Proposal for quantum many-body simulation and torsional matter-wave interferometry with a levitated nanodiamond

Hybrid spin-mechanical systems have great potential in sensing, macroscopic quantum mechanics, and quantum information science. In order to induce strong coupling between an electron spin and the center-of-mass motion of a mechanical oscillator, a large magnetic gradient usually is required, which is difficult to achieve. Here we show that strong coupling between the electron spin of a nitrogen-vacancy (NV) center and the torsional vibration of an optically levitated nanodiamond can be achieved in a uniform magnetic field. Thanks to the uniform magnetic field, multiple spins can strongly couple to the torsional vibration at the same time. We propose utilizing this coupling mechanism to realize the Lipkin-Meshkov-Glick (LMG) model by an ensemble of NV centers in a levitated nanodiamond. The quantum phase transition in the LMG model and finite number effects can be observed with this system. We also propose generating torsional superposition states and realizing torsional matter-wave interferometry with spin-torsional coupling.