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Physical Review A

Large Photon Correlations in Many-Atom Spontaneous Emission

Antonio M. Ponte Goncalves, Andree A. Tallet

Published Sep 1, 1971• 8 citations
Publisher

Abstract

The normalized second-order correlation function is calculated for the spontaneous emission radiation from many-atom systems. Very large photon correlations appear as the systems decay to the ground state. This effect is shown to be a consequence of the quantization of the radiation field.
DOI
10.1103/physreva.4.1319

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Physical Review A•May 1, 1971•33 citations
The normalized two-time intensity-fluctuation functions are calculated for the spontaneous-emission radiation from a system of NNN two-level atoms. The radiated field, when the system decays from the excited state to the ground state, does not look like a Gaussian or a coherent field.
The spontaneous emission of a set of NNN identical two-level atoms interacting with a quantized electromagnetic field is studied. The atoms are assumed to be close together compared to the mean wavelength of the emitted radiation, and their initial state is either a Dicke state or a superposition of the ground and excited state for each atom. Approximate expressions are obtained for transition probabilities, expectation values, and correlations as functions of time. The spontaneous emission for a very large separation of the atoms is also studied. In this case the directional properties of the emitted radiation, as well as the time within which the atoms decay to their ground state, depend on the position of each atom.
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.
The interaction between electromagnetic radiation and two three-level atoms is investigated. The atom-atom separation is assumed to be smaller than the corresponding mean resonance wavelength. The total radiance rate of the atomic system is calculated as a function of time. Explicit results are given for several different initial states of the atomic system. Some of them exhibit superradiance, and some act as photon-trapping states. Instead of exponential decay, the oscillations appear in the time evolution of the radiation rate due to the correlation between atoms. The decay constants and coupling decay constants show strong effects on the emission rates. Completely differing from two identical double-level atoms, the cooperative effects always exist in the three-level atomic system except for the case in which the coupling decay constants ${\ensuremath{\gamma}}_{12}$ and ${\ensuremath{\gamma}}_{21}$ are zero.
We study emission of a single photon from a spherically symmetric cloud of NNN atoms (one atom is excited; $N\ensuremath{-}1$ are in the ground state) and present an exact analytical expression for eigenvalues and eigenstates of this many-body problem. We found that some states decay much faster than the single-atom decay rate, while other states are trapped and undergo very slow decay. When the size of the atomic cloud is small compared with the radiation wavelength, we found that the radiation frequency undergoes a large shift.
In a previous investigation, a general theory for spontaneous emission from a system of NNN identical atoms or molecules was developed. This theory was based on the master equation recently derived in another paper. In that paper, the master equation relating to spontaneous emission from a system of harmonic oscillators was also derived. In the present investigation, the normally ordered correlation functions for the oscillator system are calculated and these are then used to calculate the radiation-field correlation functions in the far zone. These correlation functions are compared for two different modes of excitation, viz., (i) when each of the oscillators is excited initially to a Fock state, and (ii) when each of the oscillators is excited to some coherent state. It is found that the even-order (2n2n2n) correlation functions for the second mode of excitation (superradiant excitation) are of order N2n{N}^{2n}N2n higher than those for the first mode of excitation. It is also shown that the photoelectron counting distribution for the superradiant excitation is Poissonian. Finally, the non-Markoffian effects in the spontaneous emission are studied in detail and their connection with exact results is described.