Coherent Single Electron Spin Control in a Slanting Zeeman Field


Yasuhiro Tokura
Optical Science Laboratory

 Stimulated by electron-spin-based proposals for quantum computation, a growing interest has emerged in realizing the coherent manipulation of a single electron spin in a solid-state environment. The application of the electron’s spin―rather than its charge―as a quantum bit (qubit) is motivated by its potentially long coherence time in solids and the fact that it comprises a natural two-level system. Single electron spin resonance (SESR) plays a key role in realizing electron-spin-qubit rotation, however had not been detected in semiconductor quantum dots (QDs) so far, because of the necessary high-frequency (10 GHz) selective magnetic field in a cryogenic (100 mK) setup. Waveguides and microwave cavities as used in conventional ESR cause serious heating, limiting the operation temperature to 1 K.
 We propose a new SESR scheme that eliminates the need for an externally applied ac magnetic field, and with the potential of very high and tunable quality factors. An ac voltage is applied to let an electron in a QD oscillate under a static slanting Zeeman field. This effectively provides the electron spin with the necessary time-dependent magnetic field. Note the analogy with the Stern-Gerlach experiment, where the spin and orbital degrees of freedom are coupled by employing an inhomogenous magnetic field. The spatial oscillation of the electron within the QD involves the hybridization of orbital states.
 We estimated expected coherence time of this qubit and demonstrated that single-qubit rotation and the controlled-NOT operation are possible. This qubit is easier to manipulate than a spin qubit and has a better quality factor than a charge qubit. The concept is general and can be applied to a range of systems, such as single wall carbon nanotubes, GaAs, and SiGe QDs. This scheme also allows for the measurement ofthe intrinsic single electron spin coherence time.

[1] Y. Tokura et al., Phys. Rev. Lett. 96 (2006) 047202.

Fig. 1. Model: Ferromagnetic gate electrodes are located at either end of the dot and are magnetically polarized in the plus or minus x direction, creating a magnetic field gradient bSL. A uniform magnetic field B0 is applied in the z direction. The spin in the dot is controlled by applying an oscillating voltage Vac between the two gates.
Fig. 2. (a) Relaxation rate 1/T1 in a GaAs QD as function of external magnetic field B0 due to different phonon scattering mechanisms: deformation potential (dashed line), longitudinal (dotted line) and transversal (dash-dotted line) piezoelectric. The solid line is the total. (b) B0 dependence of the quality factor Q for a single-qubit operation.

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