© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

Lithuanian Journal of Physics

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

Mounira Berrehail, Nadjet Benchiheub, Salah Menouar, Jeong Ryeol Choi

Published Apr 24, 2022• 2 citations

Abstract

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.

DOI: 10.3952/physics.v62i1.4694

Related papers

An Approach to Exact Solutions of the Time-dependent Supersymmetric Two-Level Three-Photon Jaynes–Cummings Model

Jian-Qi Shen, Hongyi Zhu, Hong Mao

By utilizing the property of the supersymmetric structure in the two-level multiphoton Jaynes-Cummings model, an invariant is constructed in terms of the supersymmetric generators by working in the sub-Hilbert-space corresponding to a particular eigenvalue of the conserved supersymmetric generators. We obtain the exact solutions of the time-dependent Schrödinger equation which describes the time-dependent supersymmetric two-level three-photon Jaynes-Cummings model (TLTJCM) by using the invariant-related unitary transformation formulation. The case under the adiabatic approximation is also discussed. Keywords: Supersymmetric Jaynes-Cummings model; exact solutions; invariant theory; geometric phase factor; adiabatic approximation

arXiv:math-ph/0302039•Journal of the Physical Society of Japan•Jun 15, 2002•15 citations

Exact solutions to the time-dependent supersymmetric Jaynes-Cummings model and the Chiao-Wu model

J.-Q. Shen, H.Y. Zhu

The present paper obtains the exact solutions to the time-dependent supersymmetric two-level multiphoton Jaynes-Cummings model and the Chiao-Wu model that describes the propagation of a photon inside an optical fiber. On the basis of the fact that the two-level multiphoton Jaynes-Cummings model possesses a supersymmetric structure, an invariant is constructed in terms of the supersymmetric generators by working in the sub-Hilbert-space corresponding to a particular eigenvalue of the conserved supersymmetric generators (i.e., the time-independent invariant). By constructing the effective Hamiltonian that describes the interaction of the photon with the medium of the optical fiber, it is further verified that the particular solution to the Schrödinger equation is the eigenfunction of the second-quantized momentum operator of photons field. This, therefore, means that the explicit expression (rather than the hidden form that involves the chronological product) for the time-evolution operator of wave function is obtained by means of the invariant theories.

arXiv:quant-ph/0305057•Annalen der Physik•Mar 20, 2003•8 citations

Exact solution for the thermo Jaynes–Cummings model

Yuan Hong-Chun, Fan Hong-Yi

Based on the construction of supersymmetric generators, we use the Lewis–Riesenfeld invariant method to deduce the exact and explicit eigen-energy spectrum with the time-dependent thermo Jaynes–Cummings model. One of the advantages of this approach is that it can transform the hidden form, related to the chronological product, of the time evolution operator into an explicit expression. Moreover, the dynamical and statistics properties of physical quantities are obtained for the given initial states in the thermo Jaynes–Cummings system.

Chinese Physics B•Dec 1, 2009•1 citation

Invariant theory and exact solutions of the time-dependent supersymmetric two-level multiphoton Jaynes-Cummings model

Shen Jian-Qi, Zhu Hong-Yi, Jian Bo Fu

On the basis of the fact that the two-level multiphoton Jaynes-Cummings (TLMJC) model possesses a supersymmetric structure, an invariant is constructed in terms of the supersymmetric generators by working in the sub-Hilbert-space corresponding to a particular eigenvalue of the conserved supersymmetric generators (the time-independent invariant). In this paper, we investigate the invariant-related unitary transformation approach to exact solutions of the time-dependent TLMJC model.

Chinese Physics•Dec 1, 2002•5 citations

Invariant theory and exact solutions of the time-dependent supersymmetric two-level multiphoton Jaynes－Cummings model

沈建其, 朱红毅, 符建

On the basis of the fact that the two-level multiphoton Jaynes-Cummings(TLMJC)model possesses a supersymmetric structure,an invariant is constructed in terms of the supersymmetric generators by working in the sub-Hilbertspace corresponding to a particular eigenvalue of the conserved supersymmetric generators(the time-independent invariant).In this paper,wew investigate the invariant-related unitary transformation approach to exact solutions of the time-dependent TLMJC model.

