Multiphoton Bloch–Siegert shifts and level-splittings in spin-one systems

Abstract

Abstract. We consider a spin-boson model in which a spin 1 system is coupled to an oscillator. A unitary transformation is applied which allows a separation of terms responsible for the Bloch-Siegert shift, and terms responsible for the level splittings at anticrossings associated with Bloch-Siegert resonances. When the oscillator is highly excited, the system can maintain resonance for sequential multiphoton transitions. At lower levels of excitation, resonance cannot be maintained because energy exchange with the oscillator changes the level shift. An estimate for the critical excitation level of the oscillator is developed.

Excitation transfer in two two-level systems coupled to an oscillator

“…This approach, and the resulting conceptual simplification of the problem, is reasonably general and very powerful. We extended the analysis to the case of a spin-one system coupled to an oscillator [8], and obtained results for the Bloch-Siegert shift in agreement with previous work, as well as new results for the level splitting at the Bloch-Siegert resonances. The accuracy was comparable to that obtained for the spin-boson model, and it seems clear that the approach can be applied systematically to higher-spin generalizations of the spin-boson model as well.…”

Level splitting in association with the multiphoton Bloch–Siegert shift

“…Note that the approach used in this paper can be applied to other problems as well. We have used a similar unitary transformation on the spin-1 version of the problem, in which case a similar rotated Hamiltonian is obtained [10]. In this more complicated situation, we again obtain a similar unperturbed Hamiltonian which gives a good approximation for the coupled system away from the level anticrossings, and a similar perturbation which accounts for most of the level splittings at the Bloch-Siegert resonances.…”

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

“…Here, we propose to use the more complicated coupled oscillator and three-level model to test an approximation scheme that appears to have worked well in the spin-boson problem [24], and also in the generalization to the spin-1 version of the spin-boson model [25]. In this approach, the two-level or three-level system is diagonalized directly, treating the oscillator operators parametrically.…”