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Physical review. B, Condensed matter

Biexcitonic effects in transient nonlinear optical experiments in quantum wells

Gleb Finkelstein, Shimshon Bar-Ad, O. Carmel, Israel Bar-Joseph, Yehoshua B. Levinson

Published May 15, 1993• 73 citations
Publisher

Abstract

We present a model for the nonlinear optical response of quantum wells, which includes biexcitons. We show that within this model, the interaction of two laser pulses, mediated by the nonlinear susceptibility, results in oscillations and in coupling between ${\mathrm{\ensuremath{\sigma}}}^{+}$ and ${\mathrm{\ensuremath{\sigma}}}^{\mathrm{\ensuremath{-}}}$ excitons. This explains the temporal behavior of the differential absorption and four-wave mixing in recent experiments [Phys. Rev. Lett. 68, 349 (1992); 68, 1880 (1992)]. The oscillations have a frequency equal to the biexciton binding energy, and are different from known interference and quantum beat phenomena.

DOI
10.1103/physrevb.47.12964

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We present a model for the nonlinear optical response of quantum wells, which includes biexcitons. We show that within this model, the interaction of two laser pulses, mediated by the nonlinear susceptibility, results in oscillations and in coupling between \ensuremathσ+{\mathrm{\ensuremath{\sigma}}}^{+}\ensuremathσ+ and \ensuremathσ\ensuremath−{\mathrm{\ensuremath{\sigma}}}^{\mathrm{\ensuremath{-}}}\ensuremathσ\ensuremath− excitons. This explains the temporal behavior of the differential absorption and four-wave mixing in recent experiments [Phys. Rev. Lett. 68, 349 (1992); 68, 1880 (1992)]. The oscillations have a frequency equal to the biexciton binding energy, and are different from known interference and quantum beat phenomena.
We investigate the four-wave mixing response of semiconductor quantum wells having a predominantly inhomogeneous broadening of the exciton states. The influence of the biexcitons on the nonlinear emission, in proximity to the lowest exciton resonance, is studied. Using about 1 ps long pulses, we show that biexcitons are created for all excitation energies lying within the broadened exciton absorption line, and that their binding energy does not depend on the exciton energy. Reducing the temporal width of cross-linearly polarized incident laser fields to about 0.1 ps, we observe a drastic changeover from a prompt response to a photon echo, and quite interesting beating phenomena, visible in time-integrated as well as in time-resolved experiments, appear. Our observations compare well with the numerical solutions of the optical Bloch equations for a five-level scheme. The influence of the inhomogeneous broadening on the beating phenomena is discussed.
We investigate the spectral properties of the excitonic nonlinear response in a GaAs quantum-well sample containing wells of different thicknesses. We observe both the heavy-hole biexciton and the light-hole biexciton in the transient four-wave mixing spectrum and estimate their binding energy dependence on well width. For moderate excitation densities the signal for negative delay at the heavy-hole exciton and biexciton resonances is due to two-photon transitions to the biexciton states through the exciton states. The temporal behavior of the transient four-wave mixing signal from the heavy-hole exciton resonance is strongly dependent on the spectral position of the laser. We show that this effect is due to interference phenomena and to excitation-induced dephasing.
Coherently controlled four-wave-mixing (FWM) measurements have turned out to be a very sensitive tool to investigate the microscopic origin of the nonlinear optical response of semiconductor quantum-well structures, in particular if excitons are excited [1-3]. The measured signal oscillates as a function of the phase difference of the two interferometric pulses and is modulated additionally by contributions that oscillate with integer multiples of the excitonic resonance frequency. The influence of these harmonics can be measured in background free directions, i.e., the first (FWM) or second (six-wave mixing, SWM) diffracted order in direction 2k2-k1 or 3k2-2k1, respectively. Their intensity is easily quantified by inspecting the corresponding Fourier transforms (FT). Here, we report on transient interferometric SWM measurements and the influence of biexcitons on the signal.
We report measurements of two-photon transitions to the biexciton state and exciton-biexciton transitions (M band) in GaAs/Alx{\mathrm{Al}}_{\mathit{x}}Alx​${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As multiple quantum wells by spectrally resolving the self-diffraction in a four-wave-mixing experiment. Furthermore, nonlinear quantum beats between a coherently prepared population of excitons and biexcitons are observed. The analysis yields a binding energy of 1.8 meV for the biexciton in 116-A\r{} quantum wells.
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.
A theory of degenerate four-wave mixing in a semiconductor optical cavity with quantum wells is constructed. The nonlinear response of a microcavity can be four to five orders of magnitude stronger than that of an isolated quantum well. For P 2 E -and P 3 -type nonlinearities the damped diffracted signal oscillates with a period determined by the Rabi splitting. For a biexcitonic mechanism of nonlinearity, the signal contains damped overtones of the Rabi splitting and the biexciton binding energy.