Abstract
The coherence of electron spins can be enhanced significantly by preparing the nuclear spin polarizations to generate an Overhauser field with small fluctuations. We propose a theoretical model for calculating the long time dynamics of the prepared Overhauser field under nuclear spin diffusion in a quantum dot. We obtained a simplified diffusion equation that can be numerically solved, and we show quantitatively how the Knight shift and the electron-mediated nuclear spin flip-flops affect the nuclear spin diffusion. The results explain several recent experimental observations, where the measured decay time of the Overhauser field is dependent on the external magnetic field, electron spin state in double quantum dots and initial nuclear spin polarization rate.
Highlights
Electron spins in quantum dots are one of the most promising systems for realizing quantum computation [1]
We assume that an external magnetic field B0 much larger than the mean value and variance of the local Overhauser field generated by nuclei is applied along the z-direction
We established an effective method for calculating the long time dynamics of the Overhauser field under nuclear spin diffusion and showed that the confined electron in a quantum dot can both enhance the decay of the Overhauser field by mediating nuclear spin flip-flop and suppress the decay via inhomogeneous Knight shift
Summary
Electron spins in quantum dots are one of the most promising systems for realizing quantum computation [1]. Recent experiments have revealed that the Overhauser field has a typical relaxation time ranging from a few seconds to a few minutes, and even up to an hour in certain systems [22] The variation of this relaxation time is believed to be a result of diverse experimental configurations, such as different applied magnetic fields [18, 19], electron spin state in double quantum dots [18] and DNP pump time [20]. A more recent work [26] considers relaxation of the Overhauser field due to the electron-mediated nuclear spin diffusion, but not including the direct nuclear dipole–dipole interaction Such treatment ends up with the conclusion that the Overhauser field can only decay by less than 1%, in contrast to experimental facts of complete decay of the Overhauser field over a long time.
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