Fast, controlled coherent interactions between spins in separated quantum dots are a key requirement for two-qubit gates and distributed architectures in advancing quantum information in the solid state. We have performed two-color pump-probe experiments in which pulsed lasers emitting at different photon energies manipulate two subsets of electron spins in an inhomogeneous ensemble of InGaAs quantum dots. Measurements of the resulting ellipticity demonstrate the slow, power dependent onset of phase shifts in the Larmor precession in a magnetic field of one subset of oriented spins after optical orientation of the second subset. Model calculations show that these results are consistent with a Heisenberg-like interaction between the pairs of spins with strength ~ micro-eV and that this interaction results in entanglement between the spins.
Fast, controlled coherent interactions between spins in separated quantum dots are a key requirement for two-qubit gates and distributed architectures in advancing quantum information in the solid state. We have performed two-color pump-probe experiments in which pulsed lasers emitting at different photon energies manipulate two subsets of electron spins in an inhomogeneous ensemble of InGaAs quantum dots. Measurements of the resulting ellipticity demonstrate the slow, power dependent onset of phase shifts in the Larmor precession in a magnetic field of one subset of oriented spins after optical orientation of the second subset. Model calculations show that these results are consistent with a Heisenberg-like interaction between the pairs of spins with strength ~ micro-eV and that this interaction results in entanglement between the spins.
Recently, an implementation of a universal set of one- and two-quantum-bit gates for quantum computation using spin states of coupled single-electron quantum dots was proposed. It was demonstrated that it is possible to execute a coherent control of a quantum system based on two-electron spin states in a double quantum dot, allowing state preparation, coherent manipulation, and projective readout. This possibility is based on rapid electrical control of the spin exchange interaction. These results motivated us to develop a formal theoretical study of the corresponding model of two coupled spins placed in a magnetic field and subjected to a time-dependent mutual Heisenberg interaction. Using possible exact solutions of the corresponding quantum problem, we study entangling of different separable initial states in this model. It is demonstrated that the entanglement due to a time-dependent Heisenberg interaction is dominating in comparison with the entanglement due to the action of an external magnetic field.
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.
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.
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.
Solid state based quantum information processing is focused on physical implementation of all necessary elements of quantum computation and quantum information in solid state systems, mainly due to their scalability compared to e.g. optical systems. Among many proposals to realize these types of devices, such as quantum dots as charge qubits or Josephson junction circuits, we study here one of the most promising candidates, i.e., the spin of an electron confined to a quantum dot as a qubit. Experimentally, it has been shown that the relaxation rate of this two level system can be pushed above few seconds in low magnetic fields. Moreover, using spin echo techniques, \nthe spin dephasing time can be maximized up to milliseconds with the current technology. This long spin decay time is one of the main reasons that make this system desirable for quantum computation and quantum information purposes. \nWe reexamined the recent measurement based proposal called one-way quantum computation which exploits entanglement and local measurements as tools to perform quantum computation on N qubits. Although it was suggested in the original work to entangle the qubits via the nearest neighbor Ising interaction, we investigated how one can generate the so-called cluster states with the Heisenberg interaction. We extended our method to include more general forms of Heisenberg interaction such as asymmetric coupling of adjacent qubits. These forms of couplings, rather than Ising interaction, are more encountered in solid state devices, and therefore make it possible to perform one-way quantum computation with electron spins in quantum dots coupled via exchange interaction to their adjacent spins. \n \nChapters II, III, and IV of my thesis are devoted to the study of the spin-orbit interaction in heterostructure quantum dots and its effect on the spin dynamics. We observed that one can actually use spin-orbit interaction to manipulate the spin state of an electron on time scales much smaller than the spin dephasing time. Specifically, in chapter II, we studied the effect of a nearby functioning quantum point contact (QPC) on the relaxation of the electron spin and show that the charge fluctuations in QPC lead to spin relaxation of the confined electron in the presence of spin-orbit interactiom and an applied magnetic field. We also addressed the relation of this rate to the microscopic parameters of the system and found some geometrical dependence of the spin relaxation time on the orientation of the QPC on the substrate. Moreover, we showed in chapters III and IV that the spin-orbit interaction can play a positive role, in order to rotate the spin around the Bloch sphere. We considered different mechanisms, particularly, Electron Dipole Spin Resonance (EDSR) and holonomic unitary gates in quantum dots. We verified that these mechanisms of spin manipulation can be realized in solid state systems with the state of the art semiconductor technologies. \n \nChapter V of the thesis covers a slightly different topic and focuses on the role of the Coulomb interaction in electronic transport. There, we reviewed the non-analytic corrections to the Fermi liquid behavior and their consequences on the momentum occupation number of the electrons in a two dimensional electron gas (2DEG). As an example, we calculated the tunneling rate from an interacting electron reservoir onto a quantum dot and compared our result to the corresponding case for electron tunneling between bilayer 2DEGs. Moreover, within RPA approximation, we found that the electron-plasmon coupling leads to a quadratic frequency dependence of the electron self-energy at low frequencies at the Fermi surface. This correction suppresses the same order corrections due to the particle-hole bubble. \n \n \n
Single spins in semiconductor quantum dots form a promising platform for solid-state quantum information processing. The spin-up and spin-down states of a single electron or hole, trapped inside a quantum dot, can represent a single qubit with a reasonably long decoherence time. The spin qubit can be optically coupled to excited (charged exciton) states that are also trapped in the quantum dot, which provides a mechanism to quickly initialize, manipulate and measure the spin state with optical pulses, and to interface between a stationary matter qubit and a 'flying' photonic qubit for quantum communication and distributed quantum information processing. The interaction of the spin qubit with light may be enhanced by placing the quantum dot inside a monolithic microcavity. An entire system, consisting of a two-dimensional array of quantum dots and a planar microcavity, may plausibly be constructed by modern semiconductor nano-fabrication technology and could offer a path toward chip-sized scalable quantum repeaters and quantum computers. This article reviews the recent experimental developments in optical control of single quantum dot spins for quantum information processing. We highlight demonstrations of a complete set of all-optical single-qubit operations on a single quantum dot spin: initialization, an arbitrary SU(2) gate, and measurement. We review the decoherence and dephasing mechanisms due to hyperfine interaction with the nuclear-spin bath, and show how the single-qubit operations can be combined to perform spin echo sequences that extend the qubit decoherence from a few nanoseconds to several microseconds, more than 5 orders of magnitude longer than the single-qubit gate time. Two-qubit coupling is discussed, both within a single chip by means of exchange coupling of nearby spins and optically induced geometric phases, as well as over longer-distances. Long-distance spin-spin entanglement can be generated if each spin can emit a photon that is entangled with the spin, and these photons are then interfered. We review recent work demonstrating entanglement between a stationary spin qubit and a flying photonic qubit. These experiments utilize the polarization- and frequency-dependent spontaneous emission from the lowest charged exciton state to single spin Zeeman sublevels.