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

Chinese Journal of Physics

Algebraic Structure and Analytic Solutions of a Moving V-Type Three-Level Atom Interacting with a Two-Mode Cavity Field

Cuiling Zhang, Rui Dang, Jiali Zhang

Published Dec 1, 2013• 0 citations
Publisher

Abstract

In the framework of algebraic dynamics, the dynamics of a V-type three-level atom interacting with a two-mode of the quantized cavity field is considered with atomic center-of-mass motion included. The general analytical expressions for the linearized Hamiltonian and the reduced density operator are derived, which can be used to calculate the expectation values of any system operators. As an illustration, analytical expressions for the optical forces are obtained.

DOI
10.6122/cjp.51.1241

Related papers

Dynamics of atom-cavity system and elimination of momentum recoil

Li-Xiang Cen, Shun-Jin Wang

In the framework of algebraic dynamics, we investigate an atom-cavity system with atomic centre-of-mass motion included. Using nonlinear transformations, the Hamiltonian is linearized in terms of Lie algebraic generators so that the algebraic dynamical structure of the system appears quite clear and its solution is easy to handle by an algebraic dynamical method. In more detail, for the three-level system of Ξ configuration, we show that the momentum recoil of the atom can be eliminated under certain conditions.

Journal of Physics A Mathematical and General•May 5, 2000•4 citations

Light forces on moving atom in micro-cavity

Cai-Ying Ding, Lei Tan, Liwei Liu +2 more

Optical forces on moving atom were investigated in micro-cavity using fully quantum theory. In terms of the models of moving atom interacting with micro-cavity field, using algebraic dynamics method, the Hamiltonian can be diagonalized by introducing a canonical transformation. The expression of evolution operator of the system and reduced density operators are calculated straightforwardly. Analytical expressions for the forces are obtained, and the forces are discussed for a traveling-wave field and a standing-wave field respectively.

Acta Physica Sinica•Jan 1, 2008•1 citation

Moving atom-field interaction: Quantum motional decoherence and relaxation

Sanjiv Shresta, B. L. Hu

The reduced dynamics of an atomic qubit coupled both to its own quantized center of mass motion through the spatial mode functions of the electromagnetic field, as well as the vacuum modes, is calculated in the influence functional formalism. The formalism chosen can describe the entangled non-Markovian evolution of the system with a full account of the coherent back-action of the environment on the qubit. We find a slight increase in the decoherence due to the quantized center of mass motion and give a condition on the mass and qubit resonant frequency for which the effect is important. In optically resonant alkali-metal atom systems, we find the effect to be negligibly small. The framework presented here can nevertheless be used for general considerations of the coherent evolution of qubits in moving atoms in an electromagnetic field.

arXiv:quant-ph/0301180•Physical Review A•Jul 24, 2003•10 citations

Semiclassical interaction of moving two-level atoms with a cavity field: From integrability to Hamiltonian chaos

Sergey V. Prants, Leonid E. Kon’kov, Igor Leonidovich Kirilyuk

The dynamics of an ensemble of two-level atoms moving through a single-mode lossless cavity is investigated in the semiclassical and rotating-wave approximations. The dynamical system for the expectation values of the atomic and field observables is considered as a perturbation to one of the following integrable versions: (i) a model with atoms moving through a spatially inhomogeneous resonant field, and (ii) a model with atoms interacting with a nonresonant eigenmode which is assumed to be homogeneous on the cavity size. We find the general exact solutions for both the models and show that they contain special solutions describing a coherent effect of population and radiation trapping. Using the Melnikov method, we prove analytically transverse intersections of stable and unstable manifolds of a hyperbolic fixed point under a small modulation of the vacuum Rabi frequency. These intersections are believed to provide the Smale horseshoe mechanism of Hamiltonian chaos. The analytical results are accompanied with direct computation of topographical maps of maximal Lyapunov exponents that give a representative image of regularity and chaos in the atom-field system in different ranges of its control parameters--the frequency detuning, the number, and the velocity of atoms.

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•Jul 1, 1999•31 citations

A three-level atom interacting with a single mode cavity field: different configurations

N. H. Abdel-Wahab

In this paper, the problem of a three-level atom interacting with a single mode of the quantized electromagnetic cavity field is considered. The considered theoretical model describes the distinct configurations of a three-level atom. Also, this model includes a detuning and arbitrary forms of both the field and the intensity-dependent atom-field coupling. We obtain the general forms for both the constants of motion and the wavefunction when the atom is initially prepared in one of its states. We use this model for computing a number of statistical aspects of the three-level system. As an illustration, we use the model for studying the time evolution of the second-order correlation function when the atom is initially in an upper state and the field is considered in a coherent state.

