Multiphonon processes in impurity centres: nonperturbative theory

Abstract

A nonperturbative theory of the multiphonon relaxation of a strongly excited local vibration is developed. It is found that for a high initial level, the relaxation first accelerates in time, and later starts to slow down. The experimental evidence of such a non-monotonous relaxation is given by the hot luminescence in solid Xe. A theory of optical transitions in a center with strongly reduced local springs in the final electronic state is also developed. In this case a resonant increase of the local density of states of low-frequency phonons takes place, and a low frequency pseudo-local mode emerges. Appearance of such a mode in the final state means that a strong mode mixing takes place at the transition. This results in strong increase of the mean number of created low-frequency phonons. As a consequence, the zero-phonon transition practically disappears and the long-wave part of the phonon sideband is strongly enhanced, resulting in formation of so-called lambda-shaped spectrum. Multiphonon relaxation of local modePhysical processes in solids usually involve the relaxation of the vibrational energy. For example, optical excitation of F-centers or other centers in ionic crystals and self-trapped excitons usually leads to excitation of strong vibrations. In CARS experiments one usually excites strong long-wave coherent vibration, which decays via multiphonon anharmonic interaction into other phonons. Laser methods allow one to achieve also direct excitation of non-coherent vibrations of impurity molecules in crystals. The subsequent processes are essentially determined by the relaxation of these vibrations. The vibrational quanta of light molecules may exceed many times the maximal energy of phonons. In such a case the vibrational relaxation takes place as a multiphonon emission. Usually this process is considered in the frames of the perturbation theory, by applying the Fermi Golden Rule [1 -5]. However, this theory works only if the energy of the mode is small. Here we apply another method [6 -7], which works for the large energy of the mode, supposing that the relaxation rate remains less than the frequency ω l of the mode.In [6][7] it is taken into account that a strongly excited mode can be considered classically. Then the mode causes a perturbation of phonons which is quasi-periodical in time. The Coleman theorem [8] reads that the zero-point state and the operators of bosons interacting with a classical field are not invariant with respect to the transformation which changes the classical field. It means that the transformed destruction operators are not the zero operators for the initial zero-point state. This corresponds to the fact that classical field which changes in time leads to emission of phonons.