Ground state of a cross-cavity quantum Rabi model

We study a cross-cavity quantum Rabi model with ultrastrong coupling, and its analytical ground state is demonstrated to be approximately obtained by using the rotating-transformation method. Our method requires making three unitary transformations to the original Hamiltonian and ignoring the three-party cross interaction. In near-resonance and ultrastrong-coupling regimes, the ground-state fidelity is higher than 99% for a ±20% detuning range. We analytically demonstrate that the entanglement in ground state first quadratically increases with the qubit-oscillator coupling strength, then gets close to the maximum value 1. The oscillator's nonclassical property in the ground state is well explained by analytically solving the Wigner function. (paper)