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

Annual Meeting Optical Society of America

Dynamic symmetries of the vacuum field Jaynes-Cummings model

P. K. Aravind, Guanghui Hu

Published Jan 1, 1988• 0 citations
Publisher

Abstract

We use the standard Jaynes-Cummings model with the field initially in the vacuum state and the atom in an arbitrary superposition state to illustrate the concept of dynamic symmetry in quantum optics. By dynamic symmetry we mean a situation in which a Hamiltonian is expressible as a linear combination of operators obeying a Lie algebra. This circumstance permits a psuedospin (or coherence vector) treatment to be given of the dynamics of the system. We give two such interpretations of the Jaynes-Cummings model. In the first we regard the atom and the field as a pair of interacting two-level systems and formulate a SU(2)-SU(2) dynamic symmetry. In the second we interpret the composite atom-field system is a three-level system and formulate a SU(3) dynamic symmetry. The former model illustrates the ideas of Fano1 and the latter those of Hioe and Eberly.2 We give a complete pseudospin description from both points of view and also obtain all the constants of motion.

DOI
10.1364/oam.1988.fr1

Related papers

Dynamical symmetries of the vacuum field Jaynes–Cummings model

Gui-Yu Hu, P. K. Aravind

We examine the dynamics of the Jaynes–Cummings model when it is restricted to the following initial conditions: atom in an arbitrary (pure or mixed) state and field in the vacuum state. It is shown that the model exhibits two dynamical symmetries that are characterized by the Lie algebras SU(2) × SU(2) and SU(3). A pair of interacting spins in a magnetic field also possesses the former symmetry, whereas the latter symmetry naturally describes a three-level atom driven by two laser fields; thus close correspondences with these systems are established. A pseudospin treatment of the model is devised and used to carry out a systematic investigation of its dynamics. On the basis of this treatment we (a) obtain the constants of motion of the problem, (b) establish bounds on the atomic and field inversions for arbitrary model conditions, (c) expose a striking symmetry between field and atomic (i.e., dipole) squeezing, and (d) discuss the occurrence of nonclassical correlations between the atom and the cavity field.

Journal of the Optical Society of America B•Sep 1, 1989•20 citations

The Damped-vacuum-field Jaynes-Cummings Model

Gui-Yu Hu, E. Irwin, P. K. Aravind

We study the dynamics of a two-level atom interacting with a single mode of a damped cavity at 0 K when the cavity is initially in the vacuum state and the atom enters it in an arbitrary (pure or mixed) state. A complete analytical solution of this simple model is presented. On the basis of this solution we firstly investigate the pseudo-spin dynamics of the atom and the cavity field, secondly give an illustration of the Araki-Lieb theorem concerning the von Neumann entropies of interacting quantum systems and thirdly demonstrate the generation of entangled states of the atom and cavity field that are of interest in connection with the Bell inequalities.

Journal of Modern Optics•Feb 1, 1995•2 citations

Generalized symmetries, invariant solutions and conservation laws in the Jaynes-Cummings model

Luis M. Piñuelas, Pablo C. López Vázquez, Alexander Yakhno

In this study, we investigate the Jaynes--Cummings model (JCM) using Lie symmetry analysis and conservation-law theory. The dynamics is formulated as a system of partial differential equations by projecting the von Neumann equation onto the atomic degrees of freedom and representing the field mode through its characteristic function. We determined the admitted point and generalized symmetries and constructed invariant solutions by imposing quantum-mechanical constraints. The conventional dressed-state dynamics is recovered, while a second class of solutions with radial dependence expressed through Heun polynomials is obtained for coupled atom--field configurations. We also applied a generating-function methodology to derive the local conservation laws of the JCM differential system in Fourier phase space. In addition to recovering the standard excitation-number constant of motion, we obtained additional conserved currents involving atomic populations, coherence, reduced-state purity, and derivatives of the field characteristic functions. One of these currents yields, at the Fourier-space origin, a balance equation for a combination of atomic purity and coherence whose evolution is driven by atom--field coupling and joint atom--field moments. For globally pure states, the purity contribution provides an indirect connection with the development of atom--field entanglement. The symmetry structure generates generalized symmetries and an infinite hierarchy of conservation laws.

math-phCross-listedarXiv:2606.15538•Jun 16, 2026•0 citations

Quantum phase and dynamical properties of light in the Jaynes-Cummings model via phase coupling

Fan An-fu

It is pointed out here that quantum phase properties, as well as dynamical properties, of light exhibit a sensitivity to the relative phase between the atomic dipole and light when the atom is prepared in a coherent superposition of its states in the two-level Jaynes-Cummings model interacting with a coherent state of light. The existence of the coherent-trapping of light is demonstrated by looking not only at the variance of the light phase about the coherent state value, and the number-phase uncertainty relation, but also at the factorization of the electric-field operator, and the photon-number distribution. We find also the factorization expression of the compound state of the atom-field system. We show once more that the phase properties of light based on the phase operator formalism of Pegg-Barnett and the coherence properties of light based on the coherence theory of Glauber are complementary in description of the optical quantum coherence.

