Quantum dynamics of local phase differences between reservoirs of driven interacting bosons separated by simple aperture arrays

TL;DR

This paper derives a microscopic effective action for driven bosonic reservoirs separated by apertures, analyzing phase dynamics, tunneling effects, and Josephson oscillations with applications to liquid helium experiments.

Contribution

It introduces a gauge-theoretic derivation of phase dynamics in driven bosonic systems and extends it to multi-aperture arrays with microscopic couplings.

Findings

Current-phase relation transitions from linear to sinusoidal with temperature.

Interference effects in multi-aperture arrays amplify Josephson oscillations.

Effective coupled pendula equations describe multi-aperture phase dynamics.

Abstract

We present a derivation of the effective action for the relative phase of driven, aperture-coupled reservoirs of weakly-interacting condensed bosons from a (3+1)-D microscopic model with local U(1) gauge symmetry. We show that inclusion of local chemical potential and driving velocity fields as a gauge field allows derivation of the hydrodynamic equations of motion for the driven macroscopic phase differences across simple aperture arrays. For a single aperture, the current-phase equation for driven flow contains sinusoidal, linear, and current-bias contributions. We compute the renormalization group (RG) beta function of the periodic potential in the effective action for small tunneling amplitudes and use this to analyze the temperature dependence of the low-energy current-phase relation, with application to the transition from linear to sinusoidal current-phase behavior observed in experiments by Hoskinson et al. \cite{packard} for liquid $^{4}$He driven through nanoaperture arrays. Extension of the microscopic theory to a two-aperture array shows that interference between the microscopic tunneling contributions for individual apertures leads to an effective coupling between apertures which amplifies the Josephson oscillations in the array. The resulting multi-aperture current-phase equations are found to be equivalent to a set of equations for coupled pendula, with microscopically derived couplings.