  Coherent scattering of photons is a novel mechanism of optomechanical
coupