Resonance in a driven two-level system: analytical results without the rotating wave approximation

TL;DR

This paper provides exact analytical solutions for a driven two-level quantum system without relying on the rotating wave approximation, offering insights into resonance conditions and validating results against numerical calculations.

Contribution

It introduces a method for constructing exact solutions for a time-dependent two-level system, extending analysis beyond the rotating wave approximation.

Findings

Explicit solutions for N=1,2 match RWA predictions at  in certain parameters.

Solutions agree well with numerical calculations beyond RWA.

Resonance conditions are thoroughly discussed.

Abstract

We consider the problem of two-level system dynamics induced by the time-dependent field B={a(t)cos\omega t,a(t)sin\omega t,\omega_0}, with a(t) \sim cn(\nu t,k). The problem is exactly analytically solvable and we propose the scheme for constructing the solutions. For all field configurations the resonance conditions are discussed. The explicit solutions for N=1,2 we obtained coincide at \omega=0 in the proper parameter domain with predictions of the rotating wave approximation and agree nicely with numerical calculations beyond it.