Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Collective behavior ofMbosonic modes interacting with a single two-level atom

G. Benivegna, ANTONINO MESSINA

Published Jun 1, 1988• 14 citations
Publisher

Abstract

The Hamiltonian describing, without the rotating-wave approximation (RWA), the linear interaction between M bosonic modes with an Einstein spectrum and a single two-level atom is exactly and canonically transformed introducing M suitable collective independent field modes, in such a way that only one among them is coupled to the atom. Some physical consequences of this fact are analyzed and, in particular, the existence of radiation-trapping phenomena together with the possibility of atomic absorption suppression is established. The applicability of the RWA to this system is discussed and the importance of the effective-field statistics for the time evolution of the system is pointed out.

DOI
10.1103/physreva.37.4747

Related papers

Atom–field interaction without the rotating-wave approximation: quasi-classical trajectories

G. A. Finney, Julio R. Gea-Banacloche

We study the interaction between a two-level system and a harmonic oscillator without the rotating-wave approximation (RWA). In quantum optics, this model (sometimes called the spin-boson model) is traditionally thought of as a two-Ievel atom coupled to a single-mode radiation field, but it could also describe (1) a two-level ion in a trap coupled to the motion of its own center of mass or (2) a two-level particle in a solid coupled to a phonon mode. For sufficiently strong coupling, this model is known to exhibit chaos in a variety of semi-classical approximations.1

•May 8, 1994•0 citations

Interaction of aΛ-type three-level atom with a single-mode field without rotating wave approximation: perturbation theory approach

M Rastegarzadeh, Mohammad Kazem Tavassoly

In this article, by using the perturbation theory, we analytically solve the eigenvalue problem for the Hamiltonian describing the interaction of a Λ -type three-level atom with a single-mode radiation field without the rotating wave approximation (RWA). For this purpose, the atom–field interaction Hamiltonian, which contains the counter-rotating terms (CRTs), is transformed to an analytically solvable Hamiltonian by applying three successive unitary transformations. According to our calculations, the contribution of CRTs within the transformed Hamiltonian is in fact replaced by transforming the 'constant detuning' with the 'intensity-dependent detuning' in the first order, and the 'constant atom–field coupling' with the intensity-dependent coupling in the second order of the perturbation parameters. Then, by solving the eigenvalue problem for the transformed Hamiltonian, the eigenvector of the considered atom–field Hamiltonian is obtained analytically. Finally, after achieving the state vector of the atom–field system at an arbitrary time, a few nonclassical properties of the system state are investigated numerically. Meanwhile, we compare our results with the presence of RWA, from which the role of CRTs will be established.

Physica Scripta•Jan 28, 2015•19 citations

Interaction of a two-level atom with single-mode optical field beyond the rotating wave approximation

Ju Liu, Zhiyuan Li

One of the simplest models involving the atom-field interaction is the coupling of a single two-level atom with single-mode optical field. Under the rotating wave approximation, this problem is reduced to a form that can be solved exactly. But the approximation is only valid when the two levels are resonant or nearly resonant with the applied electromagnetic radiation. Here we present an analytical solution without the rotating wave approximation and applicable to general atom-field interaction far away from the resonance. We find that there exists remarkable influence of the initial phase of optical field on the Rabi oscillations and Rabi splitting, and this issue cannot be explored in the context of the rotating wave approximation. Due to the retention of the counter-rotating terms, higher-order harmonic appears during the Rabi splitting. The analytical solution suggests a way to regulate and control the quantum dynamics of a two-level atom and allows for exploring more essential features of the atom-field interaction.

Optics Express•Nov 10, 2014•12 citations

Study of Squeezing Properties in a Two-level System

Rui-hua Xie, Gong-ou Xu, Dun-huan Liu

We have studied the squeezing properties of a field and atom in a two-level system. The influence of nonlinear interactions (Le. the arbitrary intensity-dependent coupling of a single-mode field to a single two-level atom, the nonlinear interaction of the field with a nonlinear Kerr-like medium) on the squeezing is discussed in detail in the rotating wave approximation (RWA). We show numerically that the effect of the virtual-photon field suppresses dipole squeezing predicted in the RWA and leads to an increased squeeze revival period; the suppressed squeezing can be revived due to the presence of the nonlinear Kerr-like medium.

Australian Journal of Physics•Dec 1, 1995•9 citations

Structure and properties of the ground state of a two-level system arbitrarily coupled to a boson mode including the counter-rotating terms

G. Benivegna, ANTONINO MESSINA

The structure of the ground state of the Hamiltonian of a two-level system linearly coupled to a single mode of a radiation Bose-like field is studied for arbitrary values of the coupling constant including the counter-rotating terms. First of all the Hamiltonian is canonically transformed, introducing a new set of unitary operators in such a way that the eigenstates of the transformed Hamiltonian are exactly factorizable into eigenstates of the new pseudospin (1/2) and of the new field. The ground state is then found by a variational procedure. The validity of the results obtained by this approach is shown introducing a suitable class of canonical transformations by which it is possible to see that this variational ground state differs from the exact one only for perturbative contributions for which we give explicit expressions. Furthermore, we present investigations on the properties of this system in its ground state based on the calculation of the covariance of suitable pairs of operators. In this way we succeed in obtaining, among other things, a physically transparent meaning for the mathematical variational condition which determines the ground state.

