The vectorial four-wave mixing response of an individual strongly confined exciton–biexciton system with fine-structure splitting in a GaAs/AlGaAs quantum dot is measured by dual-polarization heterodyne spectral interferometry. The results are compared with theoretical predictions based on the optical Bloch equations. The system is described by a four-level scheme, which is a model system of the nonlinear excitonic response in low-dimensional semiconductors. We measure its coherence properties and determine the underlying dephasing mechanisms. An impact of the inhomogeneous broadening by spectral wandering on the coherent response is investigated. We further discuss the different four-wave mixing pathways, polarization selection rules, the time-resolved polarization state, the vectorial response in two-dimensional four-wave mixing and ensemble properties.
The vectorial four-wave mixing response of an individual strongly confined exciton–biexciton system with fine-structure splitting in a GaAs/AlGaAs quantum dot is measured by dual-polarization heterodyne spectral interferometry. The results are compared with theoretical predictions based on the optical Bloch equations. The system is described by a four-level scheme, which is a model system of the nonlinear excitonic response in low-dimensional semiconductors. We measure its coherence properties and determine the underlying dephasing mechanisms. An impact of the inhomogeneous broadening by spectral wandering on the coherent response is investigated. We further discuss the different four-wave mixing pathways, polarization selection rules, the time-resolved polarization state, the vectorial response in two-dimensional four-wave mixing and ensemble properties.
We investigate the coherent optical response of individual localized exciton–biexciton (X–XX) systems formed at interface fluctuations of a growth-interrupted GaAs/AlAs quantum well. We apply heterodyne spectral interferometry to perform two-dimensional four-wave mixing (FWM) spectroscopy. We retrieve the binding energy of bound and unbound XXs, as well as characterize the system in terms of biexciton–exciton dipole moment ratio and mutual FWM phase. Polarization selection rules of the FWM are determined. FWM hyperspectral imaging and autocorrelation analysis reveal the expected spatial colocalization of XXs with respect to their Xs. A value for the biexciton renormalization in a coherently coupled pair of Xs is retrieved. Our study gives insight into the coherent optical properties of an exciton–biexciton system with a confinement energy comparable to the biexciton binding energy.
The coherent response of excitons in semiconductor nanostructures measured in four-wave mixing (FWM) depends strongly on the inhomogeneous broadening of the exciton transition. We investigate GaAs/Al0.3Ga0.7As single quantum wells (SQW) and AlxGa1-xAs mixed crystals. Additional to the usual phase-space filling nonlinearity, excitation-induced dephasing (EID) and biexciton formation (BIF) are important. EID leads to a strong dependence of the signal on the angle between the linear input polarizations. We find that EID persists in inhomogeneous systems, showing that the mutual density-dependent dephasing rate difference between two subsystems within the inhomogeneous distribution is strongly dependent on their energy difference. BIF is strongly affecting the cross-linear polarized FWM response. The signal for positive delay is dominated by the transitions from the one-exciton state X to the two-exciton states. Here, the third-order polarization at X-XX is not at the same resonance as the first-order polarization at 0-X. Consequently, the rephasing of the microscopic third-order polarization to the macroscopic FWM photon echo is blurred by the non-perfect correlation of X and XX energies, leading to a fast and non-exponential signal decay in delay time. For inhomogeneous broadenings larger than the biexciton binding energy, we find an enhanced biexciton binding energy, and a quenching of the oscillator strength of the unbound biexciton.
Degenerate four-wave mixing (FWM) from individual localized excitonic transitions is measured using a dual-polarization extension of heterodyne spectral interferometry. A fine-structure splitting (FSS) of the localized excitons of $20--80\text{ }\ensuremath{\mu}\text{eV}$ is observed, revealing a spatially anisotropic localization in the quantum well plane, preferentially oriented along the [110] direction. The ratio of the transition dipole moments of the FSS transitions is in the range 0.7--1.4, with no significant correlation to the FSS. Retrieving both polarization components of the FWM in amplitude and phase we measure the time-resolved polarization state of the exciton after pulsed excitation, showing a coherent evolution oscillating between linear and virtually circular polarization. The polarization of the created FWM state is a result of the initial polarization state created by the first excitation pulse, its free evolution up to the arrival of the second pulse, and its conversion into the FWM controlled by the polarization of the second pulse.
