Generalized Purity and Quantum Phase Transition for Bose-Einstein condensates in a Symmetric Double Well

TL;DR

This paper uses generalized purity to analyze coherence loss and quantum phase transitions in a two-mode Bose-Einstein condensate within a symmetric double well, revealing a power law relation with particle number.

Contribution

It introduces the use of generalized purity to detect quantum phase transitions and coherence loss in Bose-Einstein condensates with cross-collision effects.

Findings

Generalized purity signals quantum phase transitions.

Power law dependence of critical parameters on particle number.

Analysis of coherence loss and delocalization in the Q-function.

Abstract

The generalized purity is employed for investigating the process of coherence loss and delocalization of the Q-function in the Bloch sphere of a two-mode Bose-Einstein condensate in a symmetrical double well with cross-collision. Quantum phase transition of the model is signaled by the generalized purity as a function of an appropriate parameter of the Hamiltonian and the number of particles (N). A power law dependence of the critical parameter with N is derived.