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

Quantum and Semiclassical Optics Journal of the European Optical Society Part B

Dicke model: quantum nonlinear dynamics and collective phenomena

S. M. Chumakov, M. Kozierowski

Published Aug 1, 1996• 36 citations
Publisher

Abstract

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.

DOI
10.1088/1355-5111/8/4/003

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

Collective effects in the collapse-revival phenomenon and squeezing in the Dicke model

Guy Z. Ramon, Constantin Brif, A. Mann

Resonant interaction of a collection of two-level atoms with a single-mode coherent cavity field is considered in the framework of the Dicke model. We focus on the role of collective atomic effects in the phenomenon of collapses and revivals of the Rabi oscillations. It is shown that the behavior of the system strongly depends on the initial atomic state. In the case of the initial half-excited Dicke state we account for a number of interesting phenomena. The correlations between the atoms result in a suppression of the revival amplitude, and the revival time is halved, compared to the uncorrelated fully excited and ground states. The phenomenon of squeezing of the radiation field in the atom-field interaction is also discussed. For the initial fully excited and ground atomic states, the field is squeezed on the short-time scale, and squeezing can be enhanced by increasing the number of atoms. Some empirical formulas are found which describe the behavior of the system in excellent agreement with numerical results. For the half-excited Dicke state, the field can be strongly squeezed on the long-time scale in the case of two atoms. This kind of squeezing is enhanced by increasing the intensity of the initial coherent field and is of the same nature as revival-time squeezing in the Jaynes-Cummings model. The appearance of this long-time squeezing can be explained using the factorization approximation for semiclassical atomic states.

arXiv:quant-ph/9809051•Physical Review A•Sep 1, 1998•26 citations

Photon statistics in spontaneous emission for the Dicke model in a lossless cavity and the generation of the Fock state

M. Kozierowski, S. M. Chumakov

Using a perturbation method, constructed in terms of SU(2)-group representations, we investigate the time evolution of the statistics of photons spontaneously emitted by a system of N identical two-level atoms immersed in a single-mode ideal cavity with s atoms initially excited. The phenomenon of collective collapses and revivals is discussed and the collapse and revival times, which are different for odd and even s, are determined. It is shown for s extremely small compared to N that at appropriately chosen time instants the model generates the s-photon-number state (Fock state).

Physical Review A•Nov 1, 1995•23 citations

Interaction of a System of Initially Unexcited Two-level Atoms with a Weak Cavity Field

M. Kozierowski, S. M. Chumakov, A. A. Mamedov

Using a perturbation method, constructed in terms of SU(2) group representations, the interaction of N initially unexcited two-level atoms and a weak single-mode cavity field is studied. The field is assumed to be initially either in a Fock state with a number of photons equal to n or in a coherent state. In the case of the photon-number state with n  3, the pure phenomenon of collective collapses and revivals manifests itself. For the initially coherent field the phenomenon of collapses and revivals arising from the photon number distribution mechanism is additionally modulated by this collective mechanism. The problem of the interaction of excited atoms with an initially coherent field has already been solved numerically by Barnett and Knight. For n=1 2 and 3 the approximate solution is compared with the exact solutions also given in this paper and the limit of applicability of our approach is established.

Journal of Modern Optics•Mar 1, 1993•14 citations

Nonlinear dynamics of the two-photon Dicke model

A. B. Klimov, J. Negro, R Farias +1 more

We derive an effective two-photon Hamiltonian for a collection of two-level atoms interacting with a quantized field in the regime of two-photon resonance. This Hamiltonian naturally includes the dynamical Stark shift terms. Considering, in detail, the case of an initially strong quantum field, we show that the effective Hamiltonian acquires nonlinear terms in the su (2) algebra generators. For this case we find the evolution operator and prove the wavefunction factorization for special initial states. We show that collective effects modify the dynamics of the atomic inversion leading to a modulation of the collapse-revival structure.

Journal of Optics B Quantum and Semiclassical Optics•Sep 2, 1999•23 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
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.
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.
Resonant interaction of a collection of two-level atoms with a single-mode coherent cavity field is considered in the framework of the Dicke model. We focus on the role of collective atomic effects in the phenomenon of collapses and revivals of the Rabi oscillations. It is shown that the behavior of the system strongly depends on the initial atomic state. In the case of the initial half-excited Dicke state we account for a number of interesting phenomena. The correlations between the atoms result in a suppression of the revival amplitude, and the revival time is halved, compared to the uncorrelated fully excited and ground states. The phenomenon of squeezing of the radiation field in the atom-field interaction is also discussed. For the initial fully excited and ground atomic states, the field is squeezed on the short-time scale, and squeezing can be enhanced by increasing the number of atoms. Some empirical formulas are found which describe the behavior of the system in excellent agreement with numerical results. For the half-excited Dicke state, the field can be strongly squeezed on the long-time scale in the case of two atoms. This kind of squeezing is enhanced by increasing the intensity of the initial coherent field and is of the same nature as revival-time squeezing in the Jaynes-Cummings model. The appearance of this long-time squeezing can be explained using the factorization approximation for semiclassical atomic states.
Using a perturbation method, constructed in terms of SU(2)-group representations, we investigate the time evolution of the statistics of photons spontaneously emitted by a system of N identical two-level atoms immersed in a single-mode ideal cavity with s atoms initially excited. The phenomenon of collective collapses and revivals is discussed and the collapse and revival times, which are different for odd and even s, are determined. It is shown for s extremely small compared to N that at appropriately chosen time instants the model generates the s-photon-number state (Fock state).
Using a perturbation method, constructed in terms of SU(2) group representations, the interaction of N initially unexcited two-level atoms and a weak single-mode cavity field is studied. The field is assumed to be initially either in a Fock state with a number of photons equal to n or in a coherent state. In the case of the photon-number state with n  3, the pure phenomenon of collective collapses and revivals manifests itself. For the initially coherent field the phenomenon of collapses and revivals arising from the photon number distribution mechanism is additionally modulated by this collective mechanism. The problem of the interaction of excited atoms with an initially coherent field has already been solved numerically by Barnett and Knight. For n=1 2 and 3 the approximate solution is compared with the exact solutions also given in this paper and the limit of applicability of our approach is established.
We derive an effective two-photon Hamiltonian for a collection of two-level atoms interacting with a quantized field in the regime of two-photon resonance. This Hamiltonian naturally includes the dynamical Stark shift terms. Considering, in detail, the case of an initially strong quantum field, we show that the effective Hamiltonian acquires nonlinear terms in the su (2) algebra generators. For this case we find the evolution operator and prove the wavefunction factorization for special initial states. We show that collective effects modify the dynamics of the atomic inversion leading to a modulation of the collapse-revival structure.