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Journal of Experimental and Theoretical Physics Letters

Delay of Superradiance as a Signature of the Non-Wiener Dynamics of the Generalized Dicke Model

Andrew I. Trubilko, Ashat M. Basharov

Published Jan 1, 2019• 5 citations
Publisher

Abstract

Delay of a superradiance pulse of an ensemble of identical atoms in a half-excited state has been detected. No such delay has been detected for an ensemble of fully excited atoms. These effects are due to the nonresonant interaction of a localized atomic ensemble with vacuum broadband environment, which is disregarded within the traditional Dicke model but is taken into account within the generalized Dicke model.

DOI
10.1134/s0021364019020140

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Delay of a superradiance pulse of an ensemble of identical atoms in a half-excited state has been detected. No such delay has been detected for an ensemble of fully excited atoms. These effects are due to the nonresonant interaction of a localized atomic ensemble with vacuum broadband environment, which is disregarded within the traditional Dicke model but is taken into account within the generalized Dicke model.
Abstract It is shown that when nonresonant interactions between atoms and a vacuum electromagnetic field are included in analysis of emission of a localized ensemble of identical atoms, a delay must appear in the cooperative radiation pulse emitted by the atomic ensemble that is initially in a half-excited state. At the same time, the emission of cooperative radiation from a completely excited ensemble for certain parameters must begin without any delay. This contradicts the familiar facts of the conventional Dicke superradiance, in the theory of which nonresonant interactions are disregarded. The model taking into account nonresonant interactions along with other factors of the Dicke model is called the generalized Dicke model.
Generalized with respect to the Stark interaction of atoms with a vacuum field of zero photon density, Dicke's model is used to describe the Raman superradiance of a localized ensemble of identical atoms in a coherent non-resonant light wave. It is shown that at a certain critical number of atoms in the ensemble the stabilization effect of the excited state of the ensemble relative to collective atomic decay is possible, with superradiance of the atomic ensemble being suppressed. When the number of atoms is close to the critical value, superradiance exhibits features that are opposite to the effects of the conventional superradiance in the pulse delay time. The identified features depend on the intensity of an external coherent field as well as make it possible to assess whether the Stark interaction of an ensemble with a photon-free vacuum electromagnetic field is significant or not.
It has been demonstrated that a quantum state of a broadband single-photon electromagnetic field can be detected and verified by recording the intensity of superradiance of an atomic ensemble governed by non- Wiener dynamics. Under these conditions, the collective relaxation of atoms in the Dike model into vacuum is completely suppressed and only the interaction of the external field with atoms generates a superradiance pulse proportional to the square of the number of atoms. In the case of a single-photon wave packet in a classical state prepared by weakening a broadband source of a family of independent coherent modes, incoherent emission of the same ensemble occurs with the intensity proportional to the number of atoms.
Fully-excited two-level atoms separated by less than the transition wavelength cooperatively emit light in a short burst, a phenomenon called superradiance by R. Dicke in 1954. The burst is characterized by a maximum intensity scaling with the square of the number of atoms NNN and a temporal width reduced by NNN compared to the single atom spontaneous decay time. Both effects are usually attributed to a synchronization of the electric dipole moments of the atoms occurring during the process of light emission. Contrary to this explanation, it was recently shown by use of a quantum path description that the peak intensity results from the quantum correlations among the atoms when occupying symmetric Dicke states. Here we investigate from this perspective the temporal evolution of the ensemble, starting in the small sample limit, i.e., when the atoms have mutual separations much smaller than the transition wavelength λλλ and pass down the ladder of symmetric Dicke states. In addition, we explore the temporal evolution for the case of non-interacting atoms with mutual separations much larger than λλλ. We show that in this case a similar superradiant burst of the emitted radiation is observed if the quantum correlations of the atoms are generated by conditional photon measurements retaining the atomic ensemble within or close to the symmetric subspace.