Work Fluctuations in Bosonic Josephson Junctions

TL;DR

This paper analyzes the work fluctuations in bosonic Josephson junctions, providing exact work distribution calculations and demonstrating how optimal control can minimize irreversible work, with relevance to ultracold atom experiments.

Contribution

It offers a detailed calculation of work statistics in bosonic Josephson junctions and introduces optimal control methods to reduce irreversible work during finite-time protocols.

Findings

Irreversible work scales differently in Josephson and Fock regimes.

Optimal control significantly reduces irreversible work.

Work statistics relate to population imbalance measurements.

Abstract

We calculate the first two moments and full probability distribution of the work performed on a system of bosonic particles in a two-mode Bose-Hubbard Hamiltonian when the self-interaction term is varied instantaneously or with a finite-time ramp. In the instantaneous case, we show how the irreversible work scales differently depending on whether the system is driven to the Josephson or Fock regime of the bosonic Josephson junction. In the finite-time case, we use optimal control techniques to substantially decrease the irreversible work to negligible values. Our analysis can be implemented in present-day experiments with ultracold atoms and we show how to relate the work statistics to that of the population imbalance of the two modes.