Spin dynamics in quantum dots on liquid helium

Liquid He-4 is free from magnetic defects, making it an ideal substrate for electrons with long-lived spin states. Such states can serve as qubit states. Here we consider the spin states of electrons electrostatically localized in quantum dots on a helium surface. Efficient gate operations in this system require spin-orbit coupling. It can be created by a nonuniform magnetic field from a current-carrying wire, can be turned on and off, and allows one to obtain large electrodipole moment and comparatively fast coupling of spins in neighboring dots. Of central importance is to understand spin decay due to the spin-orbit coupling. We establish the leading mechanism of such decay and show that the decay is sufficiently slow to enable high-fidelity single- and two-qubit gate operations.

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Figure 1

Sketches of single-electron quantum dots on the surface of liquid helium. The confining electrodes are submerged into the helium to depth $0.2–0.5\mu \mathrm{m}$. The electron vibrations within the dot have typical frequencies of 6 GHz. A permanent magnetic field $\lesssim 0.5$ T is applied parallel to the surface. Superconducting wires running across the dots produce a nonuniform magnetic field that is turned on and off by a dc current $\sim 2–5$ mA through the wires. (a) The current can be turned on and off in each dot separately. (b) The current runs through several dots, and the spin-orbit coupling is controlled by tuning the intradot vibration frequency close to resonance with the Larmor frequency.