Optimal Quantum Feshbach Engines

TL;DR

This paper presents a variational optimization framework for quantum cycles with Bose-Einstein condensates, optimizing control protocols to maximize efficiency and stability, applicable to various nonlinear quantum systems.

Contribution

It introduces a novel variational method combined with stochastic quantization to derive optimal control protocols for nonlinear Schrödinger equations in quantum thermodynamics.

Findings

Optimal protocols balance cycle duration and physical constraints.

Protocols show remarkable stability over repeated cycles.

Method extends to generic nonlinear Schrödinger equations.

Abstract

We develop an optimization framework for high-efficiency quantum cycles implemented with a trapped Bose-Einstein condensate, whose control parameters are the trap stiffness and the interaction strength tuned via a Feshbach resonance. Optimal driving protocols for each stroke of the cycle are obtained from a variational description of the condensate dynamics combined with Nelson's stochastic quantization, which maps the quantum evolution onto an effective Ornstein-Uhlenbeck process. The optimal protocol is obtained by minimizing a user-defined cost functional that selects the best trade-off between protocol duration and arbitrary physical constraints (such as the expended work or the proximity to an adiabatic evolution), and exhibits remarkable stability over repeated cycles. The method also provides a systematic route to optimal control for generic nonlinear Schr\"odinger equations, paving the way to optimal control strategies in fields as diverse as nonlinear optics, quantum fluids, and quantum plasmas.