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Coherent transient nonlinear optical spectroscopic studies of single semiconductor quantum dots: Applications to quantum information processing.

Xiaoqin Li

Published Jan 1, 2003• 0 citations
OpenAlex

Abstract

The focus of the thesis is nonlinear transient optical properties and coherent control of single interface fluctuation quantum dots (QD's). When single exciton and biexciton resonances were driven by strong resonant laser pulses, Rabi oscillations of these transitions were observed in the differential transmission (DT) geometry. These results extend the concept of coherent control to the limit of single quantum confined systems in solids and have important implications for the feasibility of building quantum information processing devices using semiconductor QD's. Exciton Rabi oscillations are equivalent to arbitrary single-bit operations. The pulsed control of the exciton-biexciton transition is utilized as the optical operation for building a two-bit controlled rotational gates (CROT) in a single QD. A fidelity of 0.79 was obtained from numerical evaluation of the gate operation itself assuming typical decay parameters measured from these dots. Next, the nonradiative quantum coherence between two orthogonally polarized excitons confined in a single QD was studied. By using pulses with large enough bandwidth and the proper polarization, two exciton states are simultaneously excited. The quantum beats between the two exciton states were temporally resolved as the relative phase between the two dipole oscillations changed. It was found that the nonradiative coherence time is limited by the lifetimes of the excitons involved even in the strong field regime. In the basis of the pseudo-spin Bloch vectors of exciton transitions, the total wavefunction following the pulsed excitation is an entangled state, i.e. the wavefunction is non-factorizable. Finally, the quantum coherence between the biexciton, exciton, and the crystal ground states was studied in a novel quantum beat experiment, where the oscillations only existed when the pump and probe pulses overlapped in time. Laser pulses generated after a passive pulse shaper with just enough bandwidth to cover both the exciton and biexciton transitions were used in this experiment. The appearance of the beats is indicative of a reasonably long coherence time between the biexciton and other states even in the presence of strong pulsed excitations.

