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arXiv:2605.00571 · Annalen der Physik

Quantum Corrections to the Josephson Dynamics: A Population‐Imbalance Approach

Oliver Hideg, Sofia Salvatore, Luca Salasnich

Published Sep 1, 2026• 0 citations
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Abstract

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 performs better than the complementary phase‐only approach in the regime of weak interactions.

DOI
10.1002/andp.70292

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We show that the orbital Josephson effect appears in a wide range of driven atomic Bose–Einstein condensed systems, including quantum ratchets, double wells and box potentials. We use three separate numerical methods: the Gross–Pitaevskii equation, exact diagonalization of the few-mode problem and the multi-configurational time-dependent Hartree for bosons algorithm. We establish the limits of mean-field and few-mode descriptions, demonstrating that the few-mode approximation represents the full many-body dynamics to high accuracy in the weak driving limit. Among other quantum measures, we compute the instantaneous particle current and the occupation of natural orbitals. We explore four separate dynamical regimes, the Rabi limit, chaos, the critical point and self-trapping; a favorable comparison is found even in the regimes of dynamical instabilities or macroscopic quantum self-trapping. Finally, we present an extension of the ( t , t ')-formalism to general time-periodic equations of motion, which permits a systematic description of the long-time dynamics of resonantly driven many-body systems, including those relevant to the orbital Josephson effect.