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Spontaneous emission and optical control of spins in quantum dots

Sophia E. Economou

Published Jan 1, 2006• 0 citations
OpenAlex

Abstract

Quantum dots are attractive due to their potential technological applications and the opportunity they provide for study of fundamental physics in the mesoscopic scale. This dissertation studies optically controlled spins in quantum dots in connection to quantum information processing. The physical realization of the quantum bit (qubit) consists of the two spin states of an extra electron confined in a quantum dot. Spin rotations are performed optically, by use of an intermediate charged exciton (trion) state. The two spin states and the trion form a $\\Lambda$-type system. The merits of this system for quantum information processing include integrability into a solid-state device, long spin coherence time, and fast and focused optical control. In this dissertation, we study the optical decay mechanisms of the trion state in the quantum dot. Using a master-equation approach, we derive microscopically the optical decay of the three- level system and find a novel term, the so-called spontaneously generated coherence (SGC). The latter, though predicted more than a decade ago for atomic $\\ Lambda$-systems satisfying certain conditions, had not been detected yet in any system. We found that in quantum dots, these conditions can be satisfied. We present the experiment which, in collaboration with our theory, constituted the first measurement of SGC. We establish the unification of SGC, polarization entanglement, and two- pathway decay. By keeping track of the spontaneously emitted photon dynamics, we find the conditions on the couplings that determine which effect will take place. We have thus placed SGC in a more quantum informational framework, characterizing it as lack of entanglement between the emitted photon and the three-level system. We develop a theory of ultrafast optical single-qubit rotations by use of 2$\\pi$ pulses, which have the two-fold advantage of minimal trion excitation and negligible spin precession. The analytically solvable hyperbolic secant pulses of Rosen and Zener for the two-level system are investigated in the context of the three-level system. Ultrafast rotations about the quantum dot growth direction are designed, the angle of spin rotation is expressed analytically, and the fidelity is studied by simulations. Adaptive feedback loops are employed to correct for unintended dynamics

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Quantum dots are attractive due to their potential technological applications and the opportunity they provide for study of fundamental physics in the mesoscopic scale. This dissertation studies optically controlled spins in quantum dots in connection to quantum information processing. The physical realization of the quantum bit (qubit) consists of the two spin states of an extra electron confined in a quantum dot. Spin rotations are performed optically, by use of an intermediate charged exciton (trion) state. The two spin states and the trion form a Lambda\\LambdaLambda-type system. The merits of this system for quantum information processing include integrability into a solid-state device, long spin coherence time, and fast and focused optical control. In this dissertation, we study the optical decay mechanisms of the trion state in the quantum dot. Using a master-equation approach, we derive microscopically the optical decay of the three- level system and find a novel term, the so-called spontaneously generated coherence (SGC). The latter, though predicted more than a decade ago for atomic Lambda\\ LambdaLambda-systems satisfying certain conditions, had not been detected yet in any system. We found that in quantum dots, these conditions can be satisfied. We present the experiment which, in collaboration with our theory, constituted the first measurement of SGC. We establish the unification of SGC, polarization entanglement, and two- pathway decay. By keeping track of the spontaneously emitted photon dynamics, we find the conditions on the couplings that determine which effect will take place. We have thus placed SGC in a more quantum informational framework, characterizing it as lack of entanglement between the emitted photon and the three-level system. We develop a theory of ultrafast optical single-qubit rotations by use of 2pi\\pipi pulses, which have the two-fold advantage of minimal trion excitation and negligible spin precession. The analytically solvable hyperbolic secant pulses of Rosen and Zener for the two-level system are investigated in the context of the three-level system. Ultrafast rotations about the quantum dot growth direction are designed, the angle of spin rotation is expressed analytically, and the fidelity is studied by simulations. Adaptive feedback loops are employed to correct for unintended dynamics
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.
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.
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.
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.
In this thesis, we will discuss results on quantum optical measurements in InAs self-assembled quantum dots (QDs). A single electron confined to a QD provides an attractive ground state qubit for many quantum information architectures. The excitation of an exciton in the QD structure via optical radiation will produce an electron-hole pair and, when combined with the ground state electron, form a quasi three-particle state called a trion. The trion transitions allow us to optically manipulate and readout the spin state. Narrow linewidth continuous wave lasers are used to probe the properties of the trion transitions in the frequency domain. We recover atomic like behavior for the QD resonances. The time dynamics of the trion system are studied by time gating a CW laser with an electro-optic modulator (EOM) and time tagging the scattered single photons from the transition using single photon detectors. These techniques are utilized in an entanglement protocol where a photon emitted during decay from the trion state to one of the electron spin states creates an entangled state between the electron spin and the photon. Under the influence of a transverse magnetic field the optical transitions from the spin states to the trion states are orthogonally polarized. The entangled state we are demonstrating is between the polarization state of the photon and the polarization state of the electron spin. We extract a corresponding fidelity of 0.6. The entangled nature of the spin state and the photon allows for the possibility to transport entanglement by means of this photonic channel. We study the coherence properties of the emitted photon using Hong Ou Mandel interference, which shows the indistinguishability of the photons (a required property for quantum information transport). Finally, we develop an experimental protocol to teleport quantum states from cavity enhanced photon pairs created in spontaneous parametric down conversion (SPDC) to a QD spin state by the interference between entangled photons from the QD and the SPDC photons.