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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Optical Stark effect in double-resonance conditions in semiconductor nanostructures

E. Yu. Perlin, Федоров Анатолий Валентинович

Published Jun 10, 1996• 1 citation
Publisher

Abstract

The theory of the optical Stark effect is developed for quantum-size structures. The effect is due to the interaction of the electron system with intense light, whose frequency, (omega) , is in resonance between two subbands in the conduction band. The probe light of the frequency (Omega) falls in resonance with the adjacent transition between the ground state and the state with an electron-hole pair. In the quasi-steady-state mode, the singularities in the interband (Omega) -light absorption spectra are related to the critical points of the bands, rearranged by the (omega) - light. The shape of the higher conduction band can be evaluated from the spectral positions of the singularities. In the case of two-photon interband transitions, a sharp dependence of the absorption on the light intensity is predicted. In the non-steady-state mode, the probe beam consists of two femtosecond (Omega) -light pulses following each other with the delay time, (tau) d. The dependence of energy, absorbed from the second pulse, on the (tau) d value is calculated. Under the (omega) -pumping, one of the two phenomena should be observed, depending on the type of band structure, namely, the decay of the induced polarization with the characteristic time approximately 1/(omega) R or oscillations with the frequency approximately (omega) R, where (omega) R is the Rabi frequency. The principal effect, controlling the decay of the Rabi oscillations, is the spreading of the packet of states generated by the (Omega) -light pulse.

DOI
10.1117/12.242147

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The theory of the optical Stark effect is developed for quantum-size structures. The effect is due to the interaction of the electron system with intense light, whose frequency, (omega) , is in resonance between two subbands in the conduction band. The probe light of the frequency (Omega) falls in resonance with the adjacent transition between the ground state and the state with an electron-hole pair. In the quasi-steady-state mode, the singularities in the interband (Omega) -light absorption spectra are related to the critical points of the bands, rearranged by the (omega) - light. The shape of the higher conduction band can be evaluated from the spectral positions of the singularities. In the case of two-photon interband transitions, a sharp dependence of the absorption on the light intensity is predicted. In the non-steady-state mode, the probe beam consists of two femtosecond (Omega) -light pulses following each other with the delay time, (tau) d. The dependence of energy, absorbed from the second pulse, on the (tau) d value is calculated. Under the (omega) -pumping, one of the two phenomena should be observed, depending on the type of band structure, namely, the decay of the induced polarization with the characteristic time approximately 1/(omega) R or oscillations with the frequency approximately (omega) R, where (omega) R is the Rabi frequency. The principal effect, controlling the decay of the Rabi oscillations, is the spreading of the packet of states generated by the (Omega) -light pulse.
The coherent response of a semiconductor three-state system to one or two intense light pulses is investigated experimentally on a 100 fs time scale. Three experiments constitute this dissertation: observation of excitonic Rabi oscillations, measurement of two-exciton coupled Stark shifting, and an attempt to observe dark states. Basic concepts of time-resolved ultrafast semiconductor spectroscopy are explained, followed by an analysis of semiconductor two- and three-state systems. Pure two- and three-state dynamics are derived from first principles, followed by the development of the appropriate semiconductor Bloch equations (SBE). Two-color pump-probe, two-color pump-pump, and pump-pump-probe techniques are explained in the context of three-state semiconductor experiments. The experimental setup is explained in detail. Resonant two-color pump-probe measurements resulted in the first observation of multiple excitonic Rabi oscillations. The common conduction band shared by the light-hole and heavy-hole excitons of an InGaAs multiple quantum well allowed us to measure hh-exciton density (Rabi) oscillations by probing lh-exciton absorption. By studying the intensity dependence of the Rabi frequency, we showed the important role of many-body effects in renormalizing the dipole energy. The shared conduction band also causes the lh-exciton resonance to Stark shift when the hh exciton is Stark shifted. We measured a transient Stark shifting of both resonances due to virtual hh-exciton transitions. We observed that the ratio of the hh-exciton shift to lh-exciton shift was 2:1 at large pump-exciton detuning, as predicted from a simple three-state dressed exciton picture. For smaller detunings we saw an increase in the ratio and a redshift of the non-dipole coupled exciton state. Both of these observations are consistent with the most recent theories and experiments on excitonic Stark shifting. For strong near-resonant pumping of both lh- and hh-exciton transitions, an intervalence-band Raman-type coherence follows from the SBE that results in a transparent eigenstate (dark state) when both pumps are equally detuned from resonance. The existence of this coherence is well-known in atomic-optical systems, but has been elusive in semiconductors. Our inconclusive experimental result is presented along with an evaluation of experimental shortcomings. In brief, the expected change is absorption was too small to see.
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.
The biexciton optical Stark-effect under resonant pumping between the exciton and biexciton levels is studied theoretically. The probabilities of biexciton two-photon absorption of a weak probe light and of one-photon biexciton-exciton transition are calculated. The optical Stark splitting manifests itself in two-photon biexciton absorption through two absorption peaks spaced 2 (Omega) apart. Omega is the Raby frequency. In the luminescence spectrum due to biexciton-exciton one-photon transition three luminescence maxima appear which are shifted with respect to the luminescence maximum in the case without pumping.
We have studied two-photon nonlinear optical effects arising in a microcavity geometry from resonant two-photon absorption or second-harmonic generation. The transmission spectrum of the cavity is shown to depend on light intensity according to a simple two-level picture with an intensity-dependent coupling: at resonance the system exhibits a two-photon Rabi splitting. The absorption spectrum of a weak probe beam in a pumped cavity is found to strongly depend on pump intensity and detuning; the resulting effect is a sort of two-photon analogue of the usual optical Stark effect. For moderate pump intensities a two-level picture with a pump-dependent coupling can account for the main results, while at higher intensities new unexpected features show up; in particular, we predict the appearance of gain in well-determined spectral regions due to hyper-Raman processes. Finally, we have shown how the coupling coefficients appearing in our formalism can be obtained from a detailed knowledge of the material and geometrical properties of a specific system. For illustrative purposes, we have estimated the required light intensities using realistic data for a GaAs-based semiconductor microcavity.
Excitonic resonances in direct-gap semiconductors have proved to exhibit similar optical non-linearities as in atoms. One example is the optical Stark effect [1] which occurs when the sample is excited by a strong pump field whose frequency is detuned from the optical transition. The optical Stark effect has been described as a coupling between the electromagnetic field and the resonance with no real absorption. It can also be seen as the creation of a virtual population in the excited state. A transient gain, quadratic in pump intensity, is associated to this effect as already observed in atomic systems [2]. This hyper-Raman process involves two pump photons and occurs at frequency 2ω p – ω0, where ω p and ω0 are the pump and atomic transition frequencies, respectively (see inset of Fig. 1).