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Journal of Nonlinear Optical Physics & Materials

Quantum Coherence in Ultrafast Semiconductor Spectroscopy

H. Haug

Published Jun 1, 1998• 1 citation
Publisher

Abstract

Coherent optical phenomena such as the optical Stark effect, Rabi flopping, photon echo and quantum beating which are well-known in atomic spectroscopy can also be observed in semiconductors by using femtosecond laser pulses. On these short time scales, the quantum coherence of the optical excitations in the solid do not only influence the optical properties but change at the same time the relaxation and dephasing kinetics. The quasi-classical Boltzmann kinetics has to be replaced by quantum kinetics. Coherence leads to the appearance of memory in the scattering integrals. For femtosecond four-wave mixing and pump-and-probe spectroscopy the use of quantum kinetics for LO-phonon and for carrier-carrier scattering will be reviewed.

DOI
10.1142/s0218863598000193

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Coherent optical phenomena such as the optical Stark effect, Rabi flopping, photon echo and quantum beating which are well-known in atomic spectroscopy can also be observed in semiconductors by using femtosecond laser pulses. On these short time scales, the quantum coherence of the optical excitations in the solid do not only influence the optical properties but change at the same time the relaxation and dephasing kinetics. The quasi-classical Boltzmann kinetics has to be replaced by quantum kinetics. Coherence leads to the appearance of memory in the scattering integrals. For femtosecond four-wave mixing and pump-and-probe spectroscopy the use of quantum kinetics for LO-phonon and for carrier-carrier scattering will be reviewed.
Summary form only given. The coherence decay of optically excited electronic systems provides one of the most powerful tools to investigate interaction processes of excited states. In semiconductors, the optical coherence phenomena are usually investigated by nonlinear techniques such as four wave mixing (FWM), photon echo, or reflectivity experiments. Exciton-phonon, exciton-exciton, or exciton-free carriers scattering processes have been explored in recent years with these techniques. As demonstrated recently, a direct measurement of the optical dephasing time can be obtained through the temporal coherent control of electronic excitations. In these experiments, the emission following the excitation by an ultrashort optical pulse sequence, is detected in a non-specular direction (secondary emission). This provides an alternative approach to FWM techniques, which allows us to analyse the scattering processes either with phonons or due to mutual collisions. Using the coherent control technique monitored through the secondary emission (SE), we report on the coherent dynamics of excitons in bare quantum wells (QW) and compare it to that of exciton-polaritons in microcavity (MC) embedded quantum wells.
We theoretically estimate the possibility of detectable coherence effects in nonlinear femtosecond pump-and-probe absorption spectroscopy of semiconductors at high excitation energies and densities by hybridizing the quantum mechanical equations of motion for the intraband and interband density matrices of the photoexcited carriers with an ensemble Monte Carlo simulation of the detailed scattering dynamics. We predict realizable experimental scenarios for Rabi-type oscillations in the transient absorption change at the excitation frequency.
Using laser pulses of duration comparable to semiconductor relaxation and dephasing times, the coherent phenomena common to two-level systems have been demonstrated in II-VI and III-V semiconductors. These light-matter interactions are characterized by electrons and holes in their initially excited states and/or a macroscopic polarization that persists after the excitation. A nonthermal carrier distribution was observed in bulk CdSe, demonstrating the extremely fast energy relaxation possible when carrier-LO-phonon scattering is included. Quantum-confined CdSe microcrystallites were then employed to limit the available decay avenues. The one and two-pair transitions were characterized, and using spectral hole-burning, energy relaxation was shown to be substantially slower than in bulk. Dipole dephasing remained very rapid. Persistent macroscopic polarization was demonstrated in semiconductors through pump and probe experiments conducted on time scales faster than the inverse linewidth of the exciton. In the first set of experiments, it was found that the exciton optical Stark shift deviates from that predicted by a steady-state theory. The shift is smaller than expected and lasts longer than the pump pulse. Both effects are explained by free evolution of the exciton's polarization. Transient exciton bleaching is observed and shown to be a result of adiabatic following. In a second study of coherent polarization, spectral oscillations at negative delay times were studied. Oscillations were measured in a wide variety of semiconductors, temporally preceding several different pump-probe phenomena. By comparison with a semiclassical theory, it was shown that spectral oscillations in the spectral region of the exciton are evidence of persistent exciton polarization. Oscillations in the band are due to four wave mixing of the pump and probe beams.
We investigate resonant time-resolved four-wave mixing on GaAs quantum wells at T=300KT=300\mathrm{K}T=300K and at elevated carrier densities using excitation with 11 fs optical pulses. The experiments are compared with non-Markovian quantum-kinetic calculations including carrier-carrier and carrier-LO-phonon scattering. A self-consistently determined two-time-dependent screened random-phase approximation Coulomb potential is used for the carrier-carrier scattering. In experiment and theory we find an unusual real-time response, which is far from an ideal photon echo. Surprisingly, we also find that the dependence of the decay time \ensuremath{\tau} of the four-wave-mixing signal versus the optically excited nonequilibrium electron-hole pair density neh{n}_{\mathrm{eh}}neh​ is quantitatively similar to the corresponding behavior of bulk GaAs. Thus both data sets can be fitted by the same form ${\ensuremath{\tau}}^{\ensuremath{-}1}={\ensuremath{\tau}}_{0}^{\ensuremath{-}1}{+cn}_{\mathrm{eh}}^{1/3}.$ This is not consistent with previous experimental work in a more limited range of carrier densities, which determined different behavior for quasi-two-dimensional (2D) and 3D, i.e., exponents of 0.3 and $0.55\ifmmode\pm\else\textpm\fi{}0.04,$ respectively.
The availability of femtosecond pulses in the optical-frequency regime allows the study of coherent effects in the interaction between semiconductors and light. Because the properties of the exciting pulses become important ingredients in spectroscopy, the theoretical analysis must treat the complete time dependence of the system. For this purpose we use the semiconductor Bloch equations (SBE),1-3 which are the coupled equations of motion for the interband polarization and the electron and hole populations for an interacting electron-hole system in the random-phase approximation. The equations describe the electron-hole Coulomb attraction leading to excitonic features; they contain phasespace filling and band-gap renormalization effects, as well as the dipole interaction with the applied light field.
State of the art of optical coherent spectroscopy of doped solids that are promising as information carriers for optical processors is reviewed. Special attention is paid to optical echo spectroscopy of doped crystals classified as the Van-Vleck paramagnets where the long-lived stimulated echo is observed with the optical-memory time reaching several hours at low temperatures. Modern elaborations of optical echo processors based on this echo phenomenon are discussed. Physical principles of femtosecond echo spectroscopy and coherent four-wave mixing spectroscopy are formulated. The abilities of these methods in the diagnostics of fast processes at room temperature are illustrated using examples of a doped polymer films. The results of elaborations of a new branch of optical spectroscopy (biphoton spectroscopy) are also presented. The advantages and possible applications of this method are demonstrated using an example of two crystals (Er 3+ :YAG and Cr 3+ :Al 2 O 3 ).