相关论文: Level crossings and new exact solutions of the two…
By applying the Bogoliubov transformations and through the introduction of the Bargmann-Hilbert spaces, we obtain analytic representations of solutions to the driven Rabi model without ${\cal Z}_2$ symmetry, and the 2-photon and two-mode…
Exact spectrum of the two-photon Rabi Hamiltonian is found, proceeding in full analogy with the solution of standard (one-photon) Rabi Hamiltonian, published by Braak in Phys. Rev. Lett. 107, 100401 (2011). The Hamiltonian is rewritten as a…
The quantum Rabi model can be solved exactly by the Bargmann transformation from real coordinate to complex variable recently [Phys. Rev. Lett. \textbf{107}, 100401 (2011)]. By the extended coherent states, we recover this solution in an…
We present a new tractable quantum Rabi model for $N$-level atoms by extending the $\mathbb Z_2$ symmetry of the two-state Rabi model. The Hamiltonian is $\mathbb Z_N$ symmetric and allows the parameters in the level separation terms to be…
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…
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…
The analytically exact solutions to the two-photon Rabi-Stark model are given by using the Bogoliubov operators approach. Transcendental functions responsible for the exact solutions are derived. The zeros of the transcendental functions…
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…
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 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…
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…
The quantum Rabi-Stark model, where the linear dipole coupling and the nonlinear Stark-like coupling are present on an equal footing, are studied within the Bogoliubov operators approach. Transcendental functions responsible for the exact…
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 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 $N$…
This paper presents a proof of the existence of novel bound states of the two-photon quantum Rabi model at the collapse point. The two-photon Rabi model is interesting not only for its important role on non-linear light-matter interaction,…
Within the Segal-Bargmann representation, a generalized Rabi model is considered that includes both two-photon and asymmetric terms. It is shown that, through a suitable transformation, nearly exact solutions can be obtained using the Bethe…
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…
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…
A two-qutrit extension of the quantum Rabi model is studied. Despite its increased complexity, the model results to be integrable under specific, physically relevant conditions. This feature allows for the emergence of analytically…
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…