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 the Physical Society of Japan

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

Hiroshi Iwasawa, Kuniaki Matsuo

Published Jul 15, 2004• 0 citations
Publisher

Abstract

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.

DOI
10.1143/jpsj.73.1699

Related papers

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

Heisenberg Equations for Non-Degenerate Two-Photon Jaynes-Cummings Model with Dynamic Stark-Shifts

Kuniaki Matsuo, Hiroshi Iwasawa

One of the simplest models for the interactions between an atom and a quantized electromagnetic field is known as the Jaynes-Cummings model GCM) [1]. In this model, the atom is assumed to have two levels, and the electromagnetic field is a single mode. For the past several years, we have investigated the model for the singlephoton, the two-photon, and the multi-photon cases. First, we studied the characteristic functions and their time behaviors for a simple JCM[Z] using the density matrix approach, and then, by using the Heisenberg equation method, we exmined the degenerate two-photon JCM[31, where the operator differential equations and their solutions are obtained. We further studied the cases of the non-degenerate two-photon JCM[4] and the mUlti-photon JCM[51. Moreover, the atomic spectrum for mUlti-photon JCM[61 and the field spectrum for multiphoton JCM[71 were explored, and these spectra were presented in the 3-dimensional pictures. We also solved the degenerate two-photon JCM with Stark-shifts [8] , and further we just published the results of the non-degeneratetwo-photon JCM with Stark-shifts[91. In this paper, we show a derivaition of the product operator alZ ( t ) = al ( t ) az ( t ). We explicitly use the idea of the constant motion operator. Since the derivations are quite complicated and it is not streightword, we showed them in detail here. The present paper is organized as follows. In section II, we show the effective non-degenerate Hamiltonians and the constant of motion operators. In section Ill, the second-order differential equation for a product operator alZ ( t ) = al ( t ) az ( t) of Mode 1 and Mode 2, will

•Dec 1, 2004•0 citations

Exact solutions of Heisenberg equations for multiphoton Jaynes–Cummings model

H. Iwasawa, Kuniaki Matsuo

The Heisenberg operator solutions for the multiphoton Jaynes–Cummings model will be presented. By solving the operator differential equations, the exact solutions for the photon annihilation operator a(t), the atomic dipole-moment operator σ−(t), and the population difference operator σz(t) are obtained. The time dynamical behaviors for the operators are compared with the results obtained by the density operator methods.

Journal of Mathematical Physics•Jun 1, 1995•3 citations

Heisenberg-Picture Operators for Two-Photon Jaynes-Cummings Model

Hiroshi Iwasawa, Kuniaki Matsuo

The dynamics of the degenerate two-photon Jaynes-Cummings model in Heisenberg picture is investigated. By solving the Heisenberg equations, the exact solutions of the photon annihilation operator a( t), the atomic dipole moment operator σ-( t), and the population difference operator σ z ( t) are obtained. We demonstrate that the correlation functions for the photon annihilation and dipole moment operators can be directly evaluated from these exact solutions. The solutions of the time-evolution operators are shown to be quite useful in the calculation of two-time correlation functions. Furthermore, some results of the dynamical behavior of the average values for the photon number <n (t)>, the in-phase field component <X 1(t)>, and the population difference <σ z (t)> are demonstrated by computer simulations.

Japanese Journal of Applied Physics•Nov 1, 1994•5 citations

Decoherence described by Milburn's theory for the two-photon Jaynes-Cummings model with stark shift

Xin Chen, Le‐Man Kuang, Mo‐Lin Ge

The Milburn equation without diffusion approximation is solved exactly for the two-photon Jaynes-Cummings model in the presence of Stark shift. This allows the study of the decoherence problem in the whole range of the decoherence parameter gamma . The influence of decoherence on atomic inversion is studied. The dynamical behaviour is adjusted in the presence of Stark shift. It is shown that even in the presence of Stark shift the revivals of atomic inversion are destroyed in the decoherence process.

