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

Collapses and revivals in the Dicke model

S. M. Chumakov, J. J. Sánchez-Mondragón

Published Jan 1, 1991• 0 citations
Publisher

Abstract

We discuss the time evolution of the atomic inversion of a system of N two-level atoms interacting with a single quantized field mode in a high-Q cavity. We present both the operator solution and analytical expressions for the corresponding revivals, and extend the well-known picture of the single-atom (JCM). The operator solution is perturbative based on the approximate dynamic symmetry of this model1; the analytical revival method was introduced recently.2

DOI
10.1364/oam.1991.wl12

Related papers

Acceleration of revivals by squeezed vacuum fields

M. Kozierowski, S. M. Chumakov

The resonant interaction of A initially unexcited two-level atoms with different quantum fields in a high-Q single-mode cavity (Dicke model) is studied analytically in one of the limits in which the eigenvalues spectrum of the model may be assumed as equidistant. The time evolution of atomic inversion of a single two-level atom coupled to squeezed vacuum or thermal cavity fields (Jaynes-Cummings model) is irregular. Here we show that the dynamical response of the inversion of an assemblage of A two-level atoms to such fields may be regular, i.e., may reveal collapses and revivals and that the properties of the model with an initial squeezed vacuum field differ from those for coherent or thermal fields.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•May 6, 1996•0 citations

Squeezed vacuum as an accelerator of revivals in the Dicke model

M. Kozierowski, S. M. Chumakov

A two-level atom interacting with a single-mode squeezed vacuum cavity field does not manifest collapses and revivals of the oscillations [Milburn, Opt. Acta 31, 671 (1984)]. Here we show that the dynamic response of the inversion of an assemblage of A two-level atoms to such a field (Dicke model) may be qualitatively different. The dynamic properties of the model with an initial squeezed vacuum field differ from those for coherent or thermal fields, which have been stressed in the title.

Physical Review A•Nov 1, 1995•5 citations

Coherence versus incoherence: Collapse and revival in a simple quantum model

Nikolay B. Narozhny, J. J. Sánchez-Mondragón, Joseph H. Eberly

We describe the temporal behavior of the dynamic elements of an exactly soluble quantum model. The model consists of a single two-level atom or spin interacting with a single mode of the quantized radiation field in the dipole approximation, the mode being initially in an arbitrary coherent state of excitation. We give new long-time numerical and closed-form approximate analytic solutions for the expectation values of the atomic dipole moment and the difference in population of the two atomic levels in the rotating wave approximation. The atomic dipole-dipole correlation function is calculated. All of the results are obtained without semiclassical or decorrelation approximations. Unusual features found in the temporal behavior of this lossless model problem are "collapse," i.e., episodic nonexponential damping of both the atomic inversion and dipole moment, and two kinds of "revival" or partial recorrelation, in the dynamic evolution, during which the initial state is nearly recovered. We give analytic formulas for the collapse function, for both of the revival times, and for the envelope of the revival maxima. Some remarks are made about the nature of irreversibility in this exactly soluble and loss-free model.

Physical Review A•Jan 1, 1981•621 citations

Dicke model: quantum nonlinear dynamics and collective phenomena

S. M. Chumakov, M. Kozierowski

We study the resonant interaction of A initially unexcited two-level atoms with single-mode Fock, coherent and thermal cavity fields of arbitrary intensity. Two mechanisms lead to a spread of the eigenfrequencies: one is due to the photon-number distribution in the initial state and the other reflects the cooperativity of the system. Both affect the evolution of the photon number and photon statistics. We present approximate expressions for the eigenvalues and eigenvectors of the system. Its regular dynamical regions are found and the difference in shape of the collapses and revivals connected with the above mechanisms is discussed.

Quantum and Semiclassical Optics Journal of the European Optical Society Part B•Aug 1, 1996•36 citations

Collapse and revival dynamics in a driven Jaynes-Cummings system

P. M. Alsing, Vassilios I. Kovanis, David A. Cardimona

A single atom coupled to a quantized mode of an electromagnetic cavity, driven by an external coherent field, is described by the Hamiltonian H djc = ig(a†σ− − aσ+) + iε(a† − a), where (a†, a) and (σ+, σ) are the raising and lowering operators for the cavity mode and atom, respectively. This is the single atom version of the Hamiltonian used in the study of optical bistability. It describes the evolution of the atom-cavity system on time scales much smaller than the inverse spontaneous emission and cavity decay rates. For 2ε/g < 1, HDJC possesses a discrete set of interaction eigenstates1 with eigenvalues E n ± = ± g n [ 1 − ( 2 ε / g ) 2 ] 3 / 4 . These form a renormalized version of the usual Jaynes-Cummings eigenstates2, which correctly take into account the effect of the driving field to all orders of magnitude. We investigate the collapse and revival nature of the dynamical evolution of the single atom in a cavity, with and without dissipation and above and below the threshold 2ε/g = 1 of the driven Jaynes-Cummings Hamiltonian.

