Bloch-Siegert shift for multiphoton resonances

Recently there has been theoretical and experimental interest in Bloch-Siegert shifts in an intense photon field. A perturbative treatment becomes difficult in this multiphoton regime. We present a unitary transform and rotated model, which allows us to get accurate results away from the level anticrossings. A simple variational energy estimate leads to a new expression for the dressed two-level system energy which is accurate, and useful over a wide range of the dimensionless coupling constant.