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

Journal of Anqing Teachers College

Application of SU(2)canonical transformation and pseudo vector model in the nondegenerate two photon jaynes cumming model

Liang Jun

Published Jan 1, 2001• 0 citations
OpenAlex

Abstract

An exact solution of nondegenerate two photon J C model are derived by the way of SU(2) linear canonical transformation and pseudo vector model.The dynamic formula of the system are shown.

Related papers

SU(2) and SU(1,1) Rotation Transformation and Pseudo-vector Model in Quantum Optics

H.Q. Gong

We construct a pseudo-vector model and realize the rotation transformation for the SU(2) and SU(1,1) dynamics. We introduce concepts of the pseudo-scalar and the scalar product in quantum optics. Several equivalents of the SU(2) and SU(1,1) unified rotation operator are given. By using this method, the two- and three-level Jaynes-Cummings model is discussed in the non-rotating wave approximation.

Journal of Modern Optics•Nov 1, 1992•1 citation

SU(2) linear canonical transformation and dynamics in the multiphoton Jaynes-Cummings interaction

Han-Qian Gong

The formulation of the evolution operator for the multiphoton Jaynes-Cummings interaction in the decomposition form is presented, in terms of the SU(2) rotation transformation proposed by the present author [J. Mod. Opt. 39, 2209 (1992)]. The study of the dynamical evolution of the photon statistics for the case of intensity dependent coupling with m-photon atomic transition exhibits a number of novel features (sub-Poissonian and oscillatory distributions). It is shown that for m=1 the field distribution oscillates exactly in a periodic sequence without the limitation of the large mean photon number n-bar, and that for m=2 the oscillatory distributions emerge at one-quarter and three-quarters of the revival time for the initially high boson excitation regardless of the initial condition of the atomic state.

Physical Review A•Jan 1, 1997•3 citations

Dynamics of the two-atom Jaynes-Cummings model with nondegenerate two-photon transitions

Eugene K. Bashkirov

An exact solution is found for the collective model of two identical two-level atoms that resonantly interact with a two-mode quantum electromagnetic field in an ideal cavity via two-photon nondegenerate transitions. In the case under study, at the initial moment, both field modes are in the coherent state and atoms are in the excited state. The time dependences of the atomic probabilities, the mean number of photons in the modes, and the statistics and squeezing of the photon modes are studied based on the exact solution.

Laser Physics•Aug 1, 2006•31 citations

Exact Solutions for Two-Photon Jaynes-Cummings Model with Dynamic Stark-Shifts

Hiroshi Iwasawa, Kuniaki Matsuo

The solutions for the degenerate two-photon Jaynes-Cummings model are investigated in the presence of the dynamic Stark-shifts. By using the Heisenberg equations of motion, the operator differential equations are established from the effective Hamiltonian. The exact solutions for these operators are derived and the effects of the Stark-shifts on the atomic and field dynamics are discussed. Especially, the behavior of the atomic population difference for the simplest case is demonstrated.

Journal of the Physical Society of Japan•Oct 1, 1999•3 citations

Quantum Jaynes–Cummings model for a two-level system with effects of parametric time-dependences

Mounira Berrehail, Nadjet Benchiheub, Salah Menouar +1 more

An approach to exact quantum solutions of the time-dependent two energy level Jaynes–Cummings model with an imaginary photon process is represented in this work. The Lewis–Riesenfeld invariant treatment and the unitary transformation method are used for this purpose. The original Schrödinger equation is reduced to an equivalent solvable one through unitary transformations by using suitable unitary operators. The reduced equation corresponds to a simpler Hamiltonian which is written as a linear combination of the generators of the reduced-dimensional SU(2) algebra. A Hermitian invariant operator is constructed based on the same algebraic formulation and its instantaneous eigenfunctions are obtained. By utilizing such eigenfunctions, the complete quantum wave functions of the system are evaluated. Such wave functions are necessary when we analyze the quantum characteristics of the system.

Lithuanian Journal of Physics•Apr 24, 2022•2 citations

Exact Solutions for Non-degenerate Two-Photon Jaynes–Cummings Model in the Presence of Dynamic Stark-Shifts

Hiroshi Iwasawa, Kuniaki Matsuo

The exact solutions for the non-degenerate tow-photon Jaynes–Cummings model in the presence of the dynamic Stark-shifts are investigated. The Heisenberg equations of motion for the respective operators are established and the exact solutions are obtained. It will be shown how the presence of the Stark-shifts in the model influences the solutions of the operator differential equation.

Journal of the Physical Society of Japan•Jul 15, 2004•0 citations
The formulation of the evolution operator for the multiphoton Jaynes-Cummings interaction in the decomposition form is presented, in terms of the SU(2) rotation transformation proposed by the present author [J. Mod. Opt. 39, 2209 (1992)]. The study of the dynamical evolution of the photon statistics for the case of intensity dependent coupling with m-photon atomic transition exhibits a number of novel features (sub-Poissonian and oscillatory distributions). It is shown that for m=1 the field distribution oscillates exactly in a periodic sequence without the limitation of the large mean photon number n-bar, and that for m=2 the oscillatory distributions emerge at one-quarter and three-quarters of the revival time for the initially high boson excitation regardless of the initial condition of the atomic state.
An exact solution is found for the collective model of two identical two-level atoms that resonantly interact with a two-mode quantum electromagnetic field in an ideal cavity via two-photon nondegenerate transitions. In the case under study, at the initial moment, both field modes are in the coherent state and atoms are in the excited state. The time dependences of the atomic probabilities, the mean number of photons in the modes, and the statistics and squeezing of the photon modes are studied based on the exact solution.
An approach to exact quantum solutions of the time-dependent two energy level Jaynes–Cummings model with an imaginary photon process is represented in this work. The Lewis–Riesenfeld invariant treatment and the unitary transformation method are used for this purpose. The original Schrödinger equation is reduced to an equivalent solvable one through unitary transformations by using suitable unitary operators. The reduced equation corresponds to a simpler Hamiltonian which is written as a linear combination of the generators of the reduced-dimensional SU(2) algebra. A Hermitian invariant operator is constructed based on the same algebraic formulation and its instantaneous eigenfunctions are obtained. By utilizing such eigenfunctions, the complete quantum wave functions of the system are evaluated. Such wave functions are necessary when we analyze the quantum characteristics of the system.