Acta Physica Sinica (Overseas Edition)•Oct 1, 1996•0 citations

Echoes in the coherent-state Jaynes–Cummings model

P. K. Aravind, Joseph O. Hirschfelder

The Jaynes–Cummings model (JCM) is used to give a detailed analysis of the long-time behavior of a two-level atom interacting with a (Glauber) coherent-state field. This work is based on the earlier work of J. H. Eberly and collaborators, who drew attention to the collapse and revival of the Rabi oscillations of the atomic inversion. We use the three components S1, S2, and S3 of the pseudospin vector S to analyze the dynamics of the atom within the rotating-wave approximation and exact resonance. We show that, at the times when the revivals peak, the variables σ = |S| and η = S3/σ become independent of (1) the transition dipole moment of the atom, (2) the intensity of the coherent-state field, and (3) the (common) frequency of the atom and the field. Thus these special values of σ and η are a universal feature of the JCM that should be observed in experiments with any two-level atom in an arbitrarily intense (but resonant) coherent-state field. The derivation of the above results was facilitated by transforming into a rotating coordinate frame in which S1 = 0 so that S2 and S3 are the only dynamical variables. The two-dimensional nature of S in this frame makes it easy to visualize the dynamical changes in the atom. The dynamics of the JCM is clarified by comparison with the closely related Buck–Sukumar model. The relationship of the phenomena discussed here to photon echoes and to quench echoes (in condensed media) is pointed out.

Journal of the Optical Society of America B•May 1, 1985•6 citations

Dynamics of entanglement in a two-mode nonlinear Jaynes-Cummings mode

A. B. M. Ahmed, S. Sivakumar

Dynamics of entanglement due to intensity-dependent interaction between a two-level atom and a single-mode electromagnetic field in a Kerr medium is studied. The form of the interaction is such that the Hamiltonian evolution is exactly solvable. The Hamiltonian is shown to be a deformed Jaynes-Cummings model admitting a closed, symmetric algebra. Dynamics of population inversion and atom-field entanglement are studied taking the initial state of the field to be either a coherent state or a squeezed vacuum. Analysis is extended to the case of a two-mode cavity field interacting with a two-level atom. For the two-mode case, the initial field is a pair coherent state or a two-mode squeezed vacuum. Effects due to nonlinearity, intensity-dependent interaction and detuning on the dynamics are discussed and compared with those of the single-mode case.

