Related papers: Parameter-dependent unitary transformation approac…
We formulate a universal method for solving an arbitrary quantum system which, in the Bargmann representation, is described by a system of linear equations with one independent variable, such as one- and multi-photon Rabi models, or $N$…
The Rabi model that describes the fundamental interaction between a two-level system with a quantized harmonic oscillator is one of the simplest and most ubiquitous models in modern physics. However, this model has not been solved exactly…
The two-mode quantum Rabi model with bilinear coupling is studied using extended squeezed states. We derive $G$-functions for each Bargmann index $q$% . They share a common structure with the $G$-function of the one-photon and two-photon…
The quantum Rabi model is a widespread description of the coupling between a two-level system and a quantized single mode of an electromagnetic resonator. Issues about this model's gauge invariance have been raised. These issues become…
The quantum Rabi model is essential for understanding interacting quantum systems. It serves as the simplest non-integrable yet solvable model describing the interaction between a two-level system and a single mode of a bosonic field. In…
The quantum Rabi model is a widespread description for the coupling between a two-level system and a quantized single mode of an electromagnetic resonator. Issues about this model's gauge invariance have been raised. These issues become…
We discuss the elementary errors in D.G. Zhang's [New. J. Phys. 23, 093014 (2021)] claimed exact solution of the quantum Rabi model. The erroneous solution is seen to be nothing more than the combined solution of the simpler Jaynes-Cummings…
We study an intensity-dependent quantum Rabi model that can be written in terms of SU(1,1) group elements and is related to the Buck-Sukumar model for the Bargmann parameter $k=1/2$. The spectrum seems to present avoiding crossings for all…
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…
Using extended coherent states, an analytically exact study has been carried out for the quantum Rabi model with two equivalent qubits. Compact transcendental functions of one variable have been derived leading to exact solutions. The…
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…
We investigate a generalisation of the Rabi system in the Bargmann-Fock representation. In this representation the eigenproblem of the considered quantum model is described by a system of two linear differential equations with one…
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 introduce the cross-cavity quantum Rabi model describing the interaction of a single two-level system with two orthogonal boson fields and propose its quantum simulation by two-dimensional, bichromatic, first-sideband driving of a single…
We explore the spectral problem of the two photon Rabi model from the point of view of complex differential equations in the Bargmann representation. The wave-functions are automatically entire but to ensure finite norm one has to…
We consider the transition from discrete to continuous spectrum which occurs in some quantum Rabi models. The subordinacy theory is used to detect and locate the essential spectrum of the intensity-dependent Rabi model, the anisotropic…
We explore an extended quantum Rabi model describing the interaction between a two-mode bosonic field and a three-level atom. Quantum phase transitions of this few degree of freedom model is found when the ratio $\eta$ of the atom energy…
We discuss the physics of the Rabi-Hubbard model describing large arrays of coupled cavities interacting with two level atoms via a Rabi non-linearity. We show that the inclusion of counter-rotating terms in the light-matter interaction,…
It is shown that in the Rabi model, for an integer value of the spectral parameter $x$, in addition to the finite number of the classical Judd states there exist infinitely many possible eigenstates. These eigenstates exist if the…
The anisotropic two-photon quantum Rabi model is studied using the Bogoliubov operator approach. The doubly degenerate exceptional states are identified through analytical methods. By adjusting the position of the last exceptional point…