Unravelling the non-Markovian spin-boson model and quantum quasi-Otto cycle

TL;DR

This paper investigates the non-Markovian dynamics of a spin-boson model describing a two-level atom in a cavity, deriving an exact master equation and proposing a quasi-Otto cycle that can outperform the traditional Otto cycle in efficiency.

Contribution

It derives an exact non-Markovian master equation for the spin-boson model and introduces a quasi-Otto cycle that leverages non-Markovian effects to enhance quantum engine efficiency.

Findings

The quasi-Otto cycle can be more efficient than the standard Otto cycle.

Repeated quasi-Otto cycles approach Otto cycle efficiency asymptotically.

An exact Lindblad-type master equation for non-Markovian dynamics is constructed.

Abstract

We use the spin-boson model to describe the dynamics of a two-level atom interacting with Fabry-P\'erot cavity modes. We solve the Schr\"odinger equation for the system-bath model without the Born-Markov approximation to derive the non-Markovian reduced dynamics of the qubit. We further construct an exact Lindblad-type master equation for it. Similar to the quantum Otto cycle, we construct a non- Markovian quasi-cyclic process based on the atom-cavity interactions, which we call the quasi-Otto cycle. For judicious choices of input state and parameters, the quasi-cycle can be more efficient as a quantum engine than the Otto cycle. We also showed that if the quasi-cycle is repeated multiple times, the efficiency of the quasi-Otto engine asymptotically approaches that of the Otto engine.