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Optics Letters

Heterodyne spectral interferometry for multidimensional nonlinear spectroscopy of individual quantum systems

W. Langbein, Brian Patton

Published Mar 29, 2006• 85 citations
Publisher

Abstract

A novel implementation of transient nonlinear spectroscopy is presented that allows the study of the transient nonlinear polarization emitted from individual electronic transitions. Both the amplitude and the phase of the polarization are retrieved, permitting the implementation of multidimensional spectroscopy in the excitation pulse delays. The technique is shown to detect mutual coherent coupling in a group of individual, localized excitonic transitions.

DOI
10.1364/ol.31.001151

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•Jan 1, 2002•0 citations
A novel implementation of transient nonlinear spectroscopy is presented that allows the study of the transient nonlinear polarization emitted from individual electronic transitions. Both the amplitude and the phase of the polarization are retrieved, permitting the implementation of multidimensional spectroscopy in the excitation pulse delays. The technique is shown to detect mutual coherent coupling in a group of individual, localized excitonic transitions.
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.
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.
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.