The Rabi problem with elliptic polarization

TL;DR

This paper analyzes the classical and quantum Rabi problem with elliptic polarization, deriving solutions using differential equations and Floquet theory, and exploring resonance shifts and limit cases.

Contribution

It extends the classical and quantum Rabi problem to elliptic polarization, providing analytical solutions and detailed analysis of resonance phenomena.

Findings

Solutions in terms of power series analogous to confluent Heun equations

Expressions for quasienergy as a function of parameters

Analysis of Bloch-Siegert shift and limit cases

Abstract

We consider the solution of the equation of motion of a classical/quantum spin subject to a monochromatical, elliptically polarized external field. The classical Rabi problem can be reduced to third order differential equations with polynomial coefficients and hence solved in terms of power series in close analogy to the confluent Heun equation occurring for linear polarization. Application of Floquet theory yields the physically interesting quasienergy as a function of the parameters of the problem and expressions for the Bloch-Siegert shift of resonance frequencies. Various limit cases cases have been thoroughly investigated.