Tuneable Gaussian Entanglement in Levitated Nanoparticle Arrays

Optically levitated nanoparticles emerged as an interesting platform for probing fundamental physics. Quantum control of their motion (including potential shaping) predisposes them for emulating various physical systems and studying quantum phenomena with massive objects. Extending these capabilities to quantum many-body systems requires feasible strategies to couple and entangle nanoparticles directly or via an optical bus. We propose a variable, deterministic scheme to generate Gaussian entanglement in the motional steady state of levitated nanoparticles using coherent scattering. Coupling multiple nanoparticles to a common cavity mode allows cooling of a collective Bogoliubov mode; cooling multiple Bogoliubov modes (by trapping each nanoparticle in multiple tweezers, each scattering into a separate cavity mode) removes most thermal noise, leading to strong entanglement. Numerical simulations for three nanoparticles show great tuneability of entanglement with realistic experimental parameters. Our proposal paves the way towards complex motional quantum states for advanced quantum sensing protocols and many-body quantum simulations.