of two hyperfine states in which the spin dynamics are confined to one dimension [J. Sabbatini et al., Phys. Rev. Lett. 107, 230402 (2011)]. The transition is engineered by controlling a Hamiltonian quench of the coupling amplitude of the two hyperfine states, and results in the formation of a random pattern of spatial domains. Using the numerical truncated Wigner phase space method, we show that in a ring BEC the number of domains formed in the phase transitions scales as predicted by the KZ theory. We also consider the same experiment performed with a harmonically trapped BEC, and investigate how the density inhomogeneity modifies the dynamics of the phase transition and the KZ scaling law for the number of domains. We then make use of the symmetry between inhomogeneous phase transitions in anisotropic systems, and an inhomogeneous quench in a homogeneous system, to engineer coupling quenches that allow us to quantify several aspects of inhomogeneous phase transitions. In particular, we quantify the effect of causality in the propagation of the phase transition front on the resulting formation of domain walls, and find indications that the density of defects is determined during the impulse to adiabatic transition after the crossing of the critical point.