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The focus of the thesis is nonlinear transient optical properties and coherent control of single interface fluctuation quantum dots (QD's). When single exciton and biexciton resonances were driven by strong resonant laser pulses, Rabi oscillations of these transitions were observed in the differential transmission (DT) geometry. These results extend the concept of coherent control to the limit of single quantum confined systems in solids and have important implications for the feasibility of building quantum information processing devices using semiconductor QD's. Exciton Rabi oscillations are equivalent to arbitrary single-bit operations. The pulsed control of the exciton-biexciton transition is utilized as the optical operation for building a two-bit controlled rotational gates (CROT) in a single QD. A fidelity of 0.79 was obtained from numerical evaluation of the gate operation itself assuming typical decay parameters measured from these dots. Next, the nonradiative quantum coherence between two orthogonally polarized excitons confined in a single QD was studied. By using pulses with large enough bandwidth and the proper polarization, two exciton states are simultaneously excited. The quantum beats between the two exciton states were temporally resolved as the relative phase between the two dipole oscillations changed. It was found that the nonradiative coherence time is limited by the lifetimes of the excitons involved even in the strong field regime. In the basis of the pseudo-spin Bloch vectors of exciton transitions, the total wavefunction following the pulsed excitation is an entangled state, i.e. the wavefunction is non-factorizable. Finally, the quantum coherence between the biexciton, exciton, and the crystal ground states was studied in a novel quantum beat experiment, where the oscillations only existed when the pump and probe pulses overlapped in time. Laser pulses generated after a passive pulse shaper with just enough bandwidth to cover both the exciton and biexciton transitions were used in this experiment. The appearance of the beats is indicative of a reasonably long coherence time between the biexciton and other states even in the presence of strong pulsed excitations.
In this thesis, the coherent interaction of single semiconductor quantum dots and ultrafast optical pulses is studied. Under certain conditions, localized exciton transitions in quantum dots can be seen as semi-isolated two-level systems. While this description is sufficient for the explanation of some observations in coherent experiments, it is sometimes necessary to explicitly consider coupling of the discreet quantum states confined to the dot with the environment. We start out from simple, classical examples of coherent spectroscopy and then turn towards experiments where the interaction with the vicinity of the dot becomes an important factor. First, a novel method for transient differential reflectivity spectroscopy of single quantum systems is introduced. It is a pure far-field optical technique which does not require any sophisticated sample preparation steps which makes it applicable to a broad range of structures. Pump pulses excite the sample structure and probe pulses read out the pump-induced changes in the system after a variable delay time. In the case of a single dipole, the signal is given in the form of the spectral inteferogram between the backscattered wave from the particle and the probe light which is reflected at the sample surface. This form of homodyne detection amplifies the weak scattered wave from the particle and thus makes this kind of spectroscopy for single quantum dots feasible. In the remainder of this thesis our spectroscopic method is applied to either characterize the coherent properties of single quantum dots, to prepare and read-out a desired quantum state or to deliberately manipulate them. Coherence times and oscillator strengths are determined for localized exciton transitions. Arbitrary population states can be written by driving coherent population oscillations using resonant pulses, while entangled superpositions of two exciton states in a single dot are investigated by quantum beats on transient differential spectra. We finally exploit the interaction between the dot and a nearby absorbing layer to switch the dot's absorption spectrum on ultrafast timescales via light-induced transient electric fields.
Transient differential transmission measurements were performed to study coherent dynamics involving the biexciton resonance confined in a single GaAs\mathrm{GaAs}GaAs quantum dot. When laser pulses with sufficient bandwidth were tuned to cover both the exciton and biexciton transitions, an oscillatory behavior in the probe transmission was observed. These oscillations persist only as long as the pump and probe pulses overlap in time, in contrast to the usual quantum beat phenomena.
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.
Excitons in quantum dots represent a remarkably good two-level system with a large optical dipole transition moment. Although most research currently focuses on enhancing their already outstanding properties as single photon emitters they become also increasingly interesting for experimental fundamental research due to their large dipole transition moment. This thesis presents studies which explore fundamental phenomena in quantum dots using coherent spectrocopy methods. First, we will first examine the optical properties of site-controlled quantum dots which were grown using a buried stressor via resonance fluorescence. Subsequently, we will show results that were obtained using photocurrent spectroscopy to study single quantum dots that are embedded in micropillar resonators. This is followed by a study of the Wigner time delay induced by a single quantum dot and which shows that the maximum delay is larger than its dephasing time T2 which is the theoretical limit for coherently scattered fraction. The next section demonstrates that the response of a resonantly driven two-level system which in our case is represented by an exciton in a seminconductor quantum dot depends significantly on the photon statistics of the exciting light field. Most strikingly, the Mollow triplet which we observe under coherent excitation vanishes under thermal excitation. The second part presents results concerned with the resonantly driven biexciton cascade via two- photon excitation. The coherent interaction between light field and excitons gives rise to a complex five-level system. Here, we show for the first time two-photon Rabi oscillations in the temporal domain. Furthermore, we examine the correlations between the different transitions. The measurements show that we can manipulate the time-ordering of the emitted photons by changing for example the laser power. All these studies share the resonant excitation scheme which allows for a coherent manipulation of the states of the quantum dot and grants access to phenomena typical for resonance fluorescence such as the Mollow triplet and Rabi oscillations. In particular the experiments on photon excitation spectroscopy and the studies on the dressed biexciton cascade show that fundamental effects of quantum optics can be explored in a scalable and application oriented setting using quantum dots.
Controlling the quantum states of charge (excitons) or spin-polarized carriers in semiconductor quantum dots (QDs) has been the focus of a considerable research effort in recent years due to the strong promise of using this approach to develop solid state quantum computing hardware. The long-term scalability of this type of quantum computing architecture is enhanced by the use of QDs emitting in the telecom band, which would exploit the established photonic infrastructure. This thesis reports the use of all optical infrared experimental techniques to control exciton dynamics in two different QD samples consisting of InAs/GaAs QDs and InAs/InP QDs within a planar microcavity. An infrared quantum control apparatus was developed and used to apply optimized shaping masks to ultrafast pulses from an optical parametric oscillator. Pulse shaping protocols designed to execute a two-qubit controlled-rotation operation on an individual semiconductor QD were demonstrated and characterized. The quantum control apparatus was then implemented in simultaneous single qubit rotations using two uncoupled, distant InAs/GaAs QDs. These optimal control experiments demonstrated high fidelity optical manipulation of exciton states in the two QDs using a single broadband laser pulse, representing a step forward on the path to a scalable QD architecture and showcasing the power of pulse shaping techniques for quantum control on solid state qubits. As an alternative to single QDs, which have very low optical signals, subsets of QDs within an ensemble can be used in quantum computing applications. To investigate the mediation of inhomogeneities in a QD ensemble, pump-probe experiments were performed on InAs/InP QDs within a dielectric Bragg stack microcavity. Two different excitation geometries showed that the angle dependence of the microcavity transmission allowed for the spectral selection of QD subsets with transition energies resonant with the cavity mode. The microcavity mitigated inhomogeneities in the ensemble while providing a basis for addressing QD subsets which could be used as distinguishable quantum bits. This thesis work shows significant advances towards an optical computing architecture using quantum states in semiconductor QDs.
Summary form only given. We use transient nonlinear optical spectroscopy to demonstrate Rabi oscillations between each of the dipole coupled states, corresponding to qubit rotations. The interface fluctuation GaAs quantum dots are probed with sub-micron spatial resolution. The resonant excitation of the biexciton requires a two-color scheme in a hyper Raman gain configuration. To demonstrate exciton Rabi oscillations, the laser wavelength is fixed at the exciton resonance. Exciton and biexciton Rabi oscillations correspond to qubit rotations of the |00> to |01> or |10> state and the |01> or |10> to |11> state respectively, depending on the polarization of the excitation field.