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The scientific interest in the analytical solution of the quantum Rabi model is due to the widespread use of this simple model in quantum optics, quantum computing, cavity QED, and nanoelectromechanical systems. This interest is related to…
We have found the algebraic structure of the two-qubit quantum Rabi model behind the possibility of its novel quasi-exact solutions with finite photon numbers by analyzing the Hamiltonian in the photon number space. The quasi-exact…
An analytical approach is proposed to study the two-photon, two-mode and intensity-dependent Rabi models. By virtue of the su(1,1) Lie algebra, all of them can be unified to the same Hamiltonian with $\mathcal{Z}_2$ symmetry. There exist…
The purpose of this paper is to study the exceptional eigenvalues of the asymmetric quantum Rabi models (AQRM), specifically, to determine the degeneracy of their eigenstates. Here, the Hamiltonian $H^{\epsilon}_{\text{Rabi}}$ of the AQRM…
We establish a density one version of Braak's conjecture on the fine structure of the spectrum of the quantum Rabi model, as well as a recent conjecture of Braak, Nguyen, Reyes-Bustos and Wakayama on the nearest neighbor spacings of the…
The Rabi Hamiltonian, describing the interaction between a two-level atomic system and a single cavity mode of the electromagnetic field, is one of the fundamental models in quantum optics. The model becomes exactly solvable by considering…
In the present paper we show that the Hamiltonian describing the resonant interaction of $N$ two-level systems with a single-mode electromagnetic quantum field in the Coulomb gauge can be diagonalized with a high degree of accuracy using a…
We use a recently derived gauge-invariant formulation of the problem of a two-level system coupled to an optical cavity, to explore the transition between the weak, and the ultra-strong coupling regimes of light-matter interaction. We…
We study the two-qubit Rabi model in the most general case where the qubits are different from each other. The spectrum of the system in the ultrastrong-coupling regime is shown to converge to two forced oscillator chains by perturbation…
The quantum Rabi model describes the ultrastrong interaction of a two-level atom coupled to a single quantized bosonic mode. As compared to the Jaynes-Cummings model, in the Rabi model the absorption and emission processes do not need to…
The two-photon Rabi Hamiltonian is a simple model describing the interaction of light with matter, with the interaction being mediated by the exchange of two photons. Although this model is exactly soluble in the rotating-wave…
We propose a quantum simulation of the quantum Rabi model in an atomic quantum dot, which is a single atom in a tight optical trap coupled to the quasiparticle modes of a superfluid Bose-Einstein condensate. This widely tunable setup allows…
Gauge invariance is the cornerstone of modern quantum field theory. Recently, it has been shown that the quantum Rabi model, describing the dipolar coupling between a two-level atom and a quantized electromagnetic field, violates this…
We introduce a modified Jaynes-Cummings model with single-photon cavity radiation field but with the atomic system instead of exchanging a single photon as in the Jaynes-Cummings model, it exchanges instead a squeezed photon. After a…
Quantum Rabi model has been exactly solved by employing the parameter-dependent unitary transformation method in both the occupation number representation and the Bargmann space. The analytical expressions for the complete energy spectrum…
We present a quantized model of harmonically confined dot atom with inherent damping in the presence of a transverse magnetic field. The model leads to a non hermitian Hamiltonian in real coordinate. We have analytically studied the effects…
The Rabi Hamiltonian, describing the coupling of a two-level system to a single quantized boson mode, is studied in the Bargmann-Fock representation. The corresponding system of differential equations is transformed into a canonical form in…
We study numerically the dynamics of the Rabi Hamiltonian, describing the interaction of a single cavity mode and a two-level atom without the rotating wave approximation, subjected to damping and dephasing reservoirs included via usual…
Symmetry transformations have proved useful in determining the algebraic structure and internal dynamical properties of physical systems. In the quantum Rabi model, invariance under parity symmetry transformation has been used to obtain…
The prototypical system constituted by a two-level atom interacting with a quantized single-mode electromagnetic field is described by the quantum Rabi model (QRM). The QRM is potentially valid at any light-matter interaction regime,…