Multiphoton Bloch-Siegert shifts and level-splittings in a three-level system

TL;DR

This paper extends the analysis of multiphoton effects and level splittings from the spin-boson model to a more complex three-level system coupled to an oscillator, demonstrating the effectiveness of a rotation-based approximation in this context.

Contribution

It generalizes the multiphoton analysis and rotation method to a three-level system, providing a useful approximation for energy levels and level splittings.

Findings

Rotation provides accurate energy level approximations in the multiphoton regime.

Good results for level splittings at anticrossings involving lower two levels.

Method is effective away from accidental or low-order resonances of upper levels.

Abstract

In previous work we studied the spin-boson model in the multiphoton regime, using a rotation that provides a separation between terms that contribute most of the level energies away from resonance, and terms responsible for the level splittings at the anticrossing. Here, we consider a generalization of the spin-boson model consisting of a three-level system coupled to an oscillator. We construct a similar rotation and apply it to the more complicated model. We find that the rotation provides a useful approximation to the energy levels in the multiphoton region of the new problem. We find that good results can be obtained for the level splittings at the anticrossings for resonances involving the lower two levels in regions away from accidental or low-order resonances of the upper two levels.