Annual Meeting Optical Society of America•Jan 1, 1992•0 citations

Interaction of two two-level atoms with two-photon transitions with a cavity radiation field

Igor Jex

Presents the interaction of two two-level atoms with two-photon transitions with a single mode of the quantized radiation field. Following the work of Iqbal J. Opt. Soc. Am B, vol.5, p.1312 (1987) and co-workers the exact solution of the field-atom dynamic in the rotating-wave approximation is found. Based on this solution the collapse-revival phenomenon in this model is studied in detail.

Quantum Optics Journal of the European Optical Society Part B•Dec 1, 1990•14 citations
We discuss the time evolution of the atomic inversion of a system of N two-level atoms interacting with a single quantized field mode in a high-Q cavity. We present both the operator solution and analytical expressions for the corresponding revivals, and extend the well-known picture of the single-atom (JCM). The operator solution is perturbative based on the approximate dynamic symmetry of this model1; the analytical revival method was introduced recently.2
The resonant interaction of A initially unexcited two-level atoms with different quantum fields in a high-Q single-mode cavity (Dicke model) is studied analytically in one of the limits in which the eigenvalues spectrum of the model may be assumed as equidistant. The time evolution of atomic inversion of a single two-level atom coupled to squeezed vacuum or thermal cavity fields (Jaynes-Cummings model) is irregular. Here we show that the dynamical response of the inversion of an assemblage of A two-level atoms to such fields may be regular, i.e., may reveal collapses and revivals and that the properties of the model with an initial squeezed vacuum field differ from those for coherent or thermal fields.
We describe the temporal behavior of the dynamic elements of an exactly soluble quantum model. The model consists of a single two-level atom or spin interacting with a single mode of the quantized radiation field in the dipole approximation, the mode being initially in an arbitrary coherent state of excitation. We give new long-time numerical and closed-form approximate analytic solutions for the expectation values of the atomic dipole moment and the difference in population of the two atomic levels in the rotating wave approximation. The atomic dipole-dipole correlation function is calculated. All of the results are obtained without semiclassical or decorrelation approximations. Unusual features found in the temporal behavior of this lossless model problem are "collapse," i.e., episodic nonexponential damping of both the atomic inversion and dipole moment, and two kinds of "revival" or partial recorrelation, in the dynamic evolution, during which the initial state is nearly recovered. We give analytic formulas for the collapse function, for both of the revival times, and for the envelope of the revival maxima. Some remarks are made about the nature of irreversibility in this exactly soluble and loss-free model.
We study the resonant interaction of A initially unexcited two-level atoms with single-mode Fock, coherent and thermal cavity fields of arbitrary intensity. Two mechanisms lead to a spread of the eigenfrequencies: one is due to the photon-number distribution in the initial state and the other reflects the cooperativity of the system. Both affect the evolution of the photon number and photon statistics. We present approximate expressions for the eigenvalues and eigenvectors of the system. Its regular dynamical regions are found and the difference in shape of the collapses and revivals connected with the above mechanisms is discussed.
A single atom coupled to a quantized mode of an electromagnetic cavity, driven by an external coherent field, is described by the Hamiltonian H djc = ig(a†σ− − aσ+) + iε(a† − a), where (a†, a) and (σ+, σ) are the raising and lowering operators for the cavity mode and atom, respectively. This is the single atom version of the Hamiltonian used in the study of optical bistability. It describes the evolution of the atom-cavity system on time scales much smaller than the inverse spontaneous emission and cavity decay rates. For 2ε/g < 1, HDJC possesses a discrete set of interaction eigenstates1 with eigenvalues E n ± = ± g n [ 1 − ( 2 ε / g ) 2 ] 3 / 4 . These form a renormalized version of the usual Jaynes-Cummings eigenstates2, which correctly take into account the effect of the driving field to all orders of magnitude. We investigate the collapse and revival nature of the dynamical evolution of the single atom in a cavity, with and without dissipation and above and below the threshold 2ε/g = 1 of the driven Jaynes-Cummings Hamiltonian.