中国物理B：英文版•Jun 12, 2005•0 citations

Exact solutions to the time‐dependent supersymmetric Jaynes‐Cummings model and the Chiao‐Wu model

Jian Qi Shen, Haotian Zhu

Abstract The present paper obtains the exact solutions to the time‐dependent supersymmetric two‐level multiphoton Jaynes‐Cummings model and the Chiao‐Wu model that describes the propagation of a photon inside an optical fiber. On the basis of the fact that the two‐level multiphoton Jaynes‐Cummings model possesses a supersymmetric structure, an invariant is constructed in terms of the supersymmetric generators by working in the sub‐Hilbert‐space corresponding to a particular eigenvalue of the conserved supersymmetric generators (i.e., the time‐independent invariant). By constructing the effective Hamiltonian that describes the interaction of the photon with the medium of the optical fiber, it is further verified that the particular solution to the Schrödinger equation is the eigenfunction of the second‐quantized momentum operator of photons field. This, therefore, means that the explicit expression (rather than the hidden form that involves the chronological product) for the time‐evolution operator of wave function is obtained by means of the invariant theories.

Annalen der Physik•Mar 19, 2003•0 citations

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.

By utilizing the property of the supersymmetric structure in the two-level multiphoton Jaynes-Cummings model, an invariant is constructed in terms of the supersymmetric generators by working in the sub-Hilbert-space corresponding to a particular eigenvalue of the conserved supersymmetric generators. We obtain the exact solutions of the time-dependent Schrödinger equation which describes the time-dependent supersymmetric two-level three-photon Jaynes-Cummings model (TLTJCM) by using the invariant-related unitary transformation formulation. The case under the adiabatic approximation is also discussed. Keywords: Supersymmetric Jaynes-Cummings model; exact solutions; invariant theory; geometric phase factor; adiabatic approximation

The present paper obtains the exact solutions to the time-dependent supersymmetric two-level multiphoton Jaynes-Cummings model and the Chiao-Wu model that describes the propagation of a photon inside an optical fiber. On the basis of the fact that the two-level multiphoton Jaynes-Cummings model possesses a supersymmetric structure, an invariant is constructed in terms of the supersymmetric generators by working in the sub-Hilbert-space corresponding to a particular eigenvalue of the conserved supersymmetric generators (i.e., the time-independent invariant). By constructing the effective Hamiltonian that describes the interaction of the photon with the medium of the optical fiber, it is further verified that the particular solution to the Schrödinger equation is the eigenfunction of the second-quantized momentum operator of photons field. This, therefore, means that the explicit expression (rather than the hidden form that involves the chronological product) for the time-evolution operator of wave function is obtained by means of the invariant theories.

Based on the construction of supersymmetric generators, we use the Lewis–Riesenfeld invariant method to deduce the exact and explicit eigen-energy spectrum with the time-dependent thermo Jaynes–Cummings model. One of the advantages of this approach is that it can transform the hidden form, related to the chronological product, of the time evolution operator into an explicit expression. Moreover, the dynamical and statistics properties of physical quantities are obtained for the given initial states in the thermo Jaynes–Cummings system.

Abstract The present paper obtains the exact solutions to the time‐dependent supersymmetric two‐level multiphoton Jaynes‐Cummings model and the Chiao‐Wu model that describes the propagation of a photon inside an optical fiber. On the basis of the fact that the two‐level multiphoton Jaynes‐Cummings model possesses a supersymmetric structure, an invariant is constructed in terms of the supersymmetric generators by working in the sub‐Hilbert‐space corresponding to a particular eigenvalue of the conserved supersymmetric generators (i.e., the time‐independent invariant). By constructing the effective Hamiltonian that describes the interaction of the photon with the medium of the optical fiber, it is further verified that the particular solution to the Schrödinger equation is the eigenfunction of the second‐quantized momentum operator of photons field. This, therefore, means that the explicit expression (rather than the hidden form that involves the chronological product) for the time‐evolution operator of wave function is obtained by means of the invariant theories.