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Physical review. B, Condensed matter

Spatiotemporal dynamics of photon echoes from continuum states in semiconductors

Stephan Glutsch, U. Siegner, D. S. Chemla

Published Aug 15, 1995• 17 citations
Publisher

Abstract

We study the dynamics of coherent emission of a semiconductor within the framework of the semiconductor Bloch equations, both in the time domain and in real space for various excitation conditions. We find that the spatial properties of the four-wave-mixing (FWM) response reflect the well-known temporal dynamics. For excitation high above the band edge, the FWM signal is emitted as a photon echo. This photon echo from continuum states of a semiconductor has the same dynamical properties as a photon echo from inhomogeneously broadened uncoupled two-level systems. However, unlike the case of two-level atoms, the polarization of the photon echo from the semiconductor continuum extends over macroscopic distances in real space. The implications of the large spatial extent of the photon echo polarization are discussed. In particular, we show that, in spite of the macroscopic size of the photon echo polarization, the wavelength of the exciting light can still be neglected.

DOI
10.1103/physrevb.52.4941

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Physical review. B, Condensed matter•Mar 15, 1994•73 citations
We study the dynamics of coherent emission of a semiconductor within the framework of the semiconductor Bloch equations, both in the time domain and in real space for various excitation conditions. We find that the spatial properties of the four-wave-mixing (FWM) response reflect the well-known temporal dynamics. For excitation high above the band edge, the FWM signal is emitted as a photon echo. This photon echo from continuum states of a semiconductor has the same dynamical properties as a photon echo from inhomogeneously broadened uncoupled two-level systems. However, unlike the case of two-level atoms, the polarization of the photon echo from the semiconductor continuum extends over macroscopic distances in real space. The implications of the large spatial extent of the photon echo polarization are discussed. In particular, we show that, in spite of the macroscopic size of the photon echo polarization, the wavelength of the exciting light can still be neglected.
Using a perturbation theory based on the density-matrix formulation, we study the nonlinear optical responses of a noninteracting three-level model system to consecutive coherent pulsed excitations, as realized in several recent experiments involving excitonic transitions in quantum wells. The terahertz emission, which is a second-order response, and the four-wave mixing signal, a third-order response, are calculated within the rotating-wave approximation, in the presence of detuning, dephasing, and inhomogeneous broadening. We study the quantum beats in the photon echo from transient four-wave mixing experiments of a three-level system. We find that the temporal profile of the photon echo signal in the four-wave mixing experiments depends very strongly on the amount of inhomogeneous broadening of the energy levels involved. Both the position and the intensity of the peaks exhibit a smooth evolution from strong quantum beats to a conventional photon echo as the inhomogeneous broadening increases. These features from our noninteracting model system are compared with a recent experiment, and found to account for a number of experimental observations.
The coherent optical response of semiconductor quantum wells is studied theoretically using the multiband semiconductor Bloch equations which include coupling of the heavy- and light-hole bands as well as many-body Coulomb effects. For the case of a two-pulse excitation scheme it is shown how the different rotational symmetries of heavy- and light-hole bands induce a strong polarization dependence of the signal in the photon echo direction. The selection rules are based on the Kane-Luttinger theory while the transition amplitudes are obtained by numerically solving the multiband semiconductor Bloch equations. In addition, the influence of valence-band mixing effects on the optical Stark effect is demonstrated.
The semiconductor Bloch equations are solved numerically for a two-pulse photon-echo configuration. The time-dependent diffracted signal is computed and the significance of many-body effects, carrier relaxation, and dephasing is investigated in detail. Assuming femtosecond-pulse excitation at various intensities and frequencies, distinctly different results are obtained if the exciton or the continuum electron-hole-pair states are excited. It is shown that pure exciton excitation produces a free-induction decay signal and no photon echo. An echo signal is obtained only if continuum states are excited either directly by choosing the central pulse frequencies appropriately or if the band-gap renormalization is sufficiently strong to shift continuum states into resonance. A continuous transition between free-induction decay and photon-echo signal is obtained with increasing excitation amplitude. A perturbative analytical analysis of the equations allows one to identify the role of the many-body effects in producing the different features.
Summary form only given. Even one decade after the pioneering photon echo experiments by Shank et al. (1988,1991) in which GaAs was investigated at room temperature using /spl ap/10 fs optical pulses, not a single experiment has actually shown directly that the coherent real-time response of semiconductor band-to-band transitions under these conditions is a photon echo indeed. Recent experiments with /spl ap/10 fs pulses exciting GaAs at low temperatures have explicitly shown that the response is not a photon echo for low excitation densities (/spl ap/10/sup 15/ cm/sup -3/). From these experiments it has also become clear that the coherent response after excitation with 10 fs pulses is distinctly different from that after excitation with 100 fs pulses. We investigate the coherent real-time response at elevated carrier densities using transient four-wave mixing and an up-conversion scheme with a time resolution of 5 fs. We focus on approximately resonant excitation (50 meV above gap) of a 0.6 /spl mu/m thin film of bulk GaAs at T=300 K.
Coherent transient spectroscopy of semiconductor nanostructures has become an active field of research in recent years. Most such experiments are analyzed in terms of a simple two-level model in which the effects of interaction and induced fields are ignored. We discuss two very different cases where inclusion of these generally-neglected effects leads to large and important modification in the temporal response of the system. In the first case, interactions between excitons strongly modify the temporal response of four-wave-mixing (FWM) signals from quantum wells. This is the temporal analog of well-known effects in the spectral domain, such as bleaching of the exciton absorption and bandgap renormalization. In the second case, the shape of a low-intensity pulse is severely distorted after transmission through a typical quantum well sample. Interferometric measurements show that reradiation of induced polarization is responsible for the distortion. The distortion depends strongly on the dephasing time and has important implications for all time-resolved measurements. 1.
Excitonic nonlinearities in the weak-excitation limit condition are examined with time-integrated and time-resolved four-wave mixing (FWM). Below an excitation of 3\ifmmode\times\else\texttimes\fi{}109{10}^{9}109 excitons/cm2{\mathrm{cm}}^{2}cm2, coherent third-order processes prevail. Echo-type signals are observed in parallel and perpendicular polarization configurations. The coherent process induced by the two-photon coherence of the two-exciton state is attributable to signals in the perpendicular configuration. The polarization dependences of a temporal profile and the intensity of FWM signals are well explained with third-order perturbational analysis that takes into account the two-exciton states and inhomogeneity.