相关论文: Algebraic equations for the exceptional eigenspect…
In our recent paper (Li and Batchelor J. Phys. A: Math. Theor. 48, 454005 (2015)) we obtained exceptional points in the eigenspectrum of the generalized Rabi model in terms of a set of algebraic equations. We also gave a proof for the…
We study the spectrum of the generalized Rabi model in which co- and counter-rotating terms have different coupling strengths. It is also equivalent to the model of a two-dimensional electron gas in a magnetic field with Rashba and…
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…
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…
We investigate the energy spectrum for hybrid mechanical systems described by non-parity-symmetric quantum Rabi models. A set of analytical solutions in terms of the confluent Heun functions and their analytical energy spectrum are…
We develop a method to find analytical solutions for the eigenstates of the quantum Rabi model. These include symmetric, anti-symmetric and asymmetric analytic solutions given in terms of the confluent Heun functions. Both regular and…
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…
General concept of a gradation slicing is used to analyze polynomial solutions of ordinary differential equations (ODE) with polynomial coefficients, ${\cal L}\psi=0$, where ${\cal L}=\sum_l p_l(z) d_z^l$, $p_l(z)$ are polynomials, $z$ is a…
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…
This article presents a review of recent developments on various aspects of the quantum Rabi model. Particular emphasis is given on the exact analytic solution obtained in terms of confluent Heun functions. The analytic solutions for…
In this report, we have studied exceptional spectra of the two-qubit quantum Rabi model in two situations. Firstly, an exceptional spectra is achieved in resonant condition, in which the frequencies of two qubit and photon field satisfy…
We examine the energy surfaces of the driven Rabi model, also known as the biased or generalised Rabi model, as a function of the coupling strength and the driving term. The energy surfaces are plotted numerically from the known analytic…
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…
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 $N$…
We introduce the anisotropic two-photon Rabi model in which the rotating and counter rotating terms enters along with two different coupling constants. Eigenvalues and eigenvectors are studied with exact means. We employ a variation of 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 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 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 analytical exact solutions to the mixed quantum Rabi model (QRM) including both one- and two-photon terms are found by using Bogoliubov operators. Transcendental functions in terms of $4 \times 4$ determinants responsible for the exact…
We study the solvability of the time-independent matrix Schr\"odinger differential equations of the quantum Rabi model and its 2-photon and two-mode generalizations in Bargmann Hilbert spaces of entire functions. We show that the Rabi model…