Selective Interactions in the Quantum Rabi Model

Abstract

We demonstrate the emergence of selective k-photon interactions in the strong and ultrastrong coupling regimes of the quantum Rabi model with a Stark coupling term. In particular, we show that the interplay between rotating and counter-rotating terms produces k-photon interactions whose resonance frequencies depend on the state of the bosonic mode. We develop an analytical framework to explain these k-photon interactions by using time-dependent perturbation theory. Finally, we propose a method to achieve the quantum simulation of the quantum Rabi model with a Stark term by using the internal and vibrational degrees of freedom of a trapped ion, and demonstrate its performance with numerical simulations considering realistic physical parameters.

Unified approach to various quantum Rabi models with arbitrary parameters*

“…[32] This model also attracted much attention in recent years. [33][34][35] Recently, the anisotropic Dicke model with the Stark coupling terms, which can be called as the anisotropic Dicke-Stark model, was demonstrated via cavity assisted Raman transitions in a configuration using counterpropagating laser beams. [36] For one atom case, it is just the anisotropic RSM.…”

Two-photon Rabi-Stark model

“…This nonlinear coupling term has been discussed in the quantum optics literature under the name of dynamical Stark shift, a quantum version of the Bloch-Siegert shift, so it was later named the quantum Rabi-Stark model (RSM) [23]. This model also attracts many attentions in recent years [23][24][25][26][27]. The nonlinear Stark coupling in the RSM can induce the spectra collapse at some critical Stark terms as well as the first-order phase transitions.…”