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The Journal of Chemical Physics

Selection rules for probing biexcitons and electron spin transitions in isotropic quantum dot ensembles

Gregory D. Scholes

Published Nov 11, 2004• 60 citations
Publisher

Abstract

Three-dimensional rotational averages are evaluated for third-order nonlinear spectroscopic measurements of quantum dots. Photon echo, transient grating, and transient absorption are explicitly considered. It is shown that (a) biexciton formation can be suppressed relative to other contributions to nonlinear spectroscopies for isotropic nanocrystal ensembles by choice of polarizations for the excitation pulses; (b) circularly polarized excitation light can differentiate between exciton spin states in nonlinear optical experiments; and (c) electron spin state flip kinetics can be probed directly in an isotropic quantum dot system by using certain sequences of linear cross-polarized pulses.

DOI
10.1063/1.1808414

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•Jan 1, 2002•0 citations
Three-dimensional rotational averages are evaluated for third-order nonlinear spectroscopic measurements of quantum dots. Photon echo, transient grating, and transient absorption are explicitly considered. It is shown that (a) biexciton formation can be suppressed relative to other contributions to nonlinear spectroscopies for isotropic nanocrystal ensembles by choice of polarizations for the excitation pulses; (b) circularly polarized excitation light can differentiate between exciton spin states in nonlinear optical experiments; and (c) electron spin state flip kinetics can be probed directly in an isotropic quantum dot system by using certain sequences of linear cross-polarized pulses.
We report the experimental results of two-pulse transient four-wave mixing near the first heavy-hole quantum-well exciton. Input pulses with similar polarizations (circular or linear) measure the exciton dephasing rate; opposite circular polarized pulses produce no four-wave mixing signal, while crossed linear polarized pulses generate a weaker signal with a faster dephasing rate. This signal is attributed to the biexcitonic transition, which was directly observed in a separate nondegenerate four-wave mixing experiment. The selection rules for these transitions are discussed and confirm the treatment of the excitonic transition as a three-level system.
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.
Exciton, trion, and biexciton dephasing rates are measured for an ensemble of InAs quantum dots using two-dimensional Fourier-transform spectroscopy. The two-dimensional spectra reveal that the dephasing rate of each excitonic state is similar for all dots in the ensemble and the rates are independent of excitation density. An additional spectral feature (too weak to be observed in the time-integrated four-wave mixing signal) appears at high excitation density and is attributed to the ${\ensuremath{\chi}}^{(5)}$ biexcitonic nonlinear response.
Transient optical nonlinearities of semiconductor quantum dots in the strongly confined regime are studied, in which the exciton, biexciton and magnetic field effects are taken into account. The photo induced band-to-band electronic transitions are considered from both the heavy-hole (hh) and light-hole (lh) valence bands to the lowest (1s) exciton state below the fundamental absorption edge. The time dependent perturbation technique for a three-level system, under the near band gap resonant excitation regime, has been employed; with the incorporation of the relaxation and dephasing mechanisms phenomenologically. The induced polarization is calculated from where the real and imaginary parts of the third-order nonlinear optical susceptibility, responsible for the occurrence of nonlinear refraction and nonlinear absorption respectively, have been derived. The temporal and detuning spectra of nonlinear refraction and absorption; and their dependence on density of biexcitons and a moderately strong magnetic field, have been analyzed. It is observed that the nonlinear refraction and nonlinear absorption enhance with increasing magnetic field in small CdS quantum dots.
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.