Two-photon interaction effects in the bad-cavity limit

Abstract

Various experimental platforms have proven to be valid testbeds for the implementation of non-dipolar light-matter interactions, where atomic systems and confined modes interact via two-photon couplings. Here, we study a damped quantum harmonic oscillator interacting with $N$ qubits via a two-photon coupling in the so-called bad-cavity limit, in the presence of finite-temperature baths and coherent and incoherent drivings. We have succeeded in applying a recently developed adiabatic elimination technique to derive an effective master equation for the qubits, presenting two fundamental differences compared to the case of a dipolar interaction: an enhancement of the qubits spontaneous-like emission rate, including a thermal contribution and a quadratic term in the coherent driving, and an increment of the effective temperature perceived by the qubits. These differences give rise to striking effects in the qubits dynamics, including a faster generation of steady-state coherence and a richer dependence on temperature of the collective effects, which can be made stronger at higher temperature.Comment: 11 pages, 4 figures. Comments welcom