Probing the spectrum of the Jaynes-Cummings-Rabi model by its isomorphism to an atom inside a parametric amplifier cavity

TL;DR

This paper demonstrates how the Jaynes-Cummings-Rabi model can be realized using a qubit in a parametric amplifier cavity, enabling exploration of the ultra-strong coupling regime and revealing entangled squeezed cat states at energy crossings.

Contribution

It establishes an isomorphism between the Rabi model and a qubit in a parametric amplifier cavity, facilitating experimental access to the full spectrum and ultra-strong coupling effects.

Findings

Observation of a narrow resonance peak in the spectrum.

Eigenstates at the crossing are entangled field-atom states.

Field states include squeezed cat states.

Abstract

We show how the Jaynes--Cummings--Rabi model of cavity quantum electrodynamics can be realized via an isomorphism to the Hamiltonian of a qubit inside a parametric amplifier cavity. This realization clears the way to observe the full spectrum of the Rabi model via a probe applied to a parametric amplifier cavity containing a qubit and a parametric oscillator operating below threshold. An important outcome of the isomorphism is that the actual frequencies are replaced by detunings which make it feasible to reach the ultra-strong coupling regime. We find that inside this regime the probed spectrum displays a narrow resonance peak that is traced back to the transition between ground and first excited states. The exact form of these states is given at an energy crossing and then extended numerically. At the crossing, the eigenstates are entangled states of field and atom where the field is found inside squeezed cat states.