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Physical Review A

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

Published Nov 1, 1995• 23 citations
Publisher

Abstract

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).

DOI
10.1103/physreva.52.4194

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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).
Applying a perturbation method, constructed in terms of SU(2) group representations, we study spontaneous emission of a system of N identical two-level atoms immersed in a single-mode ideal cavity with s atoms initially inverted. For the cases s\ensuremath{\ge}3, characterized by nonequidistant spectra of the eigenvalues of the Hamiltonian, the phenomenon of collective collapses and revivals manifests itself. For s=3 the approximate solution is compared with the exact one and the limit of good applicability of our method is established.
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.
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 consider cooperative spontaneous emission by an assembly of N two-level atoms immersed in a high-Q single-mode cavity, when s (s\ensuremath{\ll}N) atoms are initially excited. The atoms are noninteracting with each other except via the action of the electromagnetic field. The eigenvalues of the system and the time development of the mean energy of the atomic subsystem are presented in the form of power series in the parameter \ensuremath{\epsilon}=(N-s/2+1/2${)}^{\mathrm{\ensuremath{-}}1}$ using the SU(2)-group-representation technique.
The collapse and revival of quantum states appear in diverse areas of physics. In quantum optics the occurrence of such a phenomena in the evolution of an atomic state, interacting with a light field initially in a coherent state, was predicted by using the Jaynes-Cummings model (JCM), and subsequently demonstrated experimentally. In this paper we revisit the JCM with the Monte-Carlo wave function approach and investigate the time evolution of the photon emission rate of the atom in a cavity. Analytical and numerical quantum trajectory calculations show that the cavity and the initial field statistics strongly influence the photon emission dynamics. A coherent field indeed gives rise to a collapse and revival behavior that mirrors atomic state evolution. However, there are differences between the two. The emission rate for a field in a Fock number state exhibits a sinusoidal oscillation, and there exists a quiescent period for a thermal field. These properties are quite different from those in free space. It is also shown that the fluctuation in photon emission is much less than that of the atomic population.
We study the quantum statistics of single-mode radiation emitted by an atomic ensemble when the ensemble is initially prepared in a superradiant Dicke state. We show that while the radiation is well approximated by the Glauber coherent state at early times in the evolution, the emission can be truly quantum at later times. In particular, one can observe a large amount of photon-number squeezing in the emission under certain conditions; even a Fock state can be produced. We discuss the quantum statistics of the emission for various parameters, including different initial conditions for the atomic ensemble. To obtain these results, we have developed a formalism where we are able to calculate the quantum statistics of the emission over long time scales even when the number of atoms in the ensemble is quite large.