Minimum-Time Transitions between Thermal and Fixed Average Energy States of the Quantum Parametric Oscillator

TL;DR

This paper applies geometric optimal control to determine the minimum time required for quantum parametric oscillators to transition between thermal and fixed energy states, with implications for quantum heat engines and refrigerators.

Contribution

It provides a complete solution for minimum-time control of quantum parametric oscillators, advancing understanding of optimal quantum thermodynamic processes.

Findings

Derived minimum transition times for quantum heat engine cycles

Calculated quantum finite-time availability for the oscillator

Optimized control protocols for rapid state transitions

Abstract

In this article we use geometric optimal control to completely solve the problem of minimum-time transitions between thermal equilibrium and fixed average energy states of the quantum parametric oscillator, a system which has been extensively used to model quantum heat engines and refrigerators. We subsequently use the obtained results to find the minimum driving time for a quantum refrigerator and the quantum finite-time availability of the parametric oscillator, i.e. the potential work which can be extracted from this system by a very short finite-time process.