Quantum corrections to the Josephson dynamics: a population-imbalance approach

TL;DR

This paper derives quantum corrections to Josephson dynamics in coupled Bose-Einstein condensates using a population-imbalance approach, providing explicit formulas for quantum-corrected frequency and demonstrating improved accuracy over phase-only models.

Contribution

It introduces a population-imbalance based quantization method with explicit quantum corrections, outperforming phase-only models in weakly interacting regimes.

Findings

Quantum-corrected Josephson frequency derived explicitly.

Imbalance-only formulation outperforms phase-only approach.

Numerical results agree with exact diagonalization in weak interactions.

Abstract

We investigate quantum corrections to the Josephson dynamics of two weakly coupled Bose-Einstein condensates using the population imbalance as the sole dynamical variable. Starting from the two-variable action, we derive the imbalance-only Lagrangian with a position-dependent mass and quantize it via symmetric operator ordering. The leading quantum corrections to the classical potential and mass are computed via the one-loop quantum effective action, using a covariant background-field method that fully accounts for the coordinate dependence of the mass. This yields explicit expressions for the effective potential and the effective mass, from which we derive the quantum-corrected Josephson frequency. Numerical comparison with exact diagonalization of the two-site Bose-Hubbard model shows that the imbalance-only formulation outperforms the complementary phase-only approach in the regime of weak interactions, which is the natural domain of validity of the population-imbalance description.