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We consider a generalization of the spin-boson model in which two differenttwo-level systems are coupled to an oscillator, under conditions where theoscillator energy is much less than the two-level system energies, and wherethe oscillator is highly excited. We find that the two-level system transitionenergy is shifted, producing a Bloch-Siegert shift in each two-level systemsimilar to what would be obtained if the other were absent. At resonancesassociated with energy exchange between a two-level system and the oscillator,the level splitting is about the same as would be obtained in the spin-bosonmodel at a Bloch-Siegert resonance. However, there occur resonances associatedwith the transfer of excitation between one two-level system and the other, aneffect not present in the spin-boson model. We use a unitary transformationleading to a rotated system in which terms responsible for the shift andsplittings can be identified. The level splittings at the anticrossingsassociated with both energy exchange and excitation transfer resonances areaccounted for with simple two-state models and degenerate perturbation theoryusing operators that appear in the rotated Hamiltonian.

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