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Physical review. B, Condensed matter

Signatures of excitonic dark states in the time-resolved coherent response of a quantum well microcavity

Ewa Magdalena Goldys, Giuseppe Carlo La Rocca, F. Bassani

Published Apr 15, 2000• 2 citations
Publisher

Abstract

We study the coherent time-resolved response of a semiconductor microcavity excited by an ultrashort light pulse. The cavity contains embedded quantum wells and quantum well excitons are strongly coupled to cavity photons. Two experimental situations are examined. We describe a linear regime when the exciting light pulse is weak. Further, a low-temperature pump-and-probe experiment in a nonlinear regime is analyzed, with a cw pump beam circularly polarized opposite to a weak ultrashort probe pulse in conditions yielding a bipolariton-mediated optical Stark effect. In both cases we examine the response of a single quantum well and contrast it with that of several quantum wells. In the latter case light is coupled only to a symmetric linear combination (bright exciton) of excitonic states in individual quantum wells. We find distinctive fingerprints of other linear combinations of exciton states (dark excitons). In the linear regime, in addition to a pattern of Rabi oscillations between the two polariton states, additional beating frequencies appear, related to dark states. In the nonlinear case, the bipolariton formalism outlined by Ivanov et al. [Phys. Rev. B 52, 11 017 (1995)] allows one to deduce a similar additional beating frequency and a splitting of bipolariton frequencies related to their dark or bright state character. This work identifies the effect of the microcavity parameters on its coherent response and determines the experimental conditions in which the influence of dark states may be observed.

DOI
10.1103/physrevb.61.10346

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We study the coherent time-resolved response of a semiconductor microcavity excited by an ultrashort light pulse. The cavity contains embedded quantum wells and quantum well excitons are strongly coupled to cavity photons. Two experimental situations are examined. We describe a linear regime when the exciting light pulse is weak. Further, a low-temperature pump-and-probe experiment in a nonlinear regime is analyzed, with a cw pump beam circularly polarized opposite to a weak ultrashort probe pulse in conditions yielding a bipolariton-mediated optical Stark effect. In both cases we examine the response of a single quantum well and contrast it with that of several quantum wells. In the latter case light is coupled only to a symmetric linear combination (bright exciton) of excitonic states in individual quantum wells. We find distinctive fingerprints of other linear combinations of exciton states (dark excitons). In the linear regime, in addition to a pattern of Rabi oscillations between the two polariton states, additional beating frequencies appear, related to dark states. In the nonlinear case, the bipolariton formalism outlined by Ivanov et al. [Phys. Rev. B 52, 11 017 (1995)] allows one to deduce a similar additional beating frequency and a splitting of bipolariton frequencies related to their dark or bright state character. This work identifies the effect of the microcavity parameters on its coherent response and determines the experimental conditions in which the influence of dark states may be observed.
We report on the optical response of a semiconductor microcavity featuring a strong exciton–photon coupling. The weak excitation regime is investigated experimentally by means of time-resolved transmission and four-wave mixing experiments. The influence of electronic disorder on the coherent exciton–photon dynamics is discussed in terms of the solutions of the Maxwell-Bloch equations. The high excitation regime is investigated by using transient sub-picosecond pump–probe experiments. Optical amplification of the probe beam (up to a factor of five), as well as a fundamental change of the optical spectra, have been found close to and above the exciton saturation density. The observed oscillations are corresponding to the Rabi frequency of the excitons in the pump field.
We investigate a GaAs/(Ga,Al)As Fabry-P\'erot microcavity, into which (In,Ga)As quantum wells have been inserted. The cavity is wedge shaped, i.e., the detuning between the bare-exciton resonance and the bare optical cavity mode depends on the spatial position on the sample. Linear transmission spectra reveal a well-resolved Rabi splitting of 8 meV at resonance, an inhomogeneously broadened exciton transition of 4--5-meV width, and an 0.7-meV-wide Fabry-P\'erot mode. The time-resolved transmission exhibits deep beatings and a subpicosecond exponential decay: a behavior similar to that foreseen in the strong-coupling regime and in the absence of electronic disorder. Conversely, the four-wave mixing response appears weakly influenced by the cavity and not much different from what is expected for bare excitons. A photon echo, dephasing times as long as 50 ps, and only weak Rabi oscillations are observed. The experimentally observed features can be explained by a model based on the numerical solutions of the Maxwell-Bloch equations. This model confirms the dramatic influence structural disorder in the quantum wells has on the coherent nonlinear exciton-photon dynamics.
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 have used femtosecond optical spectroscopy to observe directly the vacuum Rabi oscillations associated with the coupled exciton-photon mode splitting in a semiconductor quantum microcavity. When the microcavity is impulsively excited by a coherent short optical pulse, the time-resolved emission from the cavity shows beats corresponding to the oscillation between cavity and exciton modes, with a decay corresponding to approximately twice the cavity lifetime. Interferometric pump-probe measurements clearly show the coherent evolution of the cavity polarization.
We have used femtosecond optical spectroscopy to observe directly the vacuum Rabi oscillations associated with the coupled exciton-photon mode splitting in a semiconductor quantum microcavity. When the microcavity is impulsively excited by a coherent short optical pulse, the time-resolved emission from the cavity shows beats corresponding to the oscillation between cavity and exciton modes, with a decay corresponding to approximately twice the cavity lifetime. Interferometric pump-probe measurements clearly show the coherent evolution of the cavity polarization.
Recently, several research groups have reported investigations of vacuum-field Rabi splittings (VRS) in the linear response of strongly coupled semiconductor microcavities [1-4]. We have previously reported on the dynamics of time-domain vacuum Rabi oscillations, which are most easily understood in the framework of cavity exciton-polaritons, in which the in-plane momentum k|| is conserved [2], so that at each k|| a single cavity mode interacts with only a single mode of the electromagnetic field (Jaynes-Cummings model). In high Q semiconductor microcavities, the strong coupling between two-dimensional excitons and planar distributed- Bragg-reflector cavity modes results in several-meV splittings observable in the reflectivity or absorption spectrum. In the low excitation regime, the VRS is independent of light intensity incident on the cavity, since the vacuum-Rabi frequency exceeds the externally-driven Rabi frequency (in which case the Jaynes-Cummings model is equivalent to the linear dispersion of the coupled exciton-cavity system). As the incident light intensity is increased, two different effects may be expected to contribute to the nonlinear response. First, as long as the excitonic absorption is equivalent to a two-level system, higher-lying states of the Jaynes-Cummings ladder might be observable. Second, at high intensity phase-space filling and Coulomb screening of the exciton states results in a reduced oscillator strength which leads to a reduced VRS; this effect has no analogue in the case of atom-cavity systems. In this paper, we apply several ultrafast nonlinear techniques to investigate the nonlinear response of semiconductor microcavities.