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

TL;DR

This paper studies a generalized spin-boson model with two two-level systems coupled to an oscillator, revealing excitation transfer effects and energy shifts, with analytical models explaining the observed resonances and level splittings.

Contribution

It introduces a model with two coupled two-level systems and an oscillator, analyzing excitation transfer and energy shifts using a unitary transformation and perturbation theory.

Findings

Identification of excitation transfer resonances absent in the standard spin-boson model.

Observation of Bloch-Siegert shifts in both two-level systems.

Analytical explanation of level splittings at anticrossings.

Abstract

We consider a generalization of the spin-boson model in which two different two-level systems are coupled to an oscillator, under conditions where the oscillator energy is much less than the two-level system energies, and where the oscillator is highly excited. We find that the two-level system transition energy is shifted, producing a Bloch-Siegert shift in each two-level system similar to what would be obtained if the other were absent. At resonances associated 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-boson model at a Bloch-Siegert resonance. However, there occur resonances associated with the transfer of excitation between one two-level system and the other, an effect not present in the spin-boson model. We use a unitary transformation leading to a rotated system in which terms responsible for the shift and splittings can be identified. The level splittings at the anticrossings associated with both energy exchange and excitation transfer resonances are accounted for with simple two-state models and degenerate perturbation theory using operators that appear in the rotated Hamiltonian.