Abstract
We investigate superradiantlike dynamics of a nuclear-spin bath in contact with an electron shuttle, modeled as a moving quantum dot trapping a single electron. The dot is shuttled between two external reservoirs, where electron-nuclear flip flops are associated with tunneling events. For an ideal model with uniform hyperfine interaction, realized through an isotopically enriched ``nuclear-spin island'', we discuss in detail the nuclear spin evolution and its relation to superradiance. We then show that the superradiantlike evolution is robust to various extensions of the initial setup, and derive the minimum shuttling time which allows to escape adiabatic spin evolution. We also discuss slow/fast shuttling under the inhomogeneous field of a nearby micromagnet and compare our scheme to a model with stationary quantum dot. Finally, we describe the electrical detection of nuclear entanglement in the framework of Monte Carlo wave-function simulations.
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