The three-dimensional confinement created by the ultrasmall semiconductor structures known as quantum dots greatly modifies the optical properties of the spatially localized carriers. These systems are presently of great interest to the research community, both for the improved understanding of the physics of confined structures, and for the potential applications of these systems to areas such as optoelectronics and quantum computing. Here, the techniques of transient coherent nonlinear optical spectroscopy are applied to the investigation of excitons confined within InAs/GaAs self-assembled quantum dots. These methods provide a powerful tool for the study of dynamic processes in these novel materials. The nonlinear measurements are based on the differential transmission experimental geometry, and utilize ultrafast pulsed lasers in order to temporally resolve the carrier dynamics after excitation. The experiments performed here are resonant with the ground state absorption of the quantum dots, as evidenced by comparison with the photoluminescence measurements which are used to characterize the sample. The incoherent relaxation dynamics of the population of photoexcited excitons are examined, allowing for a determination of both the lifetime of the excitons and the time scale for relaxation between the two polarization eigenstates of the system. The three-dimensional quantum confinement results in the suppression of these relaxation processes, as predicted. The use of coherent spectroscopic techniques allows for the first unambiguous demonstration of an optically-induced nonradiative Raman coherence in these quantum dots. Simultaneous excitation of both polarization states of the exciton results in a coherent superposition state, whose temporal evolution is observed through the homodyne-detection scheme. In these transient experiments, this is manifested as a beating in the nonlinear response, which allows us to directly measure the fine-structure splitting between the polarization states. Utilizing optical pulse shaping techniques, transient spectral hole burning is performed, which allows for the nonlinear response to be spectrally resolved. As expected for the strongly confined quantum dot excitons, the results show that diffusion among the localized states is not a significant effect. Temperature dependent measurements show that at elevated temperatures, extra dephasing processes, potentially related to acoustic phonon scattering, become important. Finally, this technique allows for the first direct observation of the induced absorption from the exciton to biexciton transition in these InAs quantum dots, and a measurement of the associated binding energy. These results lay the foundation for future studies in this material system, and for the possible development of quantum logic devices utilizing quantum dots.
Summary form only given.The coherent response of excitons in semiconductor nanostructures, as measured in four wave mixing (FWM) experiments, depends strongly on the inhomogeneous broadening of the exciton transition. We investigate GaAs-AlGaAs single quantum wells (SQW) of 4 nm to 25 nm well width. Two main mechanisms are found to be important. First, the excitation-induced dephasing FWM signal (EID), which leads to a strong dependence of the signal on the angle between the linear input polarizations. The presence of the EID in the mainly homogeneously broadened sample (25 nm) is shown by the beating between EID and two-photon coherence (TPC) at the exciton for negative delay and co-linear polarized excitation. It vanishes for cross-polarized excitation, thus excluding the importance of local-field effects.
The nonlinear optical response of quantum well excitons is investigated experimentally using polarization resolved four wave mixing, optical-pump optical-probe, and optical-pump Terahertz-probe spectroscopy. The four-wave mixing data reveal clear signatures of coherent biexcitons which concur with straight-forward polarization selection rules at the Γ point. The type-I samples show the well-established time-domain beating signatures in the transients as well as the corresponding spectral signatures clearly. The latter are also present in type-II samples; however, the smaller exciton and biexciton binding energies in these structures infer longer beating times which, in turn, are accompanied by faster dephasing of the type-II exciton coherences. Furthermore, the THz absorption following spectrally narrow, picosecond excitation at energies in the vicinity of the 1s exciton resonance are discussed. Here, the optical signatures yield the well-established redshifts and blueshifts for the appropriate polarization geometries in type-I quantum well samples also termed “AC Stark Effect”. The THz probe reveals intriguing spectral features which can be ascribed to coherent negative absorption following an excitation into a virtual state for an excitation below the 1s exciton resonance. Furthermore, the scattering and ionization of excitons is discussed for several excitation geometries yielding control rules for elastic and inelastic quasiparticle collisions.