Related papers: Effective Hamiltonians in the Quantum Rabi Problem
We focus on the definition of the unitary transformation leading to an effective second order Hamiltonian, inside degenerate eigensubspaces of the non-perturbed Hamiltonian. We shall prove, by working out in detail the Su-Schrieffer-Heeger…
The symmetric quantum Rabi model (QRM) is integrable due to a discrete $\mathbb{Z}_2$-symmetry of the Hamiltonian. This symmetry is generated by a known involution operator, measuring the parity of the eigenfunctions. An experimentally…
Hyperfine atomic states are among the most promising candidates for qubit encoding in quantum information processing. In atomic systems, hyperfine transitions are typically driven through a two-photon Raman process by a laser field which is…
We study the coupling between collective variables of atomic spin and light polarization in an ensemble of cold 87Rb probed with polarized light. The effects of multiple hyperfine levels manifest themselves as a rank-2 tensor…
Representations of the rotation group may be formulated in second-quantised language via Schwinger's transcription of angular momentum states onto states of an effective two-dimensional oscillator. In the case of the molecular asymmetric…
The recent progress in the analytical solution of models invented to describe theoretically the interaction of matter with light on an atomic scale is reviewed. The methods employ the classical theory of linear differential equations in the…
It is shown that the Hamiltonian formalism proposed previously in [1] to describe the nonlinear dynamics of only {\it soft} fermionic and bosonic excitations contains much more information than initially assumed. In this paper, we have…
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…
Using a new class of exactly solvable models based on the pairing interaction, we show that it is possible to construct integrable Hamiltonians with a Wigner distribution of nearest neighbor level spacings. However, these Hamiltonians…
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…
We present the effective Hamiltonian for an electron-nucleus interaction in non-relativistic limit up to the second order in the inverse nucleon mass. This Hamiltonian takes into account the distortion of electron waves and allows to…
We present a non-perturbative framework for deriving effective Hamiltonians that describe low-energy excitations in quantum many-body systems. The method combines block diagonalization based on the Cederbaum--Schirmer--Meyer transformation…
We study a quantum dot strongly coupled to a single high-finesse optical microcavity mode. We use a rotating wave approximation method, commonly used in ion-laser interactions, tegether with the Lamb-Dicke approximation to obtain an…
We study effective light-matter interactions in a circuit QED system consisting of a single $LC$ resonator, which is coupled symmetrically to multiple superconducting qubits. Starting from a minimal circuit model, we demonstrate that in…
With the fast development of quantum technology, the sizes of both digital and analog quantum systems increase drastically. In order to have better control and understanding of the quantum hardware, an important task is to characterize the…
We study cold atoms in an optical lattice with synthetic spin-orbit coupling in the Mott-insulator regime. We calculate the parameters of the corresponding tight-binding model using Peierls substitution and "localized Wannier states method"…
Entanglement and quantum squeezing have wide applications in quantum technologies due to their non-classical characteristics. Here we study entanglement and quantum squeezing in an open spin-optomechanical system, in which a Rabi model (a…
In this paper we consider a quantum harmonic oscillator interacting with the electromagnetic radiation field in the presence of a boundary condition preserving the continuous spectrum of the field, such as an infinite perfectly conducting…
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…
We study the ground state phase diagram of a nonlinear two-photon Rabi-Hubbard (RH) model in one dimension using quantum Monte Carlo (QMC) simulations and density matrix renormalization group (DMRG) calculations. Our model includes a…