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Physical review. B, Condensed matter

Coherent effects in spectrally resolved pump-probe differential reflectivity measurements at exciton resonance in GaAs quantum wells

Bipul Pal, Arvind S. Vengurlekar

Published Sep 10, 2003• 9 citations
Publisher

Abstract

We perform femtosecond spectrally resolved pump-probe differential reflectivity measurements on excitons in GaAs quantum wells in both coherent and incoherent regimes. The spectral signal is nonzero and oscillatory at $\ensuremath{-}\mathrm{ve}$ delay up to a few ps indicating persistent coherence between excitonic polarization induced by the probe pulse and the delayed pump pulse. The signal for small $+ve$ and $\ensuremath{-}\mathrm{ve}$ delay $(\ensuremath{\tau})$ shows modulation caused by quantum beats due to coexcitation of heavy and light hole excitons. The rise of the signal with $\ensuremath{\tau}$ for $\ensuremath{\tau}<0$ is rather nonexponential and is sensitive to detuning of the detection energy with respect to the exciton energy. The signal decay with $\ensuremath{\tau}$ for small $+ve$ $\ensuremath{\tau}$ shows dependence on pump-probe relative polarization. The excitonic reflectivity shows a large reduction caused by excitonic absorption saturation for both $+ve$ and $\ensuremath{-}\mathrm{ve}$ $\ensuremath{\tau}$ when the pump pulse intensity is increased to large values. To compare the experimental results with theory, we obtain an expression for the PPDR signal in terms of the third order excitonic polarization. This has an additional term not considered earlier to describe pump-probe experiments. The calculations are performed using optical Bloch equations, modified to incorporate exciton inhomogeneous broadening, quantum beats, and many body effects such as local field, excitation induced energy shift, and dephasing. These effects are found essential in explaining the observed PPDR spectral data. The delay dependence of the signal near the exciton energy is mainly controlled by inhomogeneous broadening for $\ensuremath{-}\mathrm{ve}$ $\ensuremath{\tau}.$ The signal decay for large $+ve$ $\ensuremath{\tau}$ has an exponential behavior determined by the lifetime of incoherent excitons. Experiments for collinear polarization reveal an additional exponential component for small $+ve$ delay. Theoretically, this is found to be related to exciton dephasing and is present only when many body effects are included.

