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Quantum Electronics

Elementary processes of stimulated emission

P. V. Elyutin

Published Mar 31, 2012• 2 citations
Publisher

Abstract

We consider the simplest process of stimulated emission, i.e., evolution of an excited two-level atom interacting with a quantized electromagnetic field being initially in a one-photon state under different boundary conditions imposed on the field. We study the kinetics of evolution, spectral properties and modal composition of the radiation field emerging in such processes. It is shown that in the general case this field is only partly composed of doubly occupied modes.

DOI
10.1070/qe2012v042n03abeh014790

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We consider the simplest process of stimulated emission, i.e., evolution of an excited two-level atom interacting with a quantized electromagnetic field being initially in a one-photon state under different boundary conditions imposed on the field. We study the kinetics of evolution, spectral properties and modal composition of the radiation field emerging in such processes. It is shown that in the general case this field is only partly composed of doubly occupied modes.
Usually it is assumed that the stimulated emission appears as a consequence of the Bose—Einstein statistics of photons and that to observe this effect at least two excitations have to be initially present in the atom—field system. That is, both the atom and the electromagnetic field have to be excited. In this paper we show that stimulated emission can appear exclusively as a consequence of quantum interference in a system with just a single excitation. Specifically, we consider a single two-level atom which is initially in its lower energy state and it interacts with a single-photon multi-mode wave packet. We show that for a proper choice of the photon-wave packet the atom can exhibit stimulated emission.
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.
We have considered the induced processes that occur in a driven two-level atom, where a laser photon is absorbed and emitted by the ground and by the excited states of the atom, respectively. In the low-intensity limit of the laser field, the induced spectra arising when a laser photon is absorbed by the ground state of the atom consist of two peaks describing induced-absorption and stimulated-emission processes, respectively, where the former prevails over the latter. Asymmetry of the spectral lines occurs at off-resonance and its extent depends on the detuning of the laser field. The physical, process where a laser photon is emitted by the excited state is the reverse of that arising from the absorption of a laser photon by the ground state of the atom. The former differs from the latter in that the emission of a laser photon by the excited state occurs in the low-frequency regime and that the stimulated-emission process prevails over that of the induced absorption. In this case, amplification of ultrashort pulses is likely to occur without the need of population inversion between the optical transitions. The computed spectra are graphically presented and discussed.
The author considers the stimulated emission process that occurs at the difference-frequency generation of a bichromatic field interacting with a three-level atom in the Lambda configuration. In the low-intensity limit of both laser fields and at finite detunings, there are two induced excitations whose lifetimes are much longer in comparison to those of excitations spontaneously emitted by the excited states of the atom. Conditions are established under which the two-photon stimulated emission prevails, indicating that significant amplification is likely to occur at the difference-frequency generation.
An exact solution for the problem of two two-level atoms interacting with a single-mode detuned quantized radiation field is presented. On resonance, an asymptotic result is derived for large coherent initial fields. It is shown that when the atoms are initially prepared in one of the semiclassical eigenstates, the atom-plus-field wavefunction remains almost factored into an atomic and a field part throughout the interaction. Under certain conditions, the atomic part evolves into a unique pure state at half-revival time. The effects of the cavity detuning on the dynamics of the atomic level occupation probabilities and emission spectra are studied. It is found, for non-symmetrical excitation, that far off-resonance the field acts like a virtual level by means of which the energy is transferred between the atoms. Due to non-zero detuning, nine-peaked spectra are observed and are given a clear explanation from the dressed-state viewpoint. It is established that in the case of symmetrical excitation, the intensity of the emission spectrum is two times larger than that in the case of non-symmetrical excitation.