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arXiv:cond-mat/0608518 · Journal of Physics Condensed Matter

Optically controlled single-qubit rotations in self-assembled InAs quantum dots

Clive Emary, Lu Jeu Sham

Published Jan 17, 2007• 33 citations
arXivHTMLPDF

Abstract

We present a theory of the optical control of the spin of an electron in an InAs quantum dot. We show how two Raman-detuned laser pulses can be used to obtain arbitrary single-qubit rotations via the excitation of an intermediate trion state. Our theory takes into account a finite in-plane hole g -factor and hole mixing. We show that such rotations can be performed to high fidelities with pulses lasting a few tens of picoseconds.

DOI
10.1088/0953-8984/19/5/056203

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arXiv:0905.0297•May 3, 2009•1 citation
We present a theory of the optical control of the spin of an electron in an InAs quantum dot. We show how two Raman-detuned laser pulses can be used to obtain arbitrary single-qubit rotations via the excitation of an intermediate trion state. Our theory takes into account a finite in-plane hole g -factor and hole mixing. We show that such rotations can be performed to high fidelities with pulses lasting a few tens of picoseconds.
We demonstrate coherent optical control of a single hole spin confined to an InAs/GaAs quantum dot. A superposition of hole-spin states is created by fast (10-100 ps) dissociation of a spin-polarized electron-hole pair. Full control of the hole spin is achieved by combining coherent rotations about two axes: Larmor precession of the hole spin about an external Voigt geometry magnetic field, and rotation about the optical axis due to the geometric phase shift induced by a picosecond laser pulse resonant with the hole-trion transition.
Optically driven self-assembled quantum dots are leading candidates for use in quantum computers because of their potential for high speed gate operations and relatively compact design. In this approach, each dot is charged with a single electron whose spin serves as the quantum bit (qubit). This thesis addresses the need for a universal set of gates to physically implement quantum computing and discusses initial steps toward spin-photon entanglement. Both are addressed through coherent control of the spin state in a magnetic field with optical pulses. This work experimentally demonstrates coherent rotations of the electron spin. First, the electron spin is rotated at up to 0.5 terahertz about the optical axis by a detuned picosecond optical pulse. The rotation occurs via a nearly resonant stimulated spin-flip Raman process involving a negatively charged exciton (trion). Second, rotation about an orthogonal axis is demonstrated due to electron spin precession about the magnetic field between two detuned optical pulses. The magnitude of the electron g factor is measured to be 0.4, and the rotation speed is 30 gigahertz in a 6.6 Tesla field. Geometric phases are detected in quantum dots for the first time due to cyclic Rabi oscillations driven by a resonant continuous-wave laser. These geometric phases provide another method of spin rotation and can be used in a gate. Any combination of these methods that provides spin rotation about two orthogonal axes can form an arbitrary rotation and together with a phase gate can form any unitary single qubit gate. Finally, this thesis also presents a detailed experimental procedure for creating a partial entanglement of internal variables within a quantum dot spin-exciton system, as a preliminary step to spin-photon entanglement. It has been proposed that entanglement between non-adjacent qubits in a large qubit network could occur via a photon, fueling research to demonstrate spin-photon entanglement. The experiment proposed here will create the precursor state in 25 picoseconds with a predicted fidelity of 0.985, and the precursor superposition state has a theoretical entropy of entanglement of 0.92.
The ability to manipulate the spin states of charges confined in quantum dots (QDs) is essential for the realization of a quantum computer based on such spins. Here, we present experimentally realized electron spin qubit gates in a single self-assembled InAs QD using a combination of picosecond optical pulses, spin precession about an external DC magnetic field and optically generated geometric phases. Arbitrary unitary operations on the electron spin qubit may be constructed using a combination of optical pulses and either spin precession or the optically generated geometric phases.
Self-assembled quantum dots (QDs) containing a single electron are one of the leading candidate systems for the realization of a quantum computer. The spin states of charges confined in these dots have been shown to possess a number of qualities that are attractive for use as the quantum bits (qubits) in quantum computing implementations, particularly their long lifetimes and coherence times. In addition, these spin qubits may be controlled optically, offering the prospect of ultrafast qubit gate operations, a crucial necessity for the execution of quantum algorithms. Due to the weak interaction of self-assembled QDs with light, however, the coherent optical control and read-out of the spin states of charged self-assembled QDs has proven to be a considerable challenge. This thesis presents two sets of experiments demonstrating the coherent optical control and read-out of the quantum states of a self-assembled InAs QD containing a single electron. The first utilizes mode-locked picosecond optical pulses to control the optical transitions in the dot and to detect QD level occupations. These capabilities are used to observe transient phenomena in a singly charged InAs QD such as the generation and decay of excited state population and spin precession. Further, Rabi oscillations between the electron and the lowest-lying excited state are observed, demonstrating the ability to coherently control the optical transitions of the QD, a prerequisite for spin control. These results are built upon in the second set of experiments, in which a combination of optical pulses, an externally applied DC magnetic field and a continuous-wave (CW) optical field are employed to initialize and completely control the states of a QD confined electron spin. Spin control by the use of pulse-driven two-photon Raman processes, spin precession about the external magnetic field and geometric phases generated by CW-driven cyclic evolutions in the dot is demonstrated. A number of spin qubit gate operations are shown for these spin control mechanisms, forming a foundational set of single qubit gates required for the implementation of quantum computing with singly charged self-assembled QDs.
A method is proposed for the optical rotation of the spin of an electron in a quantum dot using excited trion states to implement operations significantly faster than those of most existing proposals. Key ingredients are the geometric phase induced by 2pi hyperbolic secant pulses, use of coherently trapped states and use of naturally dark states. Our proposal covers a variety of quantum dots by addressing different parameter regimes. Numerical simulations with typical parameters for InAs self-assembled quantum dots, including their dissipative dynamics, give fidelities of the operations in excess of 99%.
We demonstrate the all-optical ultrafast manipulation and read-out of optical transitions in a single negatively charged self-assembled InAs quantum dot, an important step towards ultrafast control of the resident spin. Experiments performed at zero magnetic field show the excitation and decay of the trion (negatively charged exciton) as well as Rabi oscillations between the electron and trion states. Application of a DC magnetic field perpendicular to the growth axis of the dot enables observation of a complex quantum beat structure produced by independent precession of the ground state electron and the excited state heavy hole spins.