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Optica Acta International Journal of Optics

Excitation of Superradiant Atomic State by a Pulse of Quantum Field

N. K. Solovarov

Published Mar 1, 1980• 2 citations
Publisher

Abstract

The excitation of the system of N two-level atoms is considered with the pulse of the resonance quantum field in the state with the definite number of photons n b n > (n≫1). It is shown that the atomic system may be excited into the superradiant correlated (radiation proportional to N 2) but noncoherent (macroscopic polarization is zero) state.

DOI
10.1080/713820225

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The excitation of the system of N two-level atoms is considered with the pulse of the resonance quantum field in the state with the definite number of photons n b n > (n≫1). It is shown that the atomic system may be excited into the superradiant correlated (radiation proportional to N 2) but noncoherent (macroscopic polarization is zero) state.
We introduce a straightforward quantum-electrodynamic approach to the problem of superradiant spontaneous emission from a system of two-level atoms, and also discuss two classical superradiant systems. The same physical concepts underlie our treatment of both the quantum and classical cases. Explicit expressions are found which describe the time evolution and directional character of the radiated power. Our approach applies to an arbitrary number of atoms which are confined to a region with linear dimensions which may be large compared with the mean wavelength of the emitted radiation. The radiative decay half-life of a large many-atom system is found to be much shorter than the natural lifetime of a single atom, but not as short as the half-life of a small atomic system with the same number of atoms. The far-field radiation pattern appropriate to the case of a circular cylinder of emitters which have been excited by a plane-wave pulse is considered in detail. Polar plots are presented of the radiation patterns produced when the atoms are excited by a plane-wave pulse. Exciting pulses traveling in directions both parallel and at an angle of 10\ifmmode^\circ\else\textdegree\fi{} to the axis of the cylinder are considered. A discussion and generalization of Dicke's "coherence-brightening" criterion is given.
A system of many #we-level atoms or molecules in a collective Dieke state (1) interacting with a single resonant mode of the quantized radiation field has often been adopted as a quantum-mechanical model for a point laser (2). In a previous paper (3) we reported exact dosed-form solutions and photon statistics of coherent spontaneous emission for the model atom-field state in the l imit of infinitely large co-operation number. The purpose of this paper is to report more general results based on this modeI. We give the exact closed-form solutions and photon statistics of coherent emission in the presence of an applied field for the model atom-field state in the same limit. For an initial atomic Dicke state interacting with an applied field in a coherent (Glauber) state (a), the emitted pulse can be desoribed in terms of Glauber states only when the levels of excitation of the initial Dicke states are (~ superradiant ~ (~). For an initially highly inverted system or low excited system, the photon distributions undergo large fluctuations. The model interaction Hamil tonian is given by
Photon statistics are obtained from exact closed-form solutions for both spontaneous and stimulated coherent emissions by a large number of two-level atoms in a Dicke state. Depending on the initial excitation level of the atoms, three types of photon statistics are obtained for the emitted radiation field. Moments of the photon number of the emitted field are calculated in the case of initial atomic coherent states as well as Dicke states, and in the case of n-photon stimulating pulses as well as coherent stimulating pulses. In the particular case of an initial "superradiant" Dicke state stimulated by a coherent-radiation field, the emitted radiation pulse is also fully coherent. In other cases the photon distributions undergo large fluctuations.
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.