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physica status solidi (b)

Nonlinear Optical Nutation on Interexciton Transitions in Cu2O. Analogue of the Equidistant Three‐Level System

M. I. Shmiglyuk, P. I. Bardetskiı̆, S. D. Tiron

Published Jul 1, 1989• 1 citation
Publisher

Abstract

Abstract The nonlinear nutation on the optical transitions between the IS(Λ ) and 2P(Λ , 2Λ , Λ , Λ ) exciton states of the Cu2O yellow series is studied theoretically. An idealized case is considered when one coherent excitonic mode of a macroscopic amplitude is created in the 2P(Λ ) state by the external resonant pumping. It is shown that in this case the CO2‐laser induced dipole transition scheme is the same as for the model equidistant three‐level system. The evolution of the nonstationary state of the exciton–photon system to the stationary one due to the polarization damping is considered. The phase diagrams are investigated both, at strong and weak damping.

DOI
10.1002/pssb.2221540119

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Journal of Experimental and Theoretical Physics•Aug 1, 2013•0 citations
Abstract The nonlinear nutation on the optical transitions between the IS(Λ ) and 2P(Λ , 2Λ , Λ , Λ ) exciton states of the Cu2O yellow series is studied theoretically. An idealized case is considered when one coherent excitonic mode of a macroscopic amplitude is created in the 2P(Λ ) state by the external resonant pumping. It is shown that in this case the CO2‐laser induced dipole transition scheme is the same as for the model equidistant three‐level system. The evolution of the nonstationary state of the exciton–photon system to the stationary one due to the polarization damping is considered. The phase diagrams are investigated both, at strong and weak damping.
Abstract The non‐linear optical nutation on the transitions between IS and 2P exciton states of the Cu2O yellow series is considered theoretically taking into account their degeneracy and polarization properties. The problem is solved under various initial conditions for certain definite orientations of the electrical component of the laser field that causes the interexciton transitions. It is shown that the exciton and photon concentrations vary periodically in time within a certain range near their steady equilibrium values which coincide with the stationary ones. The nutation frequencies are found. A stationary condition is obtained and the stationary frequencies and concentrations are determined.
Abstract The three‐level optical Stark effect is due to a dynamical coupling of two excited levels. The coupling is achieved by a high intensity CO2 laser. Results of experiments on multiple quantum wells (MQW) and excitons in Cu2O are presented. In the MQW the coupling between the two lowest conduction band sublevels leads to characteristic changes in the one‐photon spectra of the lowest exciton transitions. In Cu2O the CO2 laser pulse couples 1 S and 2 P excitons. In this case the one‐photon spectrum of the 2 P exciton (dipole allowed) and also of the 1 S spectrum (quadrupole allowed) show drastic changes. Most of the experimental results can be explained quantitatively in terms of a nonlinear susceptibility.
Abstract A model which allows to treat self‐consistently many‐body exciton effects, including biexciton formation, is proposed for the theoretical description of an excitonic polarization induced by an intense electromagnetic field. In the presence of a pump field the normal spectrum of electromagnetic waves in the vicinity of the nonlinear biexciton resonance is shown to be composed of four polariton branches, where each is the superposition of two photons and two excitons. In the self‐consistent field approximation, the structure of the interconnected, strongly nonlinear exciton and biexciton resonances is studied, including optical Stark shift, multistable behaviour, etc. For a certain range of the exciton interaction parameters at sufficiently strong pump wave the system of excitons and excitonic molecules transforms abruptly to a dense coherent electron–hole “liquid”. Appearance and temporary evolution of an exciton–biexciton system after switching on a pump is also considered.
The quantum beats (QB) in the time-dependent absorption intensity of the probe pulse and the spontaneous luminescence one in Cu2O crystal at the condition of double optical resonance are studied theoretically. It is assumed that the pump is performed by the CO2 laser pulse, which couples dynamically the 1s (Γ 5 + ) and 2p (Γ 4 - , Γ 5 - , Γ 3 - , Γ 2 - ) excitonic states and leads to their splitting into two or three quasienergy levels. The frequency of the probe pulse is in the region of the Γ 5 + exciton resonance. The respective intensities for different directions of the electric field E L of the pump, the polarization ξ of the probe pulse, and the observation q are obtained. The QB take place with the doubled Raby frequency, which at different E L , ξ, and q includes different sets of matrix elements of dipole transitions between 1s (Γ 5 + ) and 2p (Γ 4 - , Γ 5 - , Γ 3 - , Γ 2 - ) levels. These unknown matrix elements can be obtained, measuring the period of the QB.
A theoretical study is carried out of quantum beats (QB) in the time-dependent intensities of absorption of a test pulse and of spontaneous luminescence in a Cu2O crystal under conditions of double optical resonance. It is assumed that pumping is effected by a CO2-laser pulse which dynamically couples the exciton levels 1s(Γ 5 + ) and 2p(Γ 4 − ,Γ 5 − ,Γ 3 − Γ 2 − ) and splits them into two or three pairs of quasi-energy levels. The frequency of the test pulse is in resonance with the frequency Γ 5 + of the exciton. The corresponding intensities for various directions of the electric vector of the pump field E L, the polarization vector ξ, and the wave vector q of the test pulse are obtained. The frequency of the quantum beats is twice the Rabi frequency, which for different values of E L, ξ and q contains different sets of matrix elements of the dipole transitions between the levels 1s(Γ 5 + ) and 2p(Γ 4 − ,Γ 5 − ,Γ 3 − Γ 2 − ). Thus, by measuring the period of the quantum beats it is possible to determine the unknown matrix elements of the indicated transitions.
Optical nutation in the exciton range of spectrum is studied in the mean field approximation taking into account exciton-photon and elastic exciton-exciton interactions. It is shown that the features of nutation development are determined by the initial exciton and photon densities, the resonance detuning, the nonlinearity parameter, and the initial phase difference. For nonzero initial exciton and photon concentrations, three regimes of temporal evolution of excitons and photons exist: periodic conversion of excitons to photons and vice versa, aperiodic conversion of photons to excitons, and the rest regime. In the rest regime, the initial exciton and photon densities are nonzero and do not change with time. The oscillation amplitudes and periods of particle densities determined by the system parameters are found. The exciton self-trapping and photon trapping appearing in the system at threshold values of the nonlinearity parameter were predicted. As this parameter increases, the oscillation amplitudes of the exciton and photon densities sharply change at the critical value of the nonlinearity parameter. These two phenomena are shown to be caused by the elastic exciton-exciton interaction, resulting in the dynamic concentration shift of the exciton level.