Minimum-Time Transitions between Thermal Equilibrium States of the Quantum Parametric Oscillator

TL;DR

This paper applies geometric optimal control to determine the fastest way to transition between thermal equilibrium states of a quantum parametric oscillator, revealing new optimal solutions not previously identified.

Contribution

It introduces a novel geometric control approach to solve the minimum-time transition problem, uncovering previously unknown optimal solutions.

Findings

Discovered new types of optimal solutions.

Solved the minimum-time transition problem exactly.

Applicable to various physical systems.

Abstract

In this article, we use geometric optimal control to completely solve the problem of minimum-time transitions between thermal equilibrium states of the quantum parametric oscillator, which finds applications in various physical contexts. We discover a new kind of optimal solutions, absent from all the previous treatments of the problem.