Periodic thermodynamics of a two spin Rabi model

TL;DR

This paper analytically solves a two-spin Rabi model under periodic driving, explores work distribution and Jarzynski equality, and characterizes non-equilibrium steady states with phase transitions.

Contribution

It provides an exact solution for the driven two-spin system, analyzes work statistics, verifies Jarzynski equality, and describes phase transitions in non-equilibrium steady states.

Findings

Work distribution can be obtained in closed form.

Jarzynski equality holds for this system.

Non-equilibrium steady states exhibit phase transitions with discontinuous derivatives.

Abstract

We consider two $s=1/2$ spins with Heisenberg coupling and a monochromatic, circularly polarized magnetic field acting only onto one of the two spins. This system turns out to be analytically solvable. Also the statistical distribution of the work performed by the driving forces during one period can be obtained in closed form and the Jarzynski equation can be checked. The mean value of this work, viewed as a function of the physical parameters, exhibits features that can be related to some kind of Rabi oscillation. Moreover, when coupled to a heat bath the two spin system will approach a non-equilibrium steady state (NESS) that can be calculated in the golden rule approximation. The occupation probabilities of the NESS are shown not to be of Boltzmann type, with the exception of a single phase with infinite quasitemperature. The parameter space of the two spin Rabi model can be decomposed into eight phase domains such that the NESS probabilities possess discontinuous derivatives at the phase boundaries. The latter property is shown to hold also for more general periodically driven $N$-level systems.