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

Abstract

We consider a generalization of the spin-boson model consisting of a three-level system in a ladder configuration coupled to an oscillator. We find that this model is much more complicated than the spin-boson model, due in part to the presence of more levels and resonances, and because the middle level can be pushed into the upper or lower levels. We make use of a unitary transformation that results in a rotated version of the problem, in which terms primarily responsible for the Bloch–Siegert shift can be isolated from other terms responsible for producing level splittings at anticrossings associated with the Bloch–Siegert resonances. We present a useful approximation to the energy levels in the multiphoton region of the new problem. Good approximate results are 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.