Abstract

The Rabi Hamiltonian $\widehat{H}=\hslash \omega {\widehat{a}}^{†}\widehat{a}+\hslash \epsilon {\widehat{\sigma }}_z/2+\hslash g(\widehat{a}+{\widehat{a}}^{†})(\widehat{\sigma }+{\widehat{\sigma }}^{†})$ is one of the most studied models in quantum optics; in it, a bosonic mode $\widehat{a}$ with characteristic frequency ω interacts with a two-level system $\widehat{\sigma }$ with frequency gap ε. The model was originally conceived to account for the interaction between an atom and a mode of an optical cavity (ω and ε being optical frequencies much larger than the coupling g), although new technologies such as trapped ions or microwave resonators coupled to superconducting qubits have allowed its implementation at much lower frequencies, paving the way for the observation of phenomena characteristic of the so-called ‘ultra-strong’ coupling regime g ∼ ω₀,ε.

© 2013 IEEE