Spin detection with a micromechanical trampoline:Towards magnetic resonance microscopy harnessing cavity optomechanics

We explore the prospects and benefits of combining the techniques of cavity optomechanics with efforts to image spins using magnetic resonance force microscopy (MRFM). In particular, we focus on a common mechanical resonator used in cavity optomechanics -- high-stress stoichiometric silicon nitride (Si$_3$N$_4$) membranes. We present experimental work with a trampoline membrane resonator that has a quality factor above $10^6$ and an order of magnitude lower mass than a comparable standard membrane resonators. Such high-stress resonators are on a trajectory to reach 0.1 $\rm{aN}/\sqrt{\rm{Hz}}$ force sensitivities at MHz frequencies by using techniques such as soft clamping and phononic-crystal control of acoustic radiation in combination with cryogenic cooling. We present a demonstration of force-detected electron spin resonance of an ensemble at room temperature using the trampoline resonators functionalized with a magnetic grain. We discuss prospects for combining such a resonator with an integrated Fabry-Perot cavity readout at cryogenic temperatures, and provide ideas for future impacts of membrane cavity optomechanical devices on MRFM of nuclear spins.