The Spectrum in Qubit-Oscillator Systems in the Ultrastrong Coupling Regime

Abstract

Recent measurement on an LC resonator magnetically coupled to a superconducting qubit [arXiv:1005[arXiv: .1559] shows that the system operates in the ultra-strong coupling regime and crosses the limit of validity for the rotating-wave approximation of the Jaynes-Cummings model. By using extended bosonic coherent states, we solve the Jaynes-Cummings model exactly without the rotating-wave approximation. Our numerically exact results for the spectrum of the flux qubit coupled to the LC resonator are fully consistent with the experimental observations. The smallest Bloch-Siegert shift obtained is consistent with that observed in this experiment. In addition, the Bloch-Siegert shifts in arbitrary level transitions and for arbitrary coupling constants are predicted.

Exact solvability of the quantum Rabi model using Bogoliubov operators

“…[13] quantum mechanically within the extended coherent stats [15,16]. Both zero bias and biased QRM can be treated simultaneously.…”

Absence of collapse in quantum Rabi oscillations

“…It is observed that the energy differences with the same k [Eq. (21)] are very small, and those with the different k [Eq. (22)] are large.…”

“…Therefore, the CRTs can no longer be ignored. Recently, much attention has been devoted to the qubit-oscillator system and the effect of the CRTs in the ultrastrong coupling regime [17][18][19][20][21][22].…”

Exact solvability and two-frequency Rabi oscillation in cavity-QED setup with moving emitter

“…With the assistance of a unitary transformation, we find the system can be effectively described by an emitter-optomechanical cavity Hamiltonian [30,31], with a negligible Kerr term. We find that effective Hamiltonian possesses a same mathematical structure with quantum Rabi model [32], and borrow the Bogliubov operators approach [33][34][35] to obtain the exact energy spectrum. It shows that, the optomechanical interaction will induce a sideband effect, and in each of the sideband, we observe the Rabi splitting which originates from the emitter-cavity coupling.…”