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arXiv:physics/0412160

On Theory of the Phonon Perturbed Superradiance

A. P. Saǐko

Published Dec 24, 2004• 0 citations
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Abstract

The paper examines superradiance in impurity crystals in the field of a coherent phonon wave excited by two ultrashort laser pulses via Raman scattering processes at the moment of preparation of the initial state of an ensemble of emitters. It is shown that by varying the power of the excitation pulses and their mutual direction of propagation, one can control the superradiance parameters and extract data on the electron-phonon coupling constant and its anisotropy.

DOI
10.48550/arxiv.physics/0412160

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The paper examines superradiance in impurity crystals in the field of a coherent phonon wave excited by two ultrashort laser pulses via Raman scattering processes at the moment of preparation of the initial state of an ensemble of emitters. It is shown that by varying the power of the excitation pulses and their mutual direction of propagation, one can control the superradiance parameters and extract data on the electron-phonon coupling constant and its anisotropy.
.By partial elimination of the boson variables an exact hierarchy of kinetic equations for a two-level crystal system interacting with an electromagnetic field is obtained and investigated. The scattering of photons by phonons is taken into account. It is shown that the presence of scattering by phonons leads to a reduction in the delay time of the superradiant pulse. The radiation intensities at the fundamental, sum, and difference frequencies are determined. The influence of radiation processes on the dynamics of the phonon subsystem is studied. Superradiance in two-level macroscopic systems is usually investigated by means of models of rigidly fixed emitters [1,2] or by representing the emitters as a Maxwellian gas [3,4]. However, in real crystals the emitters themselves vibrate. There have been various recent experiments on the generation of superradiance in impure crystals [5-8]. In connection with the interpretation of these experiments, it is of interest to consider the influence of Mandelstam-Brillouin scattering on the parameters of superradiant systems. Such a problem is also of interest in connection with the development of a superradiant laser with ferroelectric working medium [9], in particular for the detection of gravitational waves [I0]. In the theory of superradiance, Thompson [Ii, 12] has constructed a well-known model in which s contribution due to scattering of the light by phonons is determined in the first order of an expansion of the density with respect to the relative displacements of the ions. In [11-12], only the equilibrium properties of such a model were considered. In our earlier paper [13], the method of partial elimination of the boson variables proposed in [14] was developed to describe the dynamical properties of such a system. In the present paper, we investigate in detail the process of collective radiation in such a system, and we also consider the influence of the radiation processes on the dynamics of the phonon subsystem in the crystal. The Hamiltonian of Thompson's model has the form H=H.~+HF+HMF, HM= ~ ~cooRfz + ~ ~qbq+bq, Hv=Z ?~oA.a~+a~: , r q ~ (I)
Summary form only given. The investigation of coherent phonons has been a field of extensive efforts since the first observation of coherent phonons in 1990. Several excitation mechanisms for coherent phonons in solids have been identified among which the most prominent is impulsive stimulated first order Raman scattering. Coherent states exhibit an oscillating expectation value of the phonon amplitude of a given mode while the statistic properties like amplitude variances and covariances remain static. However, dynamics of these statistic variables can be driven by second-order Raman-scattering (SOR), e.g., oscillating amplitude variances (phonon squeezed states) as first reported by Garret et al. Here we report-to our knowledge for the first time-on correlated states of phonon-mode-pairs consisting of different phonons driven by ultrashort light pulses. KTaO/sub 3/, is the ideal material for this study since first order Raman processes are not allowed.
A model of semiconductor quantum dots coupled to phonons and laser light, which is relevant in the limit of strong electronic confinement, is investigated. For an arbitrary sequence of excitations by ultrafast pulses, analytical solutions are obtained for all pertinent density-matrix elements. The results are nonperturbative with respect to the coupling to both phonons and laser light. The derivation depends neither on a particular choice of electronic wave functions nor on a particular wave-vector dependence of the phonon interaction or phonon dispersion. All components of the density matrix exhibit oscillatory dependences on the pulse areas of the exciting pulses analogously to the Rabi oscillations known from simple two-level systems. Three typical applications of the general results are worked out: (a) the influence of phonons on four-wave-mixing spectra, (b) the coherent control of electronic dot occupations in the presence of phonons, and (c) the dynamics of phonon correlations including the formation of a stable polaron spatially localized in the dot and the emission of a pulsed phonon wave packet that leaves the dot.
We investigated the coherent phonon generation mechanism by irradiation of an ultrashort pulse with a simple two-level model. Our derived formulation shows that both impulsive stimulated Raman scattering (ISRS) and impulsive absorption (IA) simultaneously occur, and phonon wave packets are generated in the electronic ground and excited states by ISRS and IA, respectively. We identify the dominant process from the amplitude of the phonon oscillation. For short pulse widths, ISRS is very small and becomes larger as the pulse width increases. We also show that the initial phase is dependent on the pulse width and the detuning.
The results of theoretical and experimental superradiance studies in a pyrene-doped biphenyl crystal are presented. The superradiance nature of photon emission under certain conditions is experimentally proved for this crystal system. Experimental data fit the theory. The influence of induced radiation and of electron-phonon coupling on optical superradiance is theoretically investigated using the nonequilibrium statistical operator method. Possible superradiance applications are discussed, including coherent nonlinear spectroscopy, coherent electromagnetic pulse generation, and superradiant echo.
The Dicke superradiance on vibronic transitions of impurity crystals is considered. It is shown that parameters of the superradiance (duration and intensity of the superradiance pulse and delay times) on each vibronic transition depend on the strength of coupling of electronic states with the intramolecular impurity vibration (responsible for the vibronic structure of the optical spectrum in the form of vibrational replicas of the pure electronic line) and on the crystal temperature through the Debye-Waller factor of the lattice vibrations. Theoretical estimates of the ratios of the time delays, as well as of the superradiance pulse intensities for different vibronic transitions well agree with the results of experimental observations of two-color superradiance in the polar dielectric KCl:O 2 − . In addition, the theory describes qualitatively correctly the critical temperature dependence of the superradiance effect.