Mechanical Torque of Quantum Origin Generated by a Quantum Force in Molecular Magnets and Nanoresonator

A torsional oscillator may exhibit quantum torques in a macrospin-nanoresonator system. We demonstrate that when the system is placed in a static magnetic field with a gradient, such a torque exists in an oscillator due to quantum entanglement of mechanical modes of a torsional resonator with a tunneling spin in the presence of a microwave field. At low temperature, the torque is shown to exhibit various quantum oscillations that depend on the coupling strength, microwave frequency, Rabi frequency, and the characteristic length describing the field gradient. These features are expected to be tested in existing experimental techniques.