Physical Review A•Apr 1, 1987•19 citations

Physical background for parameters of the quantum Rabi model

И. Д. Феранчук, А. В. Леонов, O. D. Skoromnik

Abstract We investigate the applicability of the two major approximations which are most commonly employed in the study of the quantum Rabi model, namely the description of a resonant cavity mode as a single-mode quantized field and the use of the rotating wave approximation. Starting from the Hamiltonian of a two-level system interacting with a multi-mode quantized field, we perform the canonical transformation of the field operators. This allows one to partition the Hamiltonian of the system into two parts. The first part is the interaction of the two-level system with a single collective field mode, while the second one describes the interaction with field fluctuations. The first part is usually associated with the resonant cavity mode. This division enables us to determine the applicability condition of the single-mode approximation. In addition we identify simple approximate relations for the description of the eigenstates, eigenfunctions and the time evolution of the quantum Rabi model beyond the rotating wave approximation.

arXiv:1606.09146•Journal of Physics A Mathematical and Theoretical•Oct 13, 2016•10 citations
The Hamiltonian describing, without the rotating-wave approximation (RWA), the linear interaction between M bosonic modes with an Einstein spectrum and a single two-level atom is exactly and canonically transformed introducing M suitable collective independent field modes, in such a way that only one among them is coupled to the atom. Some physical consequences of this fact are analyzed and, in particular, the existence of radiation-trapping phenomena together with the possibility of atomic absorption suppression is established. The applicability of the RWA to this system is discussed and the importance of the effective-field statistics for the time evolution of the system is pointed out.
We study the interaction between a two-level system and a harmonic oscillator without the rotating-wave approximation (RWA). In quantum optics, this model (sometimes called the spin-boson model) is traditionally thought of as a two-Ievel atom coupled to a single-mode radiation field, but it could also describe (1) a two-level ion in a trap coupled to the motion of its own center of mass or (2) a two-level particle in a solid coupled to a phonon mode. For sufficiently strong coupling, this model is known to exhibit chaos in a variety of semi-classical approximations.1
In this article, by using the perturbation theory, we analytically solve the eigenvalue problem for the Hamiltonian describing the interaction of a Λ -type three-level atom with a single-mode radiation field without the rotating wave approximation (RWA). For this purpose, the atom–field interaction Hamiltonian, which contains the counter-rotating terms (CRTs), is transformed to an analytically solvable Hamiltonian by applying three successive unitary transformations. According to our calculations, the contribution of CRTs within the transformed Hamiltonian is in fact replaced by transforming the 'constant detuning' with the 'intensity-dependent detuning' in the first order, and the 'constant atom–field coupling' with the intensity-dependent coupling in the second order of the perturbation parameters. Then, by solving the eigenvalue problem for the transformed Hamiltonian, the eigenvector of the considered atom–field Hamiltonian is obtained analytically. Finally, after achieving the state vector of the atom–field system at an arbitrary time, a few nonclassical properties of the system state are investigated numerically. Meanwhile, we compare our results with the presence of RWA, from which the role of CRTs will be established.
One of the simplest models involving the atom-field interaction is the coupling of a single two-level atom with single-mode optical field. Under the rotating wave approximation, this problem is reduced to a form that can be solved exactly. But the approximation is only valid when the two levels are resonant or nearly resonant with the applied electromagnetic radiation. Here we present an analytical solution without the rotating wave approximation and applicable to general atom-field interaction far away from the resonance. We find that there exists remarkable influence of the initial phase of optical field on the Rabi oscillations and Rabi splitting, and this issue cannot be explored in the context of the rotating wave approximation. Due to the retention of the counter-rotating terms, higher-order harmonic appears during the Rabi splitting. The analytical solution suggests a way to regulate and control the quantum dynamics of a two-level atom and allows for exploring more essential features of the atom-field interaction.
We have studied the squeezing properties of a field and atom in a two-level system. The influence of nonlinear interactions (Le. the arbitrary intensity-dependent coupling of a single-mode field to a single two-level atom, the nonlinear interaction of the field with a nonlinear Kerr-like medium) on the squeezing is discussed in detail in the rotating wave approximation (RWA). We show numerically that the effect of the virtual-photon field suppresses dipole squeezing predicted in the RWA and leads to an increased squeeze revival period; the suppressed squeezing can be revived due to the presence of the nonlinear Kerr-like medium.
The structure of the ground state of the Hamiltonian of a two-level system linearly coupled to a single mode of a radiation Bose-like field is studied for arbitrary values of the coupling constant including the counter-rotating terms. First of all the Hamiltonian is canonically transformed, introducing a new set of unitary operators in such a way that the eigenstates of the transformed Hamiltonian are exactly factorizable into eigenstates of the new pseudospin (1/2) and of the new field. The ground state is then found by a variational procedure. The validity of the results obtained by this approach is shown introducing a suitable class of canonical transformations by which it is possible to see that this variational ground state differs from the exact one only for perturbative contributions for which we give explicit expressions. Furthermore, we present investigations on the properties of this system in its ground state based on the calculation of the covariance of suitable pairs of operators. In this way we succeed in obtaining, among other things, a physically transparent meaning for the mathematical variational condition which determines the ground state.
Abstract We investigate the applicability of the two major approximations which are most commonly employed in the study of the quantum Rabi model, namely the description of a resonant cavity mode as a single-mode quantized field and the use of the rotating wave approximation. Starting from the Hamiltonian of a two-level system interacting with a multi-mode quantized field, we perform the canonical transformation of the field operators. This allows one to partition the Hamiltonian of the system into two parts. The first part is the interaction of the two-level system with a single collective field mode, while the second one describes the interaction with field fluctuations. The first part is usually associated with the resonant cavity mode. This division enables us to determine the applicability condition of the single-mode approximation. In addition we identify simple approximate relations for the description of the eigenstates, eigenfunctions and the time evolution of the quantum Rabi model beyond the rotating wave approximation.