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 ultrastrong 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.

• Received 17 October 2020
• Revised 11 January 2021
• Accepted 28 January 2021

DOI:https://doi.org/10.1103/PhysRevA.103.023714