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Quantum Electronics and Laser Science Conference

Strong nonlinear coherent effects in a single semiconductor quantum dot

Pochung Chen, Carlo Piermarocchi, Lu Jeu Sham

Published Jun 25, 2003• 0 citations
Publisher

Abstract

Summary form only given. The optical properties of semiconductor quantum dots have been studied intensively in the past few years. Recently the experiment has demonstrated not only the ability to probe a single QD but also how to coherently control the exciton in a single QD on a time scale that is short compared with the decoherence time. We had proposed a scheme to use the excitons in QD as qubits and to use strong ultra-fast laser pulses to manipulate the qubits via Rabi flopping. As a result a full understanding of the multi-exciton coherent nonlinear spectroscopy with strong pump field is needed. In this work we present a non-perturbative calculation of the nonlinear CW pump-probe spectra.

DOI
10.1109/qels.2002.1031014

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Summary form only given. The optical properties of semiconductor quantum dots have been studied intensively in the past few years. Recently the experiment has demonstrated not only the ability to probe a single QD but also how to coherently control the exciton in a single QD on a time scale that is short compared with the decoherence time. We had proposed a scheme to use the excitons in QD as qubits and to use strong ultra-fast laser pulses to manipulate the qubits via Rabi flopping. As a result a full understanding of the multi-exciton coherent nonlinear spectroscopy with strong pump field is needed. In this work we present a non-perturbative calculation of the nonlinear CW pump-probe spectra.
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.
The nonlinear response of single GaAs quantum dots is studied in femtosecond near-field pump-probe experiments. At negative time delays, transient reflectivity spectra show pronounced oscillatory structure around the quantum dot exciton line, providing the first evidence for a perturbed free induction decay of the excitonic polarization. Phase-disturbing Coulomb interactions between the excitonic polarization and continuum excitations dominate the optical nonlinearity on ultrafast time scales. A theoretical analysis based on the semiconductor Bloch equations accounts for this behavior.
We report the first experimental study of the optical Stark effect in single semiconductor quantum dots (QD). For below band gap excitation, two-color pump-probe spectra show dispersive line shapes caused by a light-induced blueshift of the excitonic resonance. The line shape depends strongly on the excitation field strength and is determined by the pump-induced phase shift of the coherent QD polarization. Transient spectral oscillations can be understood as rotations of the QD polarization phase with negligible population change. Ultrafast control of the QD polarization is demonstrated.
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.
In this work, we study the resonant nonlinear optical response obtained when optical fields are used to excite charged semiconductor quantum dots (QDs). The basic physics of charged excitons (trions) created by optical excitation of charged QDs is of interest from the point of view of optically driven spin based quantum computing (QC). Stimulated Raman excitation, resonantly enhanced by the optical dipole coupling to the trion state, was used to optically generate electron spin coherence in the ground state of charged QDs. The evolution of the spin coherence was monitored through quantum beats in the phase-sensitively detected four wave mixing signal. The decay of the beats is a measure of the spin coherence time, which was found to be at least an order of magnitude greater than either the trion dipole coherence, or the Raman coherence time between excitons in a single neutral QD. A fascinating outcome of the experiment was the first observation of a contribution to the spin coherence induced by the vacuum field, which is also responsible for spontaneous emission from the trion state, known as spontaneously generated coherence (SGC). QC demands that coherent optical manipulations should be performed within the spin coherence time. We performed coherent optical control experiments, with a pair of phase-locked pump pulses, that showed the quantum nature of the coherence through interference of different quantum mechanical pathways. We showed both in experiment and theory that we can manipulate the spin coherence on the time scale of the Larmor frequency, as well as on an ultrafast femtosecond time scale, corresponding to the optical frequency of the trion state. Finally, resonant optical excitation of both the bright and nominally forbidden transitions from a single electron spin in a QD to the trion state were demonstrated. This allows for direct optical access to all the transitions required for optically driven QC with QD electron spins. We used frequency-domain nonlinear spectroscopy measurements on single QD trions to obtain the trion dipole decoherence and decay rates. Further, we demonstrated that the single electron spin coherence could be generated and detected optically, and found that the spin coherence time was significantly greater than in ensemble measurements at the same magnetic field.
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.