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Physical Review A

Coherent properties of the stimulated emission from a three-level atom

Xiao-shen Li, Chang-De Gong

Published Apr 1, 1986• 29 citations
Publisher

Abstract

First-order correlation functions of the electric field and photon-number probabilities in the case of a three-level atom interacting with two-mode radiation field are obtained to investigate the coherent properties of the stimulated emission under different initial conditions. It is found that double stimulation will cause the field to approach its initial coherent state and the oscillation of the photon-number probabilities to collapse and revive.

DOI
10.1103/physreva.33.2801

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Quantum Optics Journal of the European Optical Society Part B•Oct 1, 1991•10 citations
First-order correlation functions of the electric field and photon-number probabilities in the case of a three-level atom interacting with two-mode radiation field are obtained to investigate the coherent properties of the stimulated emission under different initial conditions. It is found that double stimulation will cause the field to approach its initial coherent state and the oscillation of the photon-number probabilities to collapse and revive.
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.
Recently Glauber has described the properties of coherent radiation fields, and has constructed the density matrix of the field in two simple cases: (1) The radiating system is a classical radiator and no reaction is considered; (2) the central-limit theorem applies to a collection of radiators. This paper investigates other simple "almost" exactly soluble problems, in which a quantum-mechanical two-level system interacts with a quantized electromagnetic field originally in a pure coherent state in a single mode. The first-order correlation function ${G}^{(1)}=〈{E}^{\ensuremath{-}}{E}^{+}〉$ is compared with $〈{E}^{\ensuremath{-}}〉〈{E}^{+}〉$ at resonance when the stimulating field is initially a pure coherent state and the two-level system is initially in its excited state. The corresponding quantities are also computed for a field whose initial density matrix is a Gaussian superposition of coherent states (e.g., blackbody radiation), as well as for a field which is initially described as having a given number of photons.
For pt.1, see ibid., p.241, 1991. The authors consider phase properties of the field in the two-mode three-level problem. Phase properties of each individual mode as well as their joint probability distribution and correlation function are studied. They find that phase properties of the field reflect the collapses and revivals of the level occupation probabilities in most situations. However, there exist exceptions, for example, in the case of Raman scattering, which allows them to conclude that the collapses and revivals of the atomic population can be completely decorrelated from the phase of the field. This takes place when the field mode is fed by the photons emitted spontaneously from a real atomic level, which affects the field occupation numbers but not its phase.