arXiv:0907.2992•Jul 17, 2009•2 citations
We use the standard Jaynes-Cummings model with the field initially in the vacuum state and the atom in an arbitrary superposition state to illustrate the concept of dynamic symmetry in quantum optics. By dynamic symmetry we mean a situation in which a Hamiltonian is expressible as a linear combination of operators obeying a Lie algebra. This circumstance permits a psuedospin (or coherence vector) treatment to be given of the dynamics of the system. We give two such interpretations of the Jaynes-Cummings model. In the first we regard the atom and the field as a pair of interacting two-level systems and formulate a SU(2)-SU(2) dynamic symmetry. In the second we interpret the composite atom-field system is a three-level system and formulate a SU(3) dynamic symmetry. The former model illustrates the ideas of Fano1 and the latter those of Hioe and Eberly.2 We give a complete pseudospin description from both points of view and also obtain all the constants of motion.
We examine the dynamics of the Jaynes–Cummings model when it is restricted to the following initial conditions: atom in an arbitrary (pure or mixed) state and field in the vacuum state. It is shown that the model exhibits two dynamical symmetries that are characterized by the Lie algebras SU(2) × SU(2) and SU(3). A pair of interacting spins in a magnetic field also possesses the former symmetry, whereas the latter symmetry naturally describes a three-level atom driven by two laser fields; thus close correspondences with these systems are established. A pseudospin treatment of the model is devised and used to carry out a systematic investigation of its dynamics. On the basis of this treatment we (a) obtain the constants of motion of the problem, (b) establish bounds on the atomic and field inversions for arbitrary model conditions, (c) expose a striking symmetry between field and atomic (i.e., dipole) squeezing, and (d) discuss the occurrence of nonclassical correlations between the atom and the cavity field.
We study the dynamics of a two-level atom interacting with a single mode of a damped cavity at 0 K when the cavity is initially in the vacuum state and the atom enters it in an arbitrary (pure or mixed) state. A complete analytical solution of this simple model is presented. On the basis of this solution we firstly investigate the pseudo-spin dynamics of the atom and the cavity field, secondly give an illustration of the Araki-Lieb theorem concerning the von Neumann entropies of interacting quantum systems and thirdly demonstrate the generation of entangled states of the atom and cavity field that are of interest in connection with the Bell inequalities.
In this study, we investigate the Jaynes--Cummings model (JCM) using Lie symmetry analysis and conservation-law theory. The dynamics is formulated as a system of partial differential equations by projecting the von Neumann equation onto the atomic degrees of freedom and representing the field mode through its characteristic function. We determined the admitted point and generalized symmetries and constructed invariant solutions by imposing quantum-mechanical constraints. The conventional dressed-state dynamics is recovered, while a second class of solutions with radial dependence expressed through Heun polynomials is obtained for coupled atom--field configurations. We also applied a generating-function methodology to derive the local conservation laws of the JCM differential system in Fourier phase space. In addition to recovering the standard excitation-number constant of motion, we obtained additional conserved currents involving atomic populations, coherence, reduced-state purity, and derivatives of the field characteristic functions. One of these currents yields, at the Fourier-space origin, a balance equation for a combination of atomic purity and coherence whose evolution is driven by atom--field coupling and joint atom--field moments. For globally pure states, the purity contribution provides an indirect connection with the development of atom--field entanglement. The symmetry structure generates generalized symmetries and an infinite hierarchy of conservation laws.
It is pointed out here that quantum phase properties, as well as dynamical properties, of light exhibit a sensitivity to the relative phase between the atomic dipole and light when the atom is prepared in a coherent superposition of its states in the two-level Jaynes-Cummings model interacting with a coherent state of light. The existence of the coherent-trapping of light is demonstrated by looking not only at the variance of the light phase about the coherent state value, and the number-phase uncertainty relation, but also at the factorization of the electric-field operator, and the photon-number distribution. We find also the factorization expression of the compound state of the atom-field system. We show once more that the phase properties of light based on the phase operator formalism of Pegg-Barnett and the coherence properties of light based on the coherence theory of Glauber are complementary in description of the optical quantum coherence.
The Jaynes–Cummings model (JCM) is used to give a detailed analysis of the long-time behavior of a two-level atom interacting with a (Glauber) coherent-state field. This work is based on the earlier work of J. H. Eberly and collaborators, who drew attention to the collapse and revival of the Rabi oscillations of the atomic inversion. We use the three components S1, S2, and S3 of the pseudospin vector S to analyze the dynamics of the atom within the rotating-wave approximation and exact resonance. We show that, at the times when the revivals peak, the variables σ = |S| and η = S3/σ become independent of (1) the transition dipole moment of the atom, (2) the intensity of the coherent-state field, and (3) the (common) frequency of the atom and the field. Thus these special values of σ and η are a universal feature of the JCM that should be observed in experiments with any two-level atom in an arbitrarily intense (but resonant) coherent-state field. The derivation of the above results was facilitated by transforming into a rotating coordinate frame in which S1 = 0 so that S2 and S3 are the only dynamical variables. The two-dimensional nature of S in this frame makes it easy to visualize the dynamical changes in the atom. The dynamics of the JCM is clarified by comparison with the closely related Buck–Sukumar model. The relationship of the phenomena discussed here to photon echoes and to quench echoes (in condensed media) is pointed out.
Dynamics of entanglement due to intensity-dependent interaction between a two-level atom and a single-mode electromagnetic field in a Kerr medium is studied. The form of the interaction is such that the Hamiltonian evolution is exactly solvable. The Hamiltonian is shown to be a deformed Jaynes-Cummings model admitting a closed, symmetric algebra. Dynamics of population inversion and atom-field entanglement are studied taking the initial state of the field to be either a coherent state or a squeezed vacuum. Analysis is extended to the case of a two-mode cavity field interacting with a two-level atom. For the two-mode case, the initial field is a pair coherent state or a two-mode squeezed vacuum. Effects due to nonlinearity, intensity-dependent interaction and detuning on the dynamics are discussed and compared with those of the single-mode case.