Quantum Criticality in a Bosonic Josephson Junction

TL;DR

This paper investigates a quantum phase transition in a bosonic Josephson junction modeled by a two-mode Bose-Hubbard system, analyzing finite-size and thermal effects on critical phenomena and quantum information measures.

Contribution

It provides a detailed analysis of the quantum phase transition, including finite-size scaling, dynamical bifurcation relations, and thermal effects, with focus on quantum information metrics.

Findings

Identification of five regimes based on interaction strength

Anomalous scaling of population imbalance at criticality

Finite-temperature effects on quantum phase transition

Abstract

In this paper we consider a bosonic Josephson junction described by a two-mode Bose-Hubbard model, and we thoroughly analyze a quantum phase transition occurring in the system in the limit of infinite bosonic population. We discuss the relation between this quantum phase transition and the dynamical bifurcation occurring in the spectrum of the Discrete Self Trapping equations describing the system at the semiclassical level. In particular, we identify five regimes depending on the strength of the effective interaction among bosons, and study the finite-size effects arising from the finiteness of the bosonic population. We devote a special attention to the critical regime which reduces to the dynamical bifurcation point in the thermodynamic limit of infinite bosonic population. Specifically, we highlight an anomalous scaling in the population imbalance between the two wells of the trapping potential, as well as in two quantities borrowed from Quantum Information Theory, i.e. the entropy of entanglement and the ground-state fidelity. Our analysis is not limited to the zero temperature case, but considers thermal effects as well.