Entanglement and dynamical phase transition in a spin-orbit-coupled Bose-Einstein condensate

TL;DR

This paper investigates the relationship between dynamical phase transitions and quantum entanglement in a spin-orbit-coupled Bose-Einstein condensate, showing entanglement peaks at phase transitions and proposing feasible detection methods.

Contribution

It demonstrates that entanglement measures can indicate dynamical phase transitions and introduces a practical criterion for entanglement detection at finite temperatures.

Findings

Entanglement peaks at dynamical phase transitions.

Correlation-based criterion effectively detects entanglement.

Entanglement measures can infer the existence of DPTs.

Abstract

Characterizing quantum phase transitions through quantum correlations has been deeply developed for a long time, while the connections between dynamical phase transitions (DPTs) and quantum entanglement is not yet well understood. In this work, we show that the time-averaged two-mode entanglement in the spin space reaches a maximal value when it undergoes a DPT induced by external perturbation in a spin-orbit-coupled Bose-Einstein condensate. We employ the von Neumann entropy and a correlation-based entanglement criterion as entanglement measures and find that both of them can infer the existence of DPT. While the von Neumann entropy works only for a pure state at zero temperature and requires state tomography to reconstruct, the experimentally more feasible correlation-based entanglement criterion acts as an excellent proxy for entropic entanglement and can determine the existence of entanglement for a mixed state at finite temperature, making itself an excellent indicator for DPT. Our work provides a deeper understanding about the connection between DPTs and quantum entanglement, and may allow the detection of DPT via entanglement become accessible as the examined criterion is suitable for measuring entanglement.