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AIP conference proceedings

Transient four-wave mixing of single exciton states: Exciton-exciton interaction and Rabi oscillations

Brian Patton

Published Jan 1, 2005• 0 citations
Publisher

Abstract

We present a novel heterodyne‐detected four‐wave mixing technique, which determines the third‐order nonlinear polarization in phase and amplitude by spectral interferometry. It allows us to measure the resonant transient four‐wave mixing of single localized excitons, both frequency and time‐resolved. In the signal, the strength of the coupling between two probed exciton transitions is directly observable. Applying a strong optical pump pulse, we observe optical Rabi oscillations of the exciton polarization. Observing decay of the third‐order polarization after the pump pulse, we can exclude the presence of signi£cant excitation‐induced dephasing.

DOI
10.1063/1.1994558

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We present a novel heterodyne‐detected four‐wave mixing technique, which determines the third‐order nonlinear polarization in phase and amplitude by spectral interferometry. It allows us to measure the resonant transient four‐wave mixing of single localized excitons, both frequency and time‐resolved. In the signal, the strength of the coupling between two probed exciton transitions is directly observable. Applying a strong optical pump pulse, we observe optical Rabi oscillations of the exciton polarization. Observing decay of the third‐order polarization after the pump pulse, we can exclude the presence of signi£cant excitation‐induced dephasing.
We present measurements and simulations of coherent control and readout of the polarization in individual exciton states. The readout is accomplished by transient four-wave mixing detected by heterodyne spectral interferometry. We observe Rabi oscillations in the polarization, which show half the period of the Rabi oscillations in the population. A decrease of the oscillation amplitude with pulse area is observed, which is not accompanied by a change in the dephasing time. This suggests the transfer of the excitation to other states as the origin of the Rabi-oscillation damping. Detuning of the excitation enables the control of the polarization in phase and amplitude and is in qualitative agreement with simulations for a two-level system. Additionally, simultaneous Rabi flopping of several spatially and energetically close exciton states is demonstrated.
Abstract We use heterodyne spectral interferometry (HSI) to investigate the transient four‐wave mixing field (FWM) from an individual localized excitonic transition. FWM intensity and spectrum as well as the spatial resolution in FWM hyperspectral imaging are measured as function of excitation intensity. A third‐order non‐linear response of the FWM followed by saturation and the onset of a Rabi‐flop are observed with increasing intensity. The intensity dependence of the spectral response depends on the excitation pulse duration. For short pulses (∼0.2 ps), having a broad spectrum, a weak broadening of the emission line, similar to excitation induced dephasing (EID), is found. For long pulses (∼0.5 ps) instead, no signatures of EID are found, but individual multi‐excitonic transitions are observed. When using the FWM intensity as image contrast by spatially scanning a region of the sample surface, a spatial resolution beyond the diffraction limit is measured in the third‐order regime, while for higher intensities the FWM saturation deteriorates the spatial resolution. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
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.
We review our recent advances in four-wave mixing spectroscopy of single semiconductor quantum dots using heterodyne spectral interferometry, a novel implementation of transient nonlinear spectroscopy allowing the study of the transient nonlinear polarization emitted from individual electronic transitions in both amplitude and phase. We present experiments on individual excitonic transitions localized in monolayer islands of GaAs/AlAs quantum wells and in self-assembled CdTe/ZnTe quantum dots. We investigate the formation of the photon echo from individual transitions, both with increasing number of transitions in the ensemble, and in the presence of temporal jitter of the energy of a single transition. The detection of amplitude and phase of the signal allows the implementation of a two-dimensional femtosecond spectroscopy, in which mutual coherent coupling of single quantum dot states can observed and quantified.
A heterodyne detection scheme was applied to micro-pump–probe spectroscopy to study the transient response of an exciton in a single semiconductor quantum dot. The elimination of the pump pulse in the frequency domain provided us a direct probing of the energy relaxation process of the quantum state excited by the pump pulse. The excitonic Rabi oscillations were also monitored by this technique, even in the presence of a strong pump pulse. This spectroscopic technique is suitable for the observation of the optical response and coherent manipulation of a semiconductor quantum dot.
Coherent optical spectroscopy in the form of nonlinear transient four-wave mixing (TFWM) and linear resonant Rayleigh scattering (RRS) has been applied to investigate the exciton dynamics of low-dimensional semiconductor heterostructures. The dephasing times of excitons are determined from the decay of the spectrally resolved non- linear signal as a function of the delay between the incident pulses in a two-beam TFWM experiment, and from the real time analysis of single speckles in RRS experiments (pure dephasing). From the density- and temperature- dependence of the dephasing times the exciton-exciton and the exciton-phonon interactions are determined. The degree of coherence of the secondary emission is determined from the speckle analysis.