Physical background for parameters of the quantum Rabi model

Abstract

We investigate the applicability of the two major approximations which are most commonly employed in the study of the quantum Rabi model, namely the description of a resonant cavity mode as a single-mode quantized field and the use of the rotating wave approximation. Starting from the Hamiltonian of a two-level system interacting with a multi-mode quantized field, we perform the canonical transformation of the field operators. This allows one to partition the Hamiltonian of the system into two parts. The first part is the interaction of the two-level system with a single collective field mode, while the second one describes the interaction with field fluctuations. The first part is usually associated with the resonant cavity mode. This division enables us to determine the applicability condition of the single-mode approximation. In addition we identify simple approximate relations for the description of the eigenstates, eigenfunctions and the time evolution of the quantum Rabi model beyond the rotating wave approximation.

20 pages, 12 figures

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• The quantum Rabi model: solution and dynamics
• Spontaneous emission in a quantum system driven by the resonant field beyond the rotating wave approximation
• Analytic approximation for eigenvalues of a class of $\mathcal{P}\mathcal{T}$ symmetric Hamiltonians
• Eigenstates of two-level systems in a single-mode quantum field: from quantum Rabi model to $N$-atom Dicke model
• Emission spectrum of a qubit under its deep strong driving in the high-frequency dispersive regime
• Dissipative Rabi model for deep strong far-off-resonant driving