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Physical review. B, Condensed matter

Phonon enhancement and saturation in a three-level system

Benjamin Fain

Published Nov 15, 1982• 7 citations
Publisher

Abstract

A model consisting of a distribution of three-level systems (defects or ionic impurities) in a lattice characterized by a given phonon spectrum is considered in detail. Equations determining the temporal behavior of such a system in an electromagnetic field are analyzed. A steady-state solution describing three-level saturation in the system is achieved. The possibility of the stimulated emission of phonons is considered. It is shown that laserlike self-excitation of phonons cannot be realized, though phonon flux enhancement may be achieved provided certain conditions are fulfilled.

DOI
10.1103/physrevb.26.5932

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A model consisting of a distribution of three-level systems (defects or ionic impurities) in a lattice characterized by a given phonon spectrum is considered in detail. Equations determining the temporal behavior of such a system in an electromagnetic field are analyzed. A steady-state solution describing three-level saturation in the system is achieved. The possibility of the stimulated emission of phonons is considered. It is shown that laserlike self-excitation of phonons cannot be realized, though phonon flux enhancement may be achieved provided certain conditions are fulfilled.
The equations, determining temporal behavior of coupled electronic and phonon subsystems in the electromagnetic field, are analyzed. The steady state solution describing saturation of the three level in such a system is achieved. It is shown that laser-like self-excitation of phonons cannot be obtained though essential phonon enhancement may be gained provided certain conditions are fulfilled. Field induced transparency is predicted between first two levels when the field saturates ground and highest levels, and the concentration of ions is high.
An inhomogeneously broadened three-level electronic system related to impurity ions embedded in a crystal with anisotropic phonon modes is considered. It is shown that such a system can sustain laserlike self-excitation under a steady-state condition, depending on the crystal properties. The anisotropy of the phonons is represented by two sets of modes which are distinguished by their lifetimes. Laserlike self-excitation has been shown to be impossible for isotropic systems. This and the influence of crystal properties on the self-excitation in anisotropic systems are discussed.
The possibility of stimulated emission of coherent phonons by impurities (ions) embedded in a crystal is considered. It is shown that when the ions with homogeneously broadened levels are subjected to an electromagnetic field, the frequency Ω of which is larger than an eigenfrequency of the ion ω21, at the Raman frequency ωq=Ω−ω21, a coherent stimulated emission of phonons may emerge. The absorption rate of the pumping electromagnetic field has a singularity near the threshold of the phonon self-excitation.
Stimulated emission is studied of phonons resonant with the metastable Zeeman-split E-bar(2{(}^{2}(2E) doublet in ruby. Initial population inversion of this two-level system is prepared by selective pulsed optical pumping, and the ensuing stimulated emission of resonant phonons is observed via an accelerated growth of the luminescence intensity emanating from the lower level. Under favorable conditions, a periodic recurrence of the process of stimulated emission is observed, which points to a phonon cavity formed by the end faces of the crystal in combination with a limited interaction length of the resonant phonons. To analyze these phenomena in detail, use is made of rate equations for the phonon occupation and the level populations with explicit account of their position dependences. With plausible assumptions an analytic solution of these equations is achieved, which excellently fits the data. The effect of lattice anharmonicity is shown to depend on the phonon energy in agreement with the theoretical prediction.
The first two successful predictions for amorphous solid experiments by tunneling-two-level-system (TTLS) was phonon echo and saturation phenomena. In this paper by generalizing TTLS to infinite-level-system model with certain randomness and nonlinearity, we prove that phonon echo is a stimulated emission process. The classical infinite-level-system (taking ℏ→0\hbar\to 0ℏ→0 limit) cannot find saturation effect, while quantum infinite-level-system can find it with certain nonlinearity assumed. We also prove that without randomness or nonlinearity neither phonon echo nor saturation exists in arbitrary infinite-level-system.
Studies the competition between absorption and stimulated emission induced by two laser fields at low intensities interacting on a two-photon resonance with a three-level atom. The induced spectrum into the ground state consists of a peak whose height and asymmetry depend strongly on the detuning. The spectra arising from the emission of a laser photon by the excited state consists of two peaks describing stimulated emission and induced absorption, respectively, where the former dominates the latter for small values of the Rabi frequencies but for higher ones, they cancel each other out.