Nanoparticle arrays levitated in a cavity for quantum sensing

Levitated nanoparticles are being investigated as ultrasensitive quantum sensors of forces and accelerations, with applications ranging from fundamental physics phenomena such as dark matter or quantum gravity to real world applications. Attention is now turning to multiparticle regimes, and an important question is whether collective effects offer advantages for sensing. We investigate here the spectral characteristics of collective motion of $N$ trapped nanoparticles interacting via the optical mode of a cavity. We find the collective motion typically exhibit two generic spectral features: a broad spectral feature, the collective bright mode (CBM) which has been previously studied; but we find also a new structure of sharp peaks , the mechanical mode comb (MMC). We can describe all the detailed spectral features of the system, with a simple closed-form expression, by reducing the motion to a 1D generic collective mode which is non-Hermitian. We show that the MMC is more advantageous than the usual CBM for increased sensitivity in force sensing. We find that the mechanical comb can autonomously repair loss of `teeth' due to particle loss, a feature that may offer robustness in sensing.