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arXiv:0807.1910 · Journal of Physics B Atomic Molecular and Optical Physics

The influence of atomic collisions on collective spontaneous emission from anf-deformed Bose–Einstein condensate

Zahra Haghshenasfard, M. H. Naderi, M. Soltanolkotabi

Published Mar 9, 2009• 3 citations
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Abstract

In this paper, we investigate the spontaneous emission of an f -deformed Bose–Einstein condensate of a gas with N identical two-level atoms immersed in a single-mode ideal cavity with s atoms initially excited. We apply an f -deformed quantum model in which Gardiner's phonon operators are deformed by an operator-valued function of the particle number operator . We consider the collisions between the atoms as a special kind of f -deformation where the collision rate κ is regarded as a corresponding deformation parameter. The time evolution of the expectation value of the atomic inversion is presented, the phenomenon of collective collapses and revivals is shown and the effects of deformation on the cooperative behaviour of the system are discussed.

DOI
10.1088/0953-4075/42/6/065505

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In this paper, we investigate the spontaneous emission of an f -deformed Bose–Einstein condensate of a gas with N identical two-level atoms immersed in a single-mode ideal cavity with s atoms initially excited. We apply an f -deformed quantum model in which Gardiner's phonon operators are deformed by an operator-valued function of the particle number operator . We consider the collisions between the atoms as a special kind of f -deformation where the collision rate κ is regarded as a corresponding deformation parameter. The time evolution of the expectation value of the atomic inversion is presented, the phenomenon of collective collapses and revivals is shown and the effects of deformation on the cooperative behaviour of the system are discussed.
In this paper, we investigate the spectrum of light scattered from a Bose-Einstein condensate in the framework of -deformed boson.We use an -deformed quantum model in which the Gardiner's phonon operators for BEC are deformed by an operator-valued function,, of the particle-number operator n .We consider the collisions between the atoms as a special kind of -deformation.The collision rateκ is regarded as the deformation parameter and the spectrum of light scattered from the deformed BEC is analyzed.In particular, we find that with increasing the values of deformation parameters κ and N 1 = η ( , total number of condensate atoms) the scattering spectrum shows deviation from the spectrum associated with nondeformed Bose-Einstein condensate.
In this paper, we investigate the propagation of a weak optical probe pulse in an f-deformed Bose- Einstein condensate (BEC) of a gas with the -type three- level atoms in the electromagnetically induced transparency (EIT) regime. We use an f- deformed generalization of an effective two- level quantum model of the three- level configuration in which the Gardiner phonon operators for BEC are deformed by an operator- valued function, f(n), of the particle- number operator n. With making use of the quantum approach of the angular momentum theory we obtain the eigenvalues and eigenfunctions of the system up to first order approximation. We consider the collisions between the atoms as a special kind of f- deformation. The collision rate k is regarded as the deformation parameter and light propagation in the deformed BEC is analyzed. In particular, we show that the absorptive and dispersive properties of the deformed condensate can be controlled effectively by changing the deformation parameter k and the total number of atoms. We find that by increasing the value of k the group velocity of the probe pulse changes, through deformed condensate, from subluminal to superluminal.
Abstract In this paper we present a general theoretical model for the interaction between a number of two-level atoms constituting Bose-Einstein condensate (BEC) and a single-mode quantized field. In addition to the usual interacting terms, we take into account interatom as well as higher-order atom-field interactions. To simplify the Hamiltonian of system, after using the Bogoliubov approximation we proceed to calculate the transformed operators of atoms and field. Then, to quantify the spontaneous emission, we get analytical expressions for the expectation value of J ^ z as the atomic population inversion (API), in the cases of number and coherent states for the atomic subsystem. Our results show that the above-mentioned model interaction leads to the appearance of collapse-revival phenomenon in API. In more detail, the revival time may be tuned by adjusting the interatom interaction constant. Also, the damping process lowers the amplitude of API, but does not change the CR times for weak damping. Moreover, increasing the damping may decrease the number of CRs in a given interval of time such that no revival occurs. Briefly, it may be concluded that in the resonant case the revival times are insensitive to the change of the higher-order atom-field interaction constant and are affected only by the interatom interactions. Finally, we express that, how we can find a practical procedure to measure the quantum states of atoms in BEC .
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.
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).
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.