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arXiv:quant-ph/9806034 · Modern Physics Letters B

Collective Spontaneous Emission in a q-Deformed Dicke Model

Stefano Mancini, Vladimir I. Man’ko, Paolo Tombesi

Published May 10, 1998• 9 citations
arXivHTMLPDF

Abstract

The q-deformation of a single quantized radiation mode interacting with a collection of two level atoms is introduced, analyzing its effects on the cooperative behavior of the system.
DOI
10.1142/s0217984998000494

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Coherent spontaneous emission from a system of NNN two-level atoms interacting with a quantized radiation field is treated for the case in which Dicke's "cooperation number" rrr is macroscopically large. It is shown how to modify the quasiclassical approach to this problem to incorporate quantum effects that are lost in the self-consistent-field approximation. The statistics of the emitted radiation are found to vary markedly with the initial state of the system of atoms. The photon statistics tend to that typical of blackbody radiation when the initial state of the atomic system is that which would result from incoherent pumping ($m\ensuremath{\sim}r$). When, on the other hand, the atoms are initially in a superradiant state ($m\ensuremath{\ll}r$), the emitted radiation may be represented approximately by a coherent state.
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.