Quantum and thermal fluctuations in bosonic Josephson junctions

TL;DR

This paper investigates quantum and thermal fluctuations in bosonic Josephson junctions using the Bose-Hubbard model, comparing finite particle number effects to the classical limit, especially near the quantum phase transition at low temperatures.

Contribution

It provides a detailed analysis of quantum fluctuations in bosonic Josephson junctions at finite temperatures and particle numbers, highlighting the convergence to classical behavior as particle number increases.

Findings

Quantum fluctuations are small for N ~ 100, diminishing as 1/N.

Differences between finite N and classical limit are minimal even at moderate N.

Behavior near the quantum phase transition is characterized for both attractive and repulsive interactions.

Abstract

We use the Bose-Hubbard Hamiltonian to study quantum fluctuations in canonical equilibrium ensembles of bosonic Josephson junctions at relatively high temperatures, comparing the results for finite particle numbers to the classical limit that is attained as $N$ approaches infinity. We consider both attractive and repulsive atom-atom interactions, with especial focus on the behavior near the T=0 quantum phase transition that occurs, for large enough $N$, when attractive interactions surpass a critical level. Differences between Bose-Hubbard results for small $N$ and those of the classical limit are quite small even when $N \sim 100$, with deviations from the limit diminishing as 1/N.