Related papers: On the spectrum of a class of quantum models
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…
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…
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 investigate the large $n$ asymptotics of the $n$-th eigenvalue for a class of unbounded self-adjoint operators defined by infinite Jacobi matrices with discrete spectrum. In the case of the quantum Rabi model we obtain the first three…
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 $N$…
Quasi-exactly solvable Rabi model is investigated within the framework of the Bargmann Hilbert space of analytic functions ${\cal B}$. On applying the theory of orthogonal polynomials, the eigenvalue equation and eigenfunctions are shown to…
This article is a response to the continued assumption, cited even in reports and reviews of recent experimental breakthroughs and advances in theoretical methods, that the antiJaynes-Cummings (AJC) interaction is an intractable energy…
We investigate first- and second-order quantum phase transitions of the anisotropic quantum Rabi model, in which the rotating- and counter-rotating terms are allowed to have different coupling strength. The model interpolates between two…
We determine the Rabi oscillations for coherent and squeezed coherent states via one- and two-photon atomic transitions in two- and three-level atoms, respectively. The effect of squeezing coherent states is to reduce the large number of…
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…
Herein, we propose an experimentally feasible scheme to show the quantum phase transition of the Jaynes-Cummings (JC) model by modulating the transition frequency of a two-level system in a quantum Rabi model with strong coupling. By tuning…
In his recent letter, Braak suggested that a regular spectrum of the Rabi model was given by the zeros of a transcendental function $G_\pm(x)$ (cf Eqs. (3)-(5) of Ref. [1]) and highlighted the role of the discrete $\mathbb{Z}_2$-symmetry,…
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…
The Jaynes-Cummings model provides a well established theoretical framework for single electron two level systems in a radiation field. Similar exactly solvable models for semiconductor light emitters such as quantum dots dominated by many…
The quantum Rabi model is a paradigmatic example of a minimal yet nontrivial light-matter interaction, whose spectrum is transcendental yet exhibits a number of regularities. Braak observed that the eigenvalues bunch or anti-bunch following…
In this note we investigate the discrete spectrum of Jacobi matrix corresponding to polynomials defined by recurrence relations with periodic coefficients. As examples we consider a)the case when period $N$ of coefficients of recurrence…
Spectral collapse, the transition from discrete to continuous spectrum, is a characteristic in quantum Rabi models. We explore this phenomenon in the two-photon quantum Rabi model in optical phase space and find that, in the so-called…
The Rabi-Stark model is a non-linear generalization of the quantum Rabi model including the dynamical Stark shift as a tunable term, which can be realized via quantum simulation on a cavity QED platform. When the Stark coupling becomes…
The Jaynes-Cummings (JC) model is a milestone in the theory of coherent interaction between a two-level system and a single bosonic field mode. This tutorial aims to give a complete description of the model, analyzing the Hamiltonian of the…
In this work the spectral theory of self-adjoint operator $A$ represented by Jacobi matrix is considered. The approach is based on the continued fraction representation of the resolvent matrix element of $A$. Different criteria of absolute…