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

Communications in Theoretical Physics

Solving Generalized Non-degenerate Two-Mode Two-Photon Jaynes–Cummings Model by Supersymmetric Unitary Transformation

Song Tong-Qiang, Zhu Yue-Jin

Published Jul 15, 2002• 6 citations
Publisher

Abstract

Based on supersymmetric quantum mechanics theory, we introduced a supersymmetric unitary transformation to diagonalize the Hamiltonian of non-degenerate two-mode two-photon Jaynes–Cummings models which include any forms of intensity-dependent coupling, field-dependent detuning, and field nonlinearity. Its eigenvalue, eigenstates, and time evolution of state vector are obtained.

DOI
10.1088/0253-6102/38/1/85

Related papers

Solving Generalized Non-degenerate Two-Mode Two-Photon Jaynes-Cummings Model by Supersymmetric Unitary Transformation

Song, Tong-Qiang, Жу +1 more

Based on supersymmetric quantum mechanics theory, we introduced a supersymmetric unitary transfor mation to diagonalize the Hamiltonian of non-degenerate two-mode two-photon Jaynes-Cummings models which include any forms of intensity-dependent coupling, field-dependent detuning, and field nonlinearity. Its eigenvalue, eigenstates,and time evolution of state vector are obtained.

理论物理通讯：英文版•Jan 1, 2002•2 citations

Solving a Generalized Jaynes-Cummings Model by Supersymmetric Unitary Transformation

Lu Huai-Xin, Wang Xiao-Qin, Fan Hong-Yi

For the generalized Jaynes-Cummings model Hamiltonian which can describe two collectively radiation atoms, we find its supersymmetric structure. Based on supersymmetric quantum mechanics theory, we introduce a supersymmetric unitary transformation, in which the supersymmetric unitary transformation operator can be constructed by supersymmetric generators of the super-Lie algebra, to diagonalize the Hamiltonian. On doing so, its eigenvalue and eigenstates are obtained.

Chinese Physics Letters•May 1, 2000•8 citations

Exactly solving the general non-degenerate multimode multiphoton Jaynes–Cummings model with field nonlinearity

Heng-Mei Li, Hong-Yi Fan

For the general non-degenerate multimode multiphoton Jaynes–Cummings (JC) model, including any forms of intensity-dependent coupling, field-dependent detuning and field nonlinearity, we obtain its energy eigenvalues and eigenstates via the supersymmetric unitary transformation (SUT) method. In addition, its pseudo-invariant eigen-operator (PIEO) is also found, which directly leads to the energy-level gap.

Journal of Physics A Mathematical and Theoretical•Sep 7, 2009•3 citations

Intensity-dependent and multi-photon Hamiltonian of two two-level atoms and two-mode field in a Kerr medium solved by virtue of supersymmetric unitary transformation

N. H. Abd El-Wahab, R. A. Zait

We consider a generalized multi-photon interaction of two collectively two-level atoms with two-mode of electromagnetic field in the presence of Kerr medium and intensity-dependent coupling. We show that this atomic system possesses supersymmetric structure. We solved this system by virtue of supersymmetric unitary transformation. The supersymmetric generators of this atomic system are constructed. The diagonalization of the corresponding Hamiltonian is performed by introducing a supersymmetric unitary transformation. Accordingly, the eigenvalues and eigenfunctions of the Hamiltonian of the atomic system are obtained. The time evolution of the atom–field wave functions is derived in an exact form for two cases of the initial states of the atoms and the field modes. Some quantum effects such as the second-order correlation function, cross-correlation, purity and Husimi Q-function are investigated. The effects of the Kerr medium, detuning parameter, intensity-dependent coupling and multi-photon transition on the evolution of these quantum effects are examined. We conclude that the supersymmetric unitary transformation method is very simple and can be applied to a variety of atomic systems which possess a supersymmetric structure.

Modern Physics Letters A•Mar 4, 2021•5 citations

Multiphoton Jaynes-Cummings model solved via supersymmetric unitary transformation

Huai-Xin Lu, Wang Xiao-qin

For multiphoton Jaynes-Cummings(JC) model Hamiltonian, we find its supersymmetric structure. Based on this, we introduce a supersymmetric unitary transformation to diagonalize the JC Hamiltonian, in so doing, its eigenvalues and eigenfunctions are obtained. The transition process is also calculated.

Chinese Physics•Aug 1, 2000•23 citations

Full spectrum of nonlinear Jaynes–Cummings and anti-Jaynes–Cummings models

Francesco Antonino Raffa, Mario Rasetti

The unitary transformation method is utilized for the closed form solution of the nonlinear generalization of the Jaynes–Cummings (JC) model, which includes arbitrary multiphoton and intensity-dependent interactions between radiation and matter. Specifically, the unitary transformation leading to the diagonalization of the relevant Hamiltonian is established and energy levels and eigenstates are derived. It is also shown that the results for the JC model can be extended to the anti-Jaynes–Cummings (AJC) model through the map between the two models.

International Journal of Quantum Information•Nov 29, 2017•2 citations
Based on supersymmetric quantum mechanics theory, we introduced a supersymmetric unitary transformation to diagonalize the Hamiltonian of non-degenerate two-mode two-photon Jaynes–Cummings models which include any forms of intensity-dependent coupling, field-dependent detuning, and field nonlinearity. Its eigenvalue, eigenstates, and time evolution of state vector are obtained.
We consider a generalized multi-photon interaction of two collectively two-level atoms with two-mode of electromagnetic field in the presence of Kerr medium and intensity-dependent coupling. We show that this atomic system possesses supersymmetric structure. We solved this system by virtue of supersymmetric unitary transformation. The supersymmetric generators of this atomic system are constructed. The diagonalization of the corresponding Hamiltonian is performed by introducing a supersymmetric unitary transformation. Accordingly, the eigenvalues and eigenfunctions of the Hamiltonian of the atomic system are obtained. The time evolution of the atom–field wave functions is derived in an exact form for two cases of the initial states of the atoms and the field modes. Some quantum effects such as the second-order correlation function, cross-correlation, purity and Husimi Q-function are investigated. The effects of the Kerr medium, detuning parameter, intensity-dependent coupling and multi-photon transition on the evolution of these quantum effects are examined. We conclude that the supersymmetric unitary transformation method is very simple and can be applied to a variety of atomic systems which possess a supersymmetric structure.
The unitary transformation method is utilized for the closed form solution of the nonlinear generalization of the Jaynes–Cummings (JC) model, which includes arbitrary multiphoton and intensity-dependent interactions between radiation and matter. Specifically, the unitary transformation leading to the diagonalization of the relevant Hamiltonian is established and energy levels and eigenstates are derived. It is also shown that the results for the JC model can be extended to the anti-Jaynes–Cummings (AJC) model through the map between the two models.