DOI
10.1103/physrevb.68.125308

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We perform femtosecond spectrally resolved pump-probe differential reflectivity measurements on excitons in GaAs quantum wells in both coherent and incoherent regimes. The spectral signal is nonzero and oscillatory at \ensuremath−ve\ensuremath{-}\mathrm{ve}\ensuremath−ve delay up to a few ps indicating persistent coherence between excitonic polarization induced by the probe pulse and the delayed pump pulse. The signal for small +ve+ve+ve and \ensuremath−ve\ensuremath{-}\mathrm{ve}\ensuremath−ve delay (\ensuremathτ)(\ensuremath{\tau})(\ensuremathτ) shows modulation caused by quantum beats due to coexcitation of heavy and light hole excitons. The rise of the signal with \ensuremathτ\ensuremath{\tau}\ensuremathτ for \ensuremathτ<0\ensuremath{\tau}<0\ensuremathτ<0 is rather nonexponential and is sensitive to detuning of the detection energy with respect to the exciton energy. The signal decay with \ensuremathτ\ensuremath{\tau}\ensuremathτ for small +ve+ve+ve \ensuremathτ\ensuremath{\tau}\ensuremathτ shows dependence on pump-probe relative polarization. The excitonic reflectivity shows a large reduction caused by excitonic absorption saturation for both +ve+ve+ve and \ensuremath−ve\ensuremath{-}\mathrm{ve}\ensuremath−ve \ensuremathτ\ensuremath{\tau}\ensuremathτ when the pump pulse intensity is increased to large values. To compare the experimental results with theory, we obtain an expression for the PPDR signal in terms of the third order excitonic polarization. This has an additional term not considered earlier to describe pump-probe experiments. The calculations are performed using optical Bloch equations, modified to incorporate exciton inhomogeneous broadening, quantum beats, and many body effects such as local field, excitation induced energy shift, and dephasing. These effects are found essential in explaining the observed PPDR spectral data. The delay dependence of the signal near the exciton energy is mainly controlled by inhomogeneous broadening for \ensuremath−ve\ensuremath{-}\mathrm{ve}\ensuremath−ve \ensuremathτ.\ensuremath{\tau}.\ensuremathτ. The signal decay for large +ve+ve+ve \ensuremathτ\ensuremath{\tau}\ensuremathτ has an exponential behavior determined by the lifetime of incoherent excitons. Experiments for collinear polarization reveal an additional exponential component for small +ve+ve+ve delay. Theoretically, this is found to be related to exciton dephasing and is present only when many body effects are included.
We study the coherent response of an optically dense exciton system in GaAs quantum wells (QWs). For this, we resonantly excite 1s1s1s heavy-hole excitons in the QWs at 8 K with subpicosecond laser pulses. The excitonic polarization is probed using time integrated (TI) degenerate four wave mixing (DFWM) measurements in self-diffraction geometry. The average power density (I1){(I}_{1})(I1​) of the leading laser pulse is systematically increased to large values, keeping that of the delayed pulse small and fixed. The dephasing rate of the excitonic coherent polarization (determined by the rate of decrease of the TI-DFWM signal with delay between the exciting pulses) attains saturation at large I1{I}_{1}I1​ after an initial rise at small I1.{I}_{1}.I1​. In comparison, the coherent polarization (as given by the DFWM signal at a fixed delay) increases initially with I1,{I}_{1},I1​, reaches a peak and then decreases at large I1.{I}_{1}.I1​.
Excitons, the bound states of an electron and a hole, in semiconductors are interesting objects and they continue to attract attention of researchers from all over the world. Despite intense research on exciton physics over last three-four decades, many interesting phenomena related to the dynamics and the nonlinear optical properties of excitons in semiconductors and their nanostructures in the coherent and incoherent regimes are still to be explored. This thesis presents our effort to study the nonlinear optical properties as well as the exciton dynamics in coherent and incoherent regime in semiconductor nanostructures including GaAs quantum wells (QWs) and InAs quantum dots (QDs). We have set up several time-resolved and steady-state optical spectroscopic measurement techniques in our laboratory to carry out our study on excitons dynamics in semiconductor QWs and QDs. We work out a clear and detailed theory of the pump-probe signal taking account of all aspect of the measurement, namely, the lock-in detection, spectral selection by the monochromator and time-integration at the slow photodetector. We have used the formalism of optical Bloch equations conventionally used to analyse wave mixing experiments. Our analysis puts the pump-probe technique on the same footing as the wave mixing experiments. We show that pumpprobe experiments can be used to study both coherent and incoherent dynamics. We also present a clear physical picture of the measured signal using the Lorentz harmonic oscillator model. We report the investigation of the coherent exciton dephasing dynamics using pumpprobe reflectivity measurement in GaAs QWs for resonant excitation. Two GaAs/AlGaAs QWs with well thicknesses 8 nm and 17.5 nm are used. We found a strong dependence of the dephasing rate of the excitons with increasing exciton density due to exciton-exciton scattering. We found that the exciton dephasing rate of 8 nm QWs at low excitation density and at low lattice temperature is larger than the corresponding dephasing rate of the 17.5 nm QWs, possibly due to larger effect of inhomogeneous broadening. We also report that the dephasing rates for both QWs are linear with the sample temperature below the 30 K. We report the study of ionization equilibrium between the exciton and the electronhole plasma population in the temperature and pressure (excitation density) phase space. Non-resonant excitation of semiconductor creates a nonequilibrium state of electron-hole plasma. We investigate this ionization equilibrium using steady state photoluminescence and time-resolved excitation correlation PL measurements. We present a clear phase diagram (in temperature and carrier density phase space) of this ionization process.A clear density-dependent increase in the ionization ratio is observed and its connection with the Mott transition is discussed. Semiconductor nanocrystals and QDs are another important area of research, mainly due to their huge potential for device application. We present a simple model which combines carrier loss kinetics, detailed balance principle in thermodynamic equilibrium and Pauli exclusion principle to quantitatively explain the observed behaviour of the experimental data.
