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Physics of the Solid State

Quantum beats in excitons in Cu2O

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

Published May 1, 1997• 0 citations
Publisher

Abstract

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.

DOI
10.1134/1.1129961

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•Jan 1, 2003•0 citations
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 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.
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.
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.
The focus of the thesis is nonlinear transient optical properties and coherent control of single interface fluctuation quantum dots (QD's). When single exciton and biexciton resonances were driven by strong resonant laser pulses, Rabi oscillations of these transitions were observed in the differential transmission (DT) geometry. These results extend the concept of coherent control to the limit of single quantum confined systems in solids and have important implications for the feasibility of building quantum information processing devices using semiconductor QD's. Exciton Rabi oscillations are equivalent to arbitrary single-bit operations. The pulsed control of the exciton-biexciton transition is utilized as the optical operation for building a two-bit controlled rotational gates (CROT) in a single QD. A fidelity of 0.79 was obtained from numerical evaluation of the gate operation itself assuming typical decay parameters measured from these dots. Next, the nonradiative quantum coherence between two orthogonally polarized excitons confined in a single QD was studied. By using pulses with large enough bandwidth and the proper polarization, two exciton states are simultaneously excited. The quantum beats between the two exciton states were temporally resolved as the relative phase between the two dipole oscillations changed. It was found that the nonradiative coherence time is limited by the lifetimes of the excitons involved even in the strong field regime. In the basis of the pseudo-spin Bloch vectors of exciton transitions, the total wavefunction following the pulsed excitation is an entangled state, i.e. the wavefunction is non-factorizable. Finally, the quantum coherence between the biexciton, exciton, and the crystal ground states was studied in a novel quantum beat experiment, where the oscillations only existed when the pump and probe pulses overlapped in time. Laser pulses generated after a passive pulse shaper with just enough bandwidth to cover both the exciton and biexciton transitions were used in this experiment. The appearance of the beats is indicative of a reasonably long coherence time between the biexciton and other states even in the presence of strong pulsed excitations.