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.
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.
We present a procedure for the optical coherent control of quantum bits within a quantum dot spin-exciton system, as a preliminary step to implementing a proposal by Yao, Liu, and Sham [Phys. Rev. Lett. 95, 030504 (2005)] for deterministic spin-photon entanglement. The experiment proposed here utilizes a series of picosecond optical pulses from a single laser to coherently control a single self-assembled quantum dot in a magnetic field, creating the precursor state in 25 ps with a predicted fidelity of 0.991. If allowed to decay in an appropriate cavity, the ideal precursor superposition state would create maximum spin-photon entanglement. Numerical simulations using values typical of InAs quantum dots give a predicted entropy of entanglement of 0.929, largely limited by radiative decay and electron spin flips.
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.
An electron spin confined to a self-assembled semiconductor quantum dot is a candidate system to act as a quantum bit, a qubit. In order to act in this capacity it must be entangled with other qubits. Both electrons and holes are confined in such dots, allowing optical manipulation and emission of light. A single photon could act as an intermediary qubit, becoming entangled with a spin and conveying the entanglement from one spin to another. By an appropriate optical pulse sequence, a superposition state has been created, which upon radiative decay would be entangled with an emitted photon. A continuous wave beam optically pumps and measures the state in the interim before the next repetition of the pulse sequence. Here I describe the pulse sequence and measurement methods, display the experimental results, and show how to compute the entanglement of our state. Numerical simulations of the coherence of the generated state agree with the measured value of 0.28 out of a possible 0.5. The main cause of deviation from the ideal value is state relaxation during control pulse sequence. The fidelity of the state to the ideal precursor state is computed to be 0.81, and the entanglement that would result upon emission of a vertically polarized photon is 0.18, and simulations suggest 0.60 is possible with optimum design.
Coherent optically driven semiconductor quantum dot systems are proposed for the implementation of quantum information processing devices. Fundamental quantum computation units, the quantum bits (qubits), are realized and optically manipulated in the exciton and spin bases. In this thesis, consecutive phase-sensitive rotations of a single qubit and their importance in the measurement of the full physical density matrix have been demonstrated experimentally in the exciton system in neutral GaAs/Al0:3Ga0:7As interface fluctuation quantum dots. The experimental work done on the exciton system serves as a foundation for consequent work on the long coherence lifetime spin-based qubits in charged quantum dots. In the spin-based system in the charged GaAs/Al0:3Ga0:7As interface fluctuation quantum dots, we demonstrate the selective excitation from the two spin ground states to the charged exciton (trion) state through phase sensitive control of the spin coherence in an ensemble of three-level spin-trion Lambda systems. This controlled excitation utilized the optically coupled and decoupled states of the electron spin in the presence of coherent transient excitation of the spin ground states in singly charged quantum dots. This progress lays the ground work for achieving complete ultrafast spin rotations.
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.