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physica status solidi (b)

Quantum Beats of Excitons in Cu2O at Double Optical Resonance

M. I. Shmiglyuk, A. I. Bobrysheva, V. Pavlov

Published Feb 1, 1997• 3 citations
Publisher

Abstract

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.

DOI
10.1002/1521-3951(199702)199:2<427::aid-pssb427>3.0.co;2-y

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Physical Review B•Dec 23, 2009•1 citation
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.
The optical Stark effect and quantum beats in a GaAs/AlGaAs quantum well are investigated theoretically for the case when the first two electron size-quantization levels are mixed dynamically by a high-intensity CO 2 laser pulse polarized perpendicular to the plane of the quantum well. The quasienergy spectrum of heavy-hole excitons and the ratio between the probabilities of exciton transition with and without a strong electromagnetic field are obtained. The time-dependent intensity of absorption of the sensing light is determined. It exhibits quantum beats at twice the electron Rabi frequency.
Abstract This paper presents a theoretical investigation of quantum beats of excitons in GaAs/AlGaAs circular cylindrical quantum wires. A three-level model of excitons, including a ground state and two excited states, has been applied to derive the renormalized wavefunctions and the time-dependent absorption intensity of excitons when the system is irradiated by a strong pump laser resonating with the distance between the two excited-levels. Our results show that a periodic oscillation form of the absorption intensity, obvious evidence of the quantum beat behavior, has appeared. Furthermore, the mechanism of the generation, as well as the effects of the wire radius and the pump laser detuning on the frequency (period) and amplitude of quantum beats, have been explained in detail. These results suggest potential applications in the fabrication of some quantum computation devices.
Multiple frequency quantum beats of a system of the coherently excited quantum confined exciton states in a high-quality semiconductor structure containing a wide InGaAs/GaAs quantum well are experimentally detected by the spectrally resolved pump-probe method. The beat signal is observed both at positive and at negative delays between the pump and probe pulses. Several quantum beat (QB) frequencies are observed in the experiments, which coincide with the interlevel spacings in the exciton system. A theoretical model is developed, which allows one to attribute the QBs at negative delay to the four-wave mixing (FWM) signal detected at the nonstandard direction. The beat signal is strongly enhanced by the interference of the FWM signal with the secondary emission induced by the probe pulse. At positive delays, the QBs are due to the interference of the quantum confined exciton states. The decay time for QBs is of the order of several picoseconds both at positive and negative delays. This is close to the relaxation time of the exciton population that allows one to consider the exciton depopulation as the main mechanism of the coherence relaxation in the system under study.
We propose and examine theoretically a four-wave-mixing experiment in which excitons in Cu2O{\text{Cu}}_{2}\text{O}Cu2​O are pumped directly into a state with wave vector k=0\mathbf{k}=\mathbf{0}k=0 by two counter-propagating cross-polarized laser pulses and which is subsequently probed by a third time-delayed pulse. Approximate analytical solutions of the time evolution equations are found which describe the time dependence of the exciton and photon densities. Most importantly, we obtain the dependence of the resulting phase-conjugated signal versus the delay time td{t}_{d}td​ between the probe and pump pulses. It is shown that the total number of photons generated in the course of the experiment is proportional to the areas of all three incoming pulses. The dependence of the resulting time-integrated signal on the delay time td{t}_{d}td​ is the same as the exciton density dependence on the time ttt. Hence, one may directly study the time evolution of the exciton condensate. The approximate analytical results are compared with a numerical solution of the evolution equations for a wide range of incident pulse intensities. It is noted that an exciton condensate arising by an alternate route can also be probed through a phase-conjugated two-photon process.