Quantum cooling by unitary transformations

TL;DR

This paper analyzes a quantum heat engine modeled as a three-level system coupled to harmonic oscillator baths, deriving its S-matrix and exploring conditions for work production and energy flow.

Contribution

It provides an analytic form of the S-matrix for a quantum heat engine and proposes a spectrum condition for engine operation.

Findings

Spectrum of the S-matrix may contain a continuous part for engine operation

Energy currents flow bidirectionally through the engine

Operation depends on the balance of energy currents

Abstract

We study the unitary time evolution of a simple quantum Hamiltonian describing a heat engine coupled to two heat baths. The engine is modeled as a three-level system. Each heat bath consists of a single harmonic oscillator. The engine is operated via time-dependent external fields. The S-matrix of the thermodynamic cycle is obtained in analytic form. We conjecture that the spectrum of this S-matrix contains a continuous part, and that this is a requirement for the operation as a heat engine. Energy currents flow in both directions through the engine. The balance of these currents determines whether the engine performs work or whether its operation requires the application of external forces.