Quantum effective action for the bosonic Josephson junction

TL;DR

This paper derives a quantum effective phase action for a bosonic Josephson junction, providing quantum corrections to the Josephson frequency useful for experimental analysis.

Contribution

It introduces a method to derive an effective phase-only action incorporating quantum effects, advancing theoretical understanding of bosonic Josephson junctions.

Findings

Quantum correction to Josephson frequency obtained

Effective phase action derived with quantum effects included

Method applicable to atomic and superconducting junction experiments

Abstract

We investigate a bosonic Josephson junction by using the path-integral formalism with relative phase and population imbalance as dynamical variables. We derive an effective only-phase action performing functional integration over the population imbalance. We then analyze the quantum effective only-phase action, which formally contains all the quantum corrections. To the second order in the derivative expansion and to the lowest order in $\hbar$, we obtain the quantum correction to the Josephson frequency of oscillation. Finally, the same quantum correction is found by adopting an alternative approach. Our predictions are a useful theoretical tool for experiments with atomic or superconducting Josephson junctions.