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arXiv:cond-mat/0608225 · Physical Review Letters

Fast Initialization of the Spin State of an Electron in a Quantum Dot in the Voigt Configuration

Clive Emary, Xiaodong Xu, Duncan G. Steel, Semion K. Saikin, Lu Jeu Sham

Published Jan 23, 2007• 81 citations
arXivHTMLPDF

Abstract

We consider the initialization of the spin state of a single electron trapped in a self-assembled quantum dot via optical pumping of a trion level. We show that with a magnetic field applied perpendicular to the growth direction of the dot, a near-unity fidelity can be obtained in a time equal to a few times the inverse of the spin-conserving trion relaxation rate. This method is several orders of magnitude faster than with the field aligned parallel, since this configuration must rely on a slow hole spin-flip mechanism. This increase in speed does result in a limit on the maximum obtainable fidelity, but we show that for InAs dots, the error is very small.

DOI
10.1103/physrevlett.98.047401

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We consider the initialization of the spin state of a single electron trapped in a self-assembled quantum dot via optical pumping of a trion level. We show that with a magnetic field applied perpendicular to the growth direction of the dot, a near-unity fidelity can be obtained in a time equal to a few times the inverse of the spin-conserving trion relaxation rate. This method is several orders of magnitude faster than with the field aligned parallel, since this configuration must rely on a slow hole spin-flip mechanism. This increase in speed does result in a limit on the maximum obtainable fidelity, but we show that for InAs dots, the error is very small.
We study the interaction of a quantum dot in the Voigt configuration with a laser pulse and particularly analyze the potential for rapid spin initialization by putting the quantum dot near a molybdenum disulfide (MoS 2 ) monolayer. The MoS 2 monolayer influences the spontaneous decay rates of the quantum dot, leading to anisotropically enhanced decay rates, for the quantum dot’s electric dipole moments parallel and perpendicular to the layer. By solving the relevant density matrix equations, we find that high spin initialization fidelity is obtained at short times. The fidelity is significantly higher than when the quantum dot is in free-space vacuum. We examine two different cases of the interaction of the quantum dot with the applied optical field. First, we use a continuous wave laser field and determine for various quantum dot—MoS 2 layer distances the field strength that leads to acceptable fidelity levels. The effect of the quality of the MoS 2 material on the fidelity of spin initialization is also examined. We also study the interaction of the quantum dot with a laser pulse and apply numerical optimal control to obtain the time-dependent field strength, which leads to maximum final fidelity for short time intervals. The latter approach gives beneficial results in comparison to the continuous wave field excitation.
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.
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%.
The preparation of a coherent heavy-hole spin via ionization of a spin-polarized electron-hole pair in an InAs/GaAs quantum dot in a Voigt geometry magnetic field is experimentally investigated. For a dot with a typical bright-exciton fine-structure splitting of $17\phantom{\rule{0.16em}{0ex}}\ensuremath{\mu}\mathrm{eV}$, the fidelity of the spin preparation is limited to 0.75, with optimum preparation occurring when the effective fine structure of the bright exciton matches the in-plane hole Zeeman energy. In principle, higher fidelities can be achieved by minimizing the bright-exciton fine-structure splitting.
We describe a proposal for fast electron-spin initialization in a negatively charged quantum dot coupled to a microcavity without the need for a strong magnetic field. We employ two-photon excitation to access trion states that are spin forbidden by one-photon excitation. Our simulation shows a maximum initialization speed of 1.31.31.3 GHz and maximum fidelity of 99.799.7%99.7 with realistic system parameters.
We demonstrate complete coherent control of a single spin qubit confined in a self-assembled InAs negatively charged quantum dot subjected to an Oblique magnetic field, and directly compare this regime with the conventional Voigt geometry. In the Oblique-field configuration, the groundstate spin eigenstates are found to be unequal superpositions of the bare electron spin, with their composition tunable via the orientation of the applied field. This tunable spin mixing provides an additional degree of freedom to engineer the spin basis and associated optical couplings in the charged quantum dot system. Although this geometry has a distinct structure with important implications, it provides a regime in which we can fully and coherently control the tailored spin qubit. We observe Rabi oscillations and Ramsey fringes, and demonstrate arbitrary single-qubit rotations, enabling a direct comparison with the Voigt case. Our results establish that spin-qubit control does not necessarily require a pure Voigt geometry and can instead be achieved under Oblique magnetic fields. This relaxes constraints on device and field alignment and offers a versatile route to design and optimize quantum information processing architectures in semiconductor quantum dots.