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arXiv:cond-mat/0109252 · Physical review. B, Condensed matter

Theory of fast quantum control of exciton dynamics in semiconductor quantum dots

Carlo Piermarocchi, Pochung Chen, Yseulte Dale, Lu Jeu Sham

Published Jan 18, 2002• 55 citations
arXivHTMLPDF

Abstract

Optical techniques for the quantum control of the dynamics of multiexciton states in a semiconductor quantum dot are explored in theory. Composite bichromatic phase-locked pulses are shown to reduce the time of elementary quantum operations on excitons and biexcitons by an order of magnitude or more. Analytic and numerical methods of designing the pulse sequences are investigated. Fidelity of the operation is used to gauge its quality. A modified quantum Fourier transform algorithm is constructed with only Rabi rotations and is shown to reduce the number of operations. Application of the designed pulses to the algorithm is tested by a numerical simulation.

DOI
10.1103/physrevb.65.075307

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Optical techniques for the quantum control of the dynamics of multiexciton states in a semiconductor quantum dot are explored in theory. Composite bichromatic phase-locked pulses are shown to reduce the time of elementary quantum operations on excitons and biexcitons by an order of magnitude or more. Analytic and numerical methods of designing the pulse sequences are investigated. Fidelity of the operation is used to gauge its quality. A modified quantum Fourier transform algorithm is constructed with only Rabi rotations and is shown to reduce the number of operations. Application of the designed pulses to the algorithm is tested by a numerical simulation.
Semiconductor quantum dots have been featured in a number of proposals for quantum computing because of the advantages afforded by confinement on the nanoscale, such as well separated, discrete energy levels and ease of optical manipulation. In addition, they can leverage established semiconductor fabrication techniques and, like the quantum dots used in this work, can be designed to match the telecommunication band, improving the scalability and potential integration of the platform into existing technologies. This thesis work applied optical pulse engineering to manipulate exciton qubits in self-assembled InAs quantum dots. Optimal quantum control theory was used to design pulse shapes that implement high fidelity single-qubit and two-qubit operations, with constraints on the numerical optimization that ensure that the pulses can be accurately implemented using a commercial 4f pulse shaper. In the case of single-qubit operations, the results showed that two uncoupled qubits can be manipulated in parallel using a single phase-shaped laser pulse, provided their optoelectronic properties are sufficiently different. It was demonstrated that targeted differences in inversion and phase between the qubits can be achieved on an ultrafast timescale with high fidelity. In the case of two-qubit operations, the controlled-rotation gate was optimized using amplitude-only and phase-only pulse shaping schemes. The shaped pulses for both schemes were shown to produce higher fidelity operations. The ability to implement robust state inversion on short timescales is particularly useful for technologies such as ultrafast optical switches, single-photon sources, and entangled-photon sources. This work has demonstrated state inversion in a single InAs quantum dot via adiabatic rapid passage using linearly chirped laser pulses. The achieved gate times were an order of magnitude shorter than previous demonstrations. Theoretical predictions of the dependence of the inversion efficiency of the exciton on the sign of the pulse chirp were also verified experimentally, allowing for the identification of phonon-mediated dephasing as the dominant source of decoherence.
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.
Pulse-shaping protocols for subpicosecond optically controlled quantum gates in semiconductor quantum dots are reported. Our emphasis is the development of shaping schemes for either amplitude or phase control of the pulse that are easily implemented using commercial pulse shapers and femtosecond laser systems. We illustrate the efficacy of our approach through simulations of a controlled-rotation gate in a realistic In(Ga)As quantum dot with electronic structure calculated using eight-band, strain-dependent $\mathbit{k}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbit{p}$ theory. Our results show that amplitude- and phase-shaping protocols both lead to substantial improvements in fidelity when compared with transform-limited pulses with equivalent gate times. Dephasing was found to have a minimal effect on the gate fidelities due to the ultrafast time scale of the quantum operations.
Shaped ultrafast pulses designed for controlled-rotation (C-ROT) operations on exciton qubits in semiconductor quantum dots are demonstrated using a quantum control apparatus operating at ∼1 eV. Optimum pulse shapes employing amplitude and phase shaping protocols are implemented using the output of an optical parametric oscillator and a programmable pulse shaping system, and characterized using autocorrelation and multiphoton intrapulse interference phase scan techniques. We apply our pulse characterization results and density matrix simulations to assess the fundamental limits on the fidelity of the C-ROT operation, providing a benchmark for the evaluation of sources of noise in other quantum control experiments. Our results indicate the effectiveness of pulse shaping techniques for achieving high fidelity quantum operations in quantum dots with a gate time below 1 ps.
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.
We report coherent optical control of a biexciton (two electron-hole pairs), confined in a single quantum dot, that shows coherent oscillations similar to the excited-state Rabi flopping in an isolated atom. The pulse control of the biexciton dynamics, combined with previously demonstrated control of the single-exciton Rabi rotation, serves as the physical basis for a two-bit conditional quantum logic gate. The truth table of the gate shows the features of an all-optical quantum gate with interacting yet distinguishable excitons as qubits. Evaluation of the fidelity yields a value of 0.7 for the gate operation. Such experimental capability is essential to a scheme for scalable quantum computation by means of the optical control of spin qubits in dots.