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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 employ a squeeze operator transformation approach to solve the anisotropic quantum Rabi model that includes a diamagnetic term. By carefully adjusting the amplitude of the diamagnetic term, we demonstrate that the anisotropic Rabi model…
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 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 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…
The interaction between an atom and a one mode external driving field is an ubiquitous problem in many branches of physics and is often modeled using the Rabi Hamiltonian. In this paper we present a series of analytically solvable…
The anisotropic Rabi model, which was proposed recently, differs from the original Rabi model: the rotating and counter-rotating terms are governed by two different coupling constants. This feature allows us to vary the counter-rotating…
We study the quantum Rabi model within the framework of the analytical solution developed in Phys. Rev. Lett. 107,100401 (2011). In particular, through time-dependent correlation functions, we give a quantitative criterion for classifying…
We propose the quantum simulation of the quantum Rabi model in all parameter regimes by means of detuned bichromatic sideband excitations of a single trapped ion. We show that current setups can reproduce, in particular, the ultrastrong and…
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 with squeezing…
We revisit the Jaynes-Cummings and anti-Jaynes-Cummings model through the lens of Lie theory, aiming to highlight the efficacy of an operator-based approach for diagonalization. We focus on explicitly delineating the steps from an…
The anisotropic Rabi model (ARM), which features tunable Jaynes-Cummings (JC) and anti-Jaynes-Cummings (AJC) interactions, has remained challenging to realize fully. We present a circuit QED implementation that provides static control over…
Using Hill's determinant method we show that the set of Judd's solutions is only a subset of all the eigenvalues with the form $E_n=n\omega-g^2/\omega$ in the spectrum of the Rabi model. Therefore Braak's solution of the quantum Rabi model…
The Jaynes-Cummings and quantum Rabi models are fundamental to cavity and circuit quantum electrodynamics, as they describe the simplest form of light-matter interaction, where a single qubit is coupled to a single bosonic mode. A scenario…
We study the ground state (GS) and excitation gap of anisotropic quantum Rabi model (QRM) which connects the fundamental QRM and the Jaynes-Cummings model (JCM). While the GS has a second-order quantum phase transition (QPT) in the low…
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 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…
We have generalized Einstein coefficients and rate equations from quantum field theoretic point of view by bringing the fundamental processes and the quantum Rabi oscillation in a single footing for the light-matter interactions for nonzero…
The dispersive regime of circuit QED is the main workhorse for todays quantum computing prototypes based on superconducting qubits. Analytic descriptions of this model typically rely on the rotating wave approximation of the interaction…
We discuss the Jaynes-Cummings model in different representations of the algebra of canonical commutation relations. The first conclusion is that all the irreducible representations lead to equivalent physical predictions. However, the…