Journal of Physics A Mathematical and General•May 7, 1995•1 citation

Nonlinear dynamical evolution of the driven two-photon Jaynes-Cummings model

Amitabh Joshi

The driven two-photon Jaynes-Cummings model (JCM) exhibits a collapse and revival phenomenon in its mean photon number on a time scale much larger than the periodic revival time for two-state inversion in the usual two-photon JCM. The time scale of revivals for these oscillations is much larger than the corresponding time scale for the driven one-photon JCM and can be explained with the Hamiltonian of type ${H}_{\ensuremath{\eta}}=\ifmmode\pm\else\textpm\fi{}\sqrt{{(J}_{\ensuremath{\eta}}^{\ifmmode\dagger\else\textdagger\fi{}}+\ensuremath{\alpha}{P}_{\ensuremath{\eta}}{)}^{2}{(J}_{\ensuremath{\eta}}+\ensuremath{\alpha}{P}_{\ensuremath{\eta}}{)}^{2}}$ constructed explicitly for this purpose. The effect of Stark shifts is also studied and it is observed that the dynamics is strongly influenced by such Stark shifts both at early stages as well as at late stages of the evolution but in different ways, and thus Stark shifts play a significant role in determining the dynamical evolution of the system.

Physical Review A•Sep 15, 2000•48 citations
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.
One of the simplest models for the interactions between an atom and a quantized electromagnetic field is known as the Jaynes-Cummings model GCM) [1]. In this model, the atom is assumed to have two levels, and the electromagnetic field is a single mode. For the past several years, we have investigated the model for the singlephoton, the two-photon, and the multi-photon cases. First, we studied the characteristic functions and their time behaviors for a simple JCM[Z] using the density matrix approach, and then, by using the Heisenberg equation method, we exmined the degenerate two-photon JCM[31, where the operator differential equations and their solutions are obtained. We further studied the cases of the non-degenerate two-photon JCM[4] and the mUlti-photon JCM[51. Moreover, the atomic spectrum for mUlti-photon JCM[61 and the field spectrum for multiphoton JCM[71 were explored, and these spectra were presented in the 3-dimensional pictures. We also solved the degenerate two-photon JCM with Stark-shifts [8] , and further we just published the results of the non-degeneratetwo-photon JCM with Stark-shifts[91. In this paper, we show a derivaition of the product operator alZ ( t ) = al ( t ) az ( t ). We explicitly use the idea of the constant motion operator. Since the derivations are quite complicated and it is not streightword, we showed them in detail here. The present paper is organized as follows. In section II, we show the effective non-degenerate Hamiltonians and the constant of motion operators. In section Ill, the second-order differential equation for a product operator alZ ( t ) = al ( t ) az ( t) of Mode 1 and Mode 2, will
The dynamics of the degenerate two-photon Jaynes-Cummings model in Heisenberg picture is investigated. By solving the Heisenberg equations, the exact solutions of the photon annihilation operator a( t), the atomic dipole moment operator σ-( t), and the population difference operator σ z ( t) are obtained. We demonstrate that the correlation functions for the photon annihilation and dipole moment operators can be directly evaluated from these exact solutions. The solutions of the time-evolution operators are shown to be quite useful in the calculation of two-time correlation functions. Furthermore, some results of the dynamical behavior of the average values for the photon number <n (t)>, the in-phase field component <X 1(t)>, and the population difference <σ z (t)> are demonstrated by computer simulations.
The Milburn equation without diffusion approximation is solved exactly for the two-photon Jaynes-Cummings model in the presence of Stark shift. This allows the study of the decoherence problem in the whole range of the decoherence parameter gamma . The influence of decoherence on atomic inversion is studied. The dynamical behaviour is adjusted in the presence of Stark shift. It is shown that even in the presence of Stark shift the revivals of atomic inversion are destroyed in the decoherence process.
The driven two-photon Jaynes-Cummings model (JCM) exhibits a collapse and revival phenomenon in its mean photon number on a time scale much larger than the periodic revival time for two-state inversion in the usual two-photon JCM. The time scale of revivals for these oscillations is much larger than the corresponding time scale for the driven one-photon JCM and can be explained with the Hamiltonian of type ${H}_{\ensuremath{\eta}}=\ifmmode\pm\else\textpm\fi{}\sqrt{{(J}_{\ensuremath{\eta}}^{\ifmmode\dagger\else\textdagger\fi{}}+\ensuremath{\alpha}{P}_{\ensuremath{\eta}}{)}^{2}{(J}_{\ensuremath{\eta}}+\ensuremath{\alpha}{P}_{\ensuremath{\eta}}{)}^{2}}$ constructed explicitly for this purpose. The effect of Stark shifts is also studied and it is observed that the dynamics is strongly influenced by such Stark shifts both at early stages as well as at late stages of the evolution but in different ways, and thus Stark shifts play a significant role in determining the dynamical evolution of the system.