Three-dimensional squeezing of optically levitated nanospheres

We propose a protocol to measure impulses beyond the standard quantum limit. The protocol reduces noise in all three spatial dimensions and consists of squeezing a mechanical system's state via a series of jumps in the frequency of the harmonic potential. We quantify how decoherence in a realistic system of an optically levitated, dielectric nanoparticle limits the ultimate sensitivity. We predict that $\sim$10 dB of squeezing is achievable with current technology, enabling quantum-enhanced detection of weak impulses.