Quantum Information Approach to Bose-Einstein Condensate in a Tilted Double-Well System

TL;DR

This paper investigates how tilt affects the ground state transitions of bosons in a double-well system using quantum information measures, revealing size-dependent transition behaviors.

Contribution

It introduces the use of fidelity susceptibility, quantum discord, and total correlation to analyze ground state transitions in a tilted double-well Bose-Einstein condensate.

Findings

Multiple ground state transitions depend on tilt magnitude.

Quantum correlations peak at transition regions and decay with particle number.

Mean-field theory fails to explain finite-size transition regions.

Abstract

We study the ground state properties of bosons in a tilted double-well system. We use fidelity susceptibility to identify the possible ground state transitions under different tilt values. For a very small tilt (for example $10^{-10}$), two transitions are found. For a moderate tilt (for example $10^{-3}$), only one transition is found. For a large tilt (for example $10^{-1}$), no transition is found. We explain this by analyzing the spectrum of the ground state. The quantum discord and total correlation of the ground state under different tilts are also calculated to indicate those transitions. In the transition region, both quantities have peaks decaying exponentially with particle number $N$. This means for a finite-size system the transition region cannot be explained by the mean-field theory, but in the large-$N$ limit it can be.