Relaxation of a nuclear spin placed on a biased nanomechanical oscillator

We propose a mechanism to decrease the time needed to initialize nuclear spin qubits by resonant coupling of the nuclear spins to a heat bath composed of nanomechanical degrees of freedom. To achieve this, we suggest that the nuclear spins be attached to the tip of a cantilever oscillating in a nonuniform magnetic field. The gradient of the magnetic field couples the spin and mechanical degrees of freedom, inducing an additional spin-relaxation mechanism. The nanomechanical oscillator can also serve as one of the contacts of a tunnel junction, facilitating a voltage control of the nuclear spin-relaxation time. We derive an explicit microscopic expression for the relaxation rate of nuclear spins and analyze its voltage and temperature dependencies.