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

arXiv:physics/0609022 · Journal of Physics A Mathematical and General

The supersymmetric Jaynes–Cummings model and its solutions

Abdulaziz D Alhaidari

Published Nov 30, 2006• 5 citations
arXivHTMLPDF

Abstract

The super-algebraic structure of a generalized version of the Jaynes–Cummings model is investigated. We find that a Z 2 graded extension of the so (2,1) Lie algebra is the underlying symmetry of this model. It is isomorphic to the four-dimensional super-algebra u (1/1) with two odd and two even elements. Differential matrix operators are taken as realization of the elements of the superalgebra to which the model Hamiltonian belongs. Several examples with various choices of superpotentials are presented. The energy spectrum and corresponding wavefunctions are obtained analytically.

DOI
10.1088/0305-4470/39/50/007

Related papers

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

Exact solution for Super-Jaynes-Cummings model

Huai-Xin Lu, Wang Xiao-qing, Zhang Yong-de

Based on the linear quantum transformation theory, we further propose a supersymmetric unitary transformation, whose operator can be constructed by the supersymmetric generators of Lie superalgebra. Therefore, by making use of the supersymmetric unitary transformation, we can obtain the eigenspectrum, the eigenstates and the super-partition function for the Super-Jaynes-Cummings model when the coupling constants are Grassmann valued.

Chinese Physics•May 1, 2000•13 citations

Models for Supersymmetric Quantum Mechanics

Michael Baake, R. Delbourgo, PD Jarvis

An algebraic view of supersymmetric quantum mechanics is taken, emphasising the couplings between bosonic and fermionic modes in the supercharges. A class of model Hamiltonians is introduced wherein the fermionic (bosonic) operators are canonical and the bosonic (fermionic) ones satisfy a Lie algebra (superalgebra) whose representation theory permits the complete solution of the model in principle. The kinematical symmetry of such models is also described. The examples of one and two bosonic models, with 5U(2) and 5U(3) dynamical algebras respectively, are analysed in detail.

Australian Journal of Physics•Jun 1, 1991•0 citations

Underlying SUSY in a generalized Jaynes–Cummings model

F. H. Maldonado-Villamizar, Carlos A. González-Gutiérrez, L. Villanueva-Vergara +1 more

We present a general qubit-boson interaction Hamiltonian that describes the Jaynes-Cummings model and its extensions as a single Hamiltonian class. Our model includes non-linear processes for both the free qubit and boson field as well as non-linear, multi-boson excitation exchange between them. It shows an underlying algebra with supersymmetric quantum mechanics features allowing an operator based diagonalization that simplifies the calculations of observables. As a practical example, we show the evolution of the population inversion and the boson quadratures for an initial state consisting of the qubit in the ground state interacting with a coherent field for a selection of cases covering the standard Jaynes-Cummings model and some of its extensions including Stark shift, Kerr-like, intensity dependent coupling, multi-boson exchange and algebraic deformations.

arXiv:2010.13867•Scientific Reports•Aug 13, 2021•15 citations

Quantization of Some Generalized Jaynes-Cummings Models in a Kerr-Like Medium

Adjimon Joseph Adanmitonde, Gabriel Y. H. Avossevou, F. A. Dossa

Based on fundamental principles of quantum mechanics, we present a method for a rigorous analytic construction of the spectra of the one- and two-photon Jaynes-Cummings models in a Kerr medium. To obtain an idea of the method, we consider a first generalized Jaynes-Cummings model with a real, linear superpotential using techniques of supersymmetric quantum mechanics. The Hamiltonian of this model is written as a combination of operators generating the underlying superalgebra whose elements are defined as differential matrix operators. Based on the formalism of supersymmetric quantum mechanics and the properties of sets of common observables, we derive solutions of the one- and two-photon models expressed in terms of confluent hypergeometric functions. Finally, using numerical analysis, we study the influence of the Kerr effect on the energy spectra of the physical system.

Theoretical and Mathematical Physics•Jun 1, 2020•2 citations

Dynamical Superalgebra of the "Dressed" Jaynes-Cummings Model

Carla Buzano, Mario Rasetti, Maria Luisa Rastello

We show how, by resorting to a one-fermion realization of the Pauli operators, the Hamiltonian of the Jaynes-Cummings (JC) model can be identified as an element of the superalgebra u(1|1), which plays the role of a dynamical algebra. The extension of this notion to osp(2|2) allows adding both virtual and real two-photon processes to the JC Hamiltonian. The exact diagonalization problem is tackled here in the special case when the coupling constants of the fermionic terms of the "dressed" JC Hamiltonian are assumed to nilpotent Grassman-Banach numbers.

Physical Review Letters•Jan 9, 1989•66 citations
The super-algebraic structure of a generalized version of the Jaynes–Cummings model is investigated. We find that a Z 2 graded extension of the so (2,1) Lie algebra is the underlying symmetry of this model. It is isomorphic to the four-dimensional super-algebra u (1/1) with two odd and two even elements. Differential matrix operators are taken as realization of the elements of the superalgebra to which the model Hamiltonian belongs. Several examples with various choices of superpotentials are presented. The energy spectrum and corresponding wavefunctions are obtained analytically.
An algebraic view of supersymmetric quantum mechanics is taken, emphasising the couplings between bosonic and fermionic modes in the supercharges. A class of model Hamiltonians is introduced wherein the fermionic (bosonic) operators are canonical and the bosonic (fermionic) ones satisfy a Lie algebra (superalgebra) whose representation theory permits the complete solution of the model in principle. The kinematical symmetry of such models is also described. The examples of one and two bosonic models, with 5U(2) and 5U(3) dynamical algebras respectively, are analysed in detail.
We present a general qubit-boson interaction Hamiltonian that describes the Jaynes-Cummings model and its extensions as a single Hamiltonian class. Our model includes non-linear processes for both the free qubit and boson field as well as non-linear, multi-boson excitation exchange between them. It shows an underlying algebra with supersymmetric quantum mechanics features allowing an operator based diagonalization that simplifies the calculations of observables. As a practical example, we show the evolution of the population inversion and the boson quadratures for an initial state consisting of the qubit in the ground state interacting with a coherent field for a selection of cases covering the standard Jaynes-Cummings model and some of its extensions including Stark shift, Kerr-like, intensity dependent coupling, multi-boson exchange and algebraic deformations.
Based on fundamental principles of quantum mechanics, we present a method for a rigorous analytic construction of the spectra of the one- and two-photon Jaynes-Cummings models in a Kerr medium. To obtain an idea of the method, we consider a first generalized Jaynes-Cummings model with a real, linear superpotential using techniques of supersymmetric quantum mechanics. The Hamiltonian of this model is written as a combination of operators generating the underlying superalgebra whose elements are defined as differential matrix operators. Based on the formalism of supersymmetric quantum mechanics and the properties of sets of common observables, we derive solutions of the one- and two-photon models expressed in terms of confluent hypergeometric functions. Finally, using numerical analysis, we study the influence of the Kerr effect on the energy spectra of the physical system.
We show how, by resorting to a one-fermion realization of the Pauli operators, the Hamiltonian of the Jaynes-Cummings (JC) model can be identified as an element of the superalgebra u(1|1), which plays the role of a dynamical algebra. The extension of this notion to osp(2|2) allows adding both virtual and real two-photon processes to the JC Hamiltonian. The exact diagonalization problem is tackled here in the special case when the coupling constants of the fermionic terms of the "dressed" JC Hamiltonian are assumed to nilpotent Grassman-Banach numbers.