Cross-cavity quantum Rabi model

Abstract

We introduce the cross-cavity quantum Rabi model describing the interaction of a single two-level system with two orthogonal boson fields and propose its quantum simulation by two-dimensional, bichromatic, first-sideband driving of a single trapped ion. We provide an introductory survey of the model, including its diagonalization in the two-level system basis, numerical spectra and its characteristics in the weak, ultra strong and deep strong coupling regimes. We also show that the particular case of degenerate field frequencies and balanced couplings allows us to cast the model as two parity deformed oscillators in any given coupling regime.

14 pages, 7 figures

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• Simulating para-Fermi oscillators
• Squeezed displaced entangled states in the quantum Rabi model
• Dissipative dynamics in a tunable Rabi dimer with periodic harmonic driving
• Formation of spectral triplets induced by parity deformation in a quantum dot-cavity system
• Para-particle oscillator simulations on a trapped ion quantum computer
• Tripartite multiphoton Jaynes-Cummings model: Analytical solution and Wigner nonclassicalities
• Engineering $\mathrm{SU}(1,1)\otimes \mathrm{SU}(1,1)$ vibrational states