Physica Scripta•Jul 27, 2007•42 citations

AN ALGEBRAIC APPROACH TO THE INTERACTION OF A THREE-LEVEL ATOM INTERACTING WITH QUANTIZED RADIATION FIELD

Xu‐Bo Zou, Jing‐Bo Xu, Xiao-Chun Gao +1 more

The system of a three-level atom in the Ξ configuration coupled to two quantized field modes with arbitrary detuning and density-dependent multiphoton interaction is studied by dynamical algebraic method. With the help of an su(3) algebraic structure, we diagonalize the Hamiltonian by making use of unitary transformations and obtain the eigenvalues, eigenstates and time evolution operator for the system. Based on this su(3) structure, we also show that the system of a three-level atom in the Ξ configuration can be exactly transformed to an effective two-level Hamiltonian by an unitary transformation. Finally, we show that there exist an su (N) algebraic structure in the system of a N-level atom interacting with N-1 field modes.

International Journal of Modern Physics B•Jun 10, 2000•0 citations
In the framework of algebraic dynamics, the dynamics of a V-type three-level atom interacting with a two-mode of the quantized cavity field is considered with atomic center-of-mass motion included. The general analytical expressions for the linearized Hamiltonian and the reduced density operator are derived, which can be used to calculate the expectation values of any system operators. As an illustration, analytical expressions for the optical forces are obtained.
In the framework of algebraic dynamics, we investigate an atom-cavity system with atomic centre-of-mass motion included. Using nonlinear transformations, the Hamiltonian is linearized in terms of Lie algebraic generators so that the algebraic dynamical structure of the system appears quite clear and its solution is easy to handle by an algebraic dynamical method. In more detail, for the three-level system of Ξ configuration, we show that the momentum recoil of the atom can be eliminated under certain conditions.
Optical forces on moving atom were investigated in micro-cavity using fully quantum theory. In terms of the models of moving atom interacting with micro-cavity field, using algebraic dynamics method, the Hamiltonian can be diagonalized by introducing a canonical transformation. The expression of evolution operator of the system and reduced density operators are calculated straightforwardly. Analytical expressions for the forces are obtained, and the forces are discussed for a traveling-wave field and a standing-wave field respectively.
The reduced dynamics of an atomic qubit coupled both to its own quantized center of mass motion through the spatial mode functions of the electromagnetic field, as well as the vacuum modes, is calculated in the influence functional formalism. The formalism chosen can describe the entangled non-Markovian evolution of the system with a full account of the coherent back-action of the environment on the qubit. We find a slight increase in the decoherence due to the quantized center of mass motion and give a condition on the mass and qubit resonant frequency for which the effect is important. In optically resonant alkali-metal atom systems, we find the effect to be negligibly small. The framework presented here can nevertheless be used for general considerations of the coherent evolution of qubits in moving atoms in an electromagnetic field.
The dynamics of an ensemble of two-level atoms moving through a single-mode lossless cavity is investigated in the semiclassical and rotating-wave approximations. The dynamical system for the expectation values of the atomic and field observables is considered as a perturbation to one of the following integrable versions: (i) a model with atoms moving through a spatially inhomogeneous resonant field, and (ii) a model with atoms interacting with a nonresonant eigenmode which is assumed to be homogeneous on the cavity size. We find the general exact solutions for both the models and show that they contain special solutions describing a coherent effect of population and radiation trapping. Using the Melnikov method, we prove analytically transverse intersections of stable and unstable manifolds of a hyperbolic fixed point under a small modulation of the vacuum Rabi frequency. These intersections are believed to provide the Smale horseshoe mechanism of Hamiltonian chaos. The analytical results are accompanied with direct computation of topographical maps of maximal Lyapunov exponents that give a representative image of regularity and chaos in the atom-field system in different ranges of its control parameters--the frequency detuning, the number, and the velocity of atoms.
In this paper, the problem of a three-level atom interacting with a single mode of the quantized electromagnetic cavity field is considered. The considered theoretical model describes the distinct configurations of a three-level atom. Also, this model includes a detuning and arbitrary forms of both the field and the intensity-dependent atom-field coupling. We obtain the general forms for both the constants of motion and the wavefunction when the atom is initially prepared in one of its states. We use this model for computing a number of statistical aspects of the three-level system. As an illustration, we use the model for studying the time evolution of the second-order correlation function when the atom is initially in an upper state and the field is considered in a coherent state.
The system of a three-level atom in the Ξ configuration coupled to two quantized field modes with arbitrary detuning and density-dependent multiphoton interaction is studied by dynamical algebraic method. With the help of an su(3) algebraic structure, we diagonalize the Hamiltonian by making use of unitary transformations and obtain the eigenvalues, eigenstates and time evolution operator for the system. Based on this su(3) structure, we also show that the system of a three-level atom in the Ξ configuration can be exactly transformed to an effective two-level Hamiltonian by an unitary transformation. Finally, we show that there exist an su (N) algebraic structure in the system of a N-level atom interacting with N-1 field modes.