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.

Spontaneous emission in a quantum system driven by a resonant field beyond the rotating wave approximation

“…(12), (13) can be used in the entire ranges of f and n values. However, according to [13], the main applications of the considered problem are based on relatively weak interaction but intense driving field (f ≪ 1; n ≫ 1, f √ n ∼ 1). Usually the driving field is described by the coherent state [13,15].…”

“…However, according to [13], the main applications of the considered problem are based on relatively weak interaction but intense driving field (f ≪ 1; n ≫ 1, f √ n ∼ 1). Usually the driving field is described by the coherent state [13,15]. However, in the case of n ≫ 1 fluctuations of the field amplitude ∆n ≈ √ n ≪ n and the coherent state is appoximately equal to the Fock field state with the quantum number n =n [2].…”

Analytical diagonalisation of the Hamiltonian of the quantum Rabi model in the Coulomb gauge

“…Различные приложения данной модели и ее обобщений и в настоящее время остаются весьма актуальными (см. [6][7][8][9][10] и цитированную в них литературу).…”

Exact solution for the quantum Rabi model with the $\boldsymbol{\mathsf{A}}^{2}$ term

“…Presently there exist systems (ion bound to the cavity [13,14], super-conducting qubit [15][16][17], polaritons [18]) that provide the strong interaction [19][20][21][22][23] between an atom and the field, which corresponds to the situation when the dimensionless coupling constant f of the atom-field interaction in QRM reaches values of the order of unity [24][25][26]. This motivates both experimental and theoretical investigations of physical effects appearing in this fully quantum regime [6,24,[27][28][29][30][31].…”