This dissertation presents investigations of fundamental optical nonlinearities in semi-conductor microstructures. Two distinct effects are studied. In the first part the excitonic optical Stark effect in InGaAs and GaAs multiple quantum-well structures is investigated by means of pump-probe spectroscopy. For nonresonant excitation below the excitonic transition the direction of the shift of the resonance depends on the polarization of the pump and probe pulses. In particular, for anti-circular polarization a surprising red-shift is observed. For resonant excitation, induced absorption energetically above and below the exciton transition and bleaching of the resonance is found. Experiments using both resonant and nonresonant excitation reveal the importance of bound and unbound two-exciton states in absorption changes of the 1s heavy-hole exciton resonance. It is found that higher-order Coulomb contributions determine the intensity as well as the time dependence of the differential excitonic absorption. In addition, the influence of light-hole excitons is analyzed. It is shown that the direction of the optical Stark shift for nonresonant excitation depends also sensitively on the heavy-hole to light-hole splitting and the detuning of the pump pulse. For very high pump intensities and nonresonant excitation the absorption is split when a circularly polarized pump and a linearly polarized probe beam are used. For co-circular excitation traces of hyper-Raman gain are observed. In the second part of this dissertation, the nonlinear optical response of semiconductor microcavities in the nonperturbative regime is studied in resonant single-beam transmission and pump-probe experiments. In both types of experiment, a pronounced third transmission peak lying spectrally between the two normal modes is observed. Its dependence on the probe intensity, pump intensity, pump-probe delay, exciton-cavity detuning and pump detuning is investigated. For single-beam transmission, the energy of the third peak parallels the position of the cavity resonance. It is more pronounced for circularly polarized excitation and lasts longer than the two normal modes. For pump-probe experiments, the third peak increases with decreasing probe intensity and increasing pump intensity. Its energy is close to the low-energy side of the pump spectrum and virtually unaffected by the cavity-exciton detuning. The appearance of the third peak requires temporal overlap of pump and probe pulses. The origin of this complex nonlinearity is the quantum nature of light, which induces intraband polarizations in the presence of a coherent driving field and a finite carrier density. It is found that the coupling of the intraband polarizations via guided modes to the polarization of the fundamental longitudinal mode is responsible for the third transmission peak. A fully quantized theory reproduces the experimental observations.
We perform two beam time integrated (TI) degenerate four wave mixing (DFWM) measurements on 8~nm GaAs quantum wells (QW). Pulses from a Ti-Sapphire laser resonantly excite only 1s heavy hole excitons. The power density of the leading pulse (I1) is increased, keeping that of the delayed pulse fixed and relatively small. We measure the TI-DFWM signal at different delays as well as the DFWM spectra at a fixed delay, as I1 is increased. We find that the dephasing rate, after an initial increase with I1, becomes independent of I1 for large I1. The spectrally integrated DFWM signal, which probes the coherent polarization of the resonantly excited QWs, initially increases with I1, reaches a peak and then decreases as 1/(root)I1 at large I1. The results are compared with theoretical models of exciton coherence.
We present a simple but mathematically complete first-principles theory for the pump-probe differential reflectivity experiment at negative delay (probe preceding the pump) to show how it gives information about the perturbed-free-induction-decay of coherent polarization. The calculation, involving the optical Bloch equations to describe the induced polarization and the Ewald-Oseen idea to calculate the reflected signal as a consequence of the free oscillations of perturbed dipoles, also explicitly includes the process of lock-in detection of a double-chopped signal after it has passed through a monochromator. The theory giving a closed form expression for the measured signal in both time and spectal domains is compared with experiments on high quality GaAs quantum well sample. The dephasing time inferred experimentally at 4 K compares remarkably well with the inverse of the absorption linewidth of the continuous-wave photoluminescence excitation spectrum. Spectrally-resolved signal at negative delay calculated from our theoretical expression nicely reproduces the coherent spectral oscillations observed in our experiments, although exact fitting of the experimental spectra with the theoretical expression is difficult on account of multiple resonances.
Transient pump-probe signals of a GaAs/Alx{\mathrm{Al}}_{\mathrm{x}}Alx​${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$As quantum well are investigated both theoretically and experimentally for different excitation conditions. The calculations are based on a microscopic density-matrix approach taking higher-order correlations into account. We present spectrally resolved transients which provide insights into the nature of the differential transmission change. Especially the complex phase signature of heavy-hole--light-hole quantum beats in dependence of the detection energy allows for an identification of different microscopic processes in the pump-probe signal. The theoretical results are verified experimentally by comparison with the coherent and incoherent parts of the time-resolved data. We find a dominant role of the Coulomb-induced correlations up to the ${\mathrm{\ensuremath{\chi}}}^{(3)}$ relevant four-point level in the coherent signature in comparison to the Pauli blocking contributions.