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arXiv:1501.01952

Complete All-Optical Quantum Control of Electron Spins in InAs/GaAs Quantum Dot Molecule

Guy Cohen

Published Jan 8, 2015• 1 citation
arXivHTMLPDF

Abstract

The spin states of electrons and holes confined in InAs quantum dot molecules have recently come to fore as a promising system for the storage or manipulation of quantum information. We describe here a feasible scheme for complete quantum optical control of two electron spin qubits in two vertically-stacked singly-charged InAs quantum dots coupled by coherent electron tunneling. With an applied magnetic field transverse to the growth direction, we construct a universal set of gates that corresponds to the possible Raman transitions between the spin states. We detail the procedure to decompose a given two-qubit unitary operation, so as to realize it with a successive application of up to 8 of these gates. We give the pulse shapes for the laser pulses used to implement this universal set of gates and demonstrate the realization of the two-qubit quantum Fourier transform with fidelity of 0.881 and duration of 414 ps. Our proposal therefore offers an accessible path to universal computation in quantum dot molecules and points to the advantages of using pulse shaping incoherent manipulation of optically active quantum dots to mitigate the negative effects of unintended dynamics and spontaneous emission.

DOI
10.48550/arxiv.1501.01952

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The spin states of electrons and holes confined in InAs quantum dot molecules have recently come to fore as a promising system for the storage or manipulation of quantum information. We describe here a feasible scheme for complete quantum optical control of two electron spin qubits in two vertically-stacked singly-charged InAs quantum dots coupled by coherent electron tunneling. With an applied magnetic field transverse to the growth direction, we construct a universal set of gates that corresponds to the possible Raman transitions between the spin states. We detail the procedure to decompose a given two-qubit unitary operation, so as to realize it with a successive application of up to 8 of these gates. We give the pulse shapes for the laser pulses used to implement this universal set of gates and demonstrate the realization of the two-qubit quantum Fourier transform with fidelity of 0.881 and duration of 414 ps. Our proposal therefore offers an accessible path to universal computation in quantum dot molecules and points to the advantages of using pulse shaping incoherent manipulation of optically active quantum dots to mitigate the negative effects of unintended dynamics and spontaneous emission.
Recent studies in self-assembled InAs quantum dots (QDs) for applications in quantum information processing have demonstrated initialization, readout and long decoherence time of an electron spin confined in a single QD. These arguably fulfill three out of the five DiVincenzo criteria for the physical implementation of quantum computation. Based on recent developments self-assembled InAs quantum dot molecules (QDMs), several advancements in the optical manipulation of two-electron spin states have been made. As a continuation of these studies towards a full two-qubit system, this thesis addresses one of the remaining criteria concerning a universal set of quantum gates. The physical platform for two-qubit gates is provided by two electrons confined in the QDM where the Coulomb exchange interaction gives rise to the singlet and triplet manifolds. In a transverse magnetic field, an eight-level system consisting of four singlet-triplet spin states, four optical excited states and twelve dipole allowed transitions arises. Spin initialization via multi-laser optical pumping is demonstrated with near unity fidelity for three of the spin states, while the remaining one can, in principle, be achieved by coherent optical pumping using four CW lasers. The effects of dynamic nuclear spin polarization, arising from the coupling between the electrons and the surrounding nuclei, is evident in the frequency pulling and pushing lineshapes in absorption profiles. This thesis shows that the optical nuclear spin locking that was demonstrated in a single QD earlier is effective in QDMs, yielding a long spin decoherence time of about 1 microsecond. Spectroscopic evidence suggests that this is accompanied by the first evidence of a narrowing in the Overhauser field distribution. The results reveal that stabilization of nuclear spin polarization in both QDs is achieved by optical manipulations in the top QD, demonstrating the effect of non-local nuclear spin locking. Finally, it is shown theoretically that pulsed excitation results in single spin rotations and in conjunction with the Coulomb exchange interaction, provides the ingredients for a universal two-qubit gate. A feasible experimental demonstration of the two-qubit gate is proposed, along with the methodology for the population readout of individual spin states.
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.
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.
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.
We present a feasible scheme for performing an optically controlled phase gate between two conduction electron spin qubits in adjacent self-assembled quantum dots. Interaction between the dots is mediated by the tunneling of the valence hole state, which is activated only by applying a laser pulse of the right polarization and frequency. Combining the hole tunneling with the Pauli blocking effect, we obtain conditional dynamics for the two quantum dots, which is the essence of our gating operations. Our results are of explicit relevance to the recent generation of vertically stacked self-assembled InAs quantum dots, and show that by a design which avoids unintended dynamics the gate could be implemented in theory in the 10-ps range and with a fidelity over 90%. Our proposal therefore offers an accessible path to the demonstration of ultrafast quantum logic in quantum dots.