Finite-size effects in a bosonic Josephson junction

TL;DR

This paper explores finite-size quantum effects in a bosonic Josephson junction, extending mean-field theory with $1/N$ corrections using time-dependent atomic coherent states, and validates findings with numerical simulations.

Contribution

It introduces a $1/N$ correction to mean-field results in the bosonic Josephson junction using a variational approach with atomic coherent states.

Findings

Good agreement between numerical simulations and ACS predictions for Josephson oscillations with few atoms.

ACS approach better reproduces spontaneous symmetry breaking than mean-field theory.

The $1/N$ correction improves mean-field predictions but is unreliable for the onset of macroscopic quantum self-trapping.

Abstract

We investigate finite-size quantum effects in the dynamics of $N$ bosonic particles which are tunneling between two sites adopting the two-site Bose-Hubbard model. By using time-dependent atomic coherent states (ACS) we extend the standard mean-field equations of this bosonic Josephson junction, which are based on time-dependent Glauber coherent states. In this way we find $1/N$ corrections to familiar mean-field (MF) results: the frequency of macroscopic oscillation between the two sites, the critical parameter for the dynamical macroscopic quantum self trapping (MQST), and the attractive critical interaction strength for the spontaneous symmetry breaking (SSB) of the ground state. To validate our analytical results we perform numerical simulations of the quantum dynamics. In the case of Josephson oscillations around a balanced configuration we find that also for a few atoms the numerical results are in good agreement with the predictions of time-dependent ACS variational approach, provided that the time evolution is not too long. Also the numerical results of SSB are better reproduced by the ACS approach with respect to the MF one. Instead the onset of MQST is correctly reproduced by ACS theory only in the large $N$ regime and, for this phenomenon, the $1/N$ correction to the MF formula is not reliable.