  Nanoparticles trapped in optical tweezers emerged as an interesting platform
for investigating fundamental effects in quantum physics. The ability to shape
the optical trapping potential using spatial light modulation and quantum
control of their motion using coherent scattering to an optical cavity mode
predispose them for emulating a range of physical systems and studying quantum
phenomena with massive objects. To extend these capabilities of levitated
nanoparticles to quantum many-body systems, it is crucial to develop feasible
strategies to couple and entangle multiple particles either directly or via a
common optical bus. Here, we propose a variable and deterministic scheme to
generate Gaussian entanglement in the motional steady state of multiple
levitated nanoparticles using coherent scattering to multiple cavity modes.
Coupling multiple nanoparticles to a common optical cavity mode allows cooling
of a collective Bogoliubov mode to its quantum ground state; cooling multiple
Bogoliubov modes (enabled by trapping each particle in multiple tweezers such
that each tweezer scatters photons into a separate cavity mode) removes most
thermal noise, leading to strong entanglement between nanoparticles. We present
numerical simulations for three nanoparticles showing great tuneability of the
generated entanglement with realistic experimental parameters. Our proposal
thus paves the way towards creating complex quantum states of multiple
levitated nanoparticles for advanced quantum sensing protocols and many-body
quantum simulations.

Quantum Physics