Energy transfer using unitary transformations

TL;DR

This paper analyzes a quantum system of two harmonic oscillators coupled through a three-level system acting as an energy transfer engine, with an analytic S-matrix and conserved quanta leading to quasi-periodic evolution.

Contribution

It provides an analytic form of the S-matrix for a driven quantum energy transfer system with conserved quanta, revealing its spectral and dynamical properties.

Findings

The S-matrix is obtained analytically.

Total quanta are conserved during evolution.

System exhibits quasi-periodic behavior.

Abstract

We study the unitary time evolution of a simple quantum Hamiltonian describing two harmonic oscillators coupled via a three-level system. The latter acts as an engine transferring energy from one oscillator to the other and is driven in a cyclic manner by time-dependent external fields. The S-matrix of the cycle is obtained in analytic form. The total number of quanta contained in the system is a conserved quantity. As a consequence the spectrum of the S-matrix is purely discrete and the evolution of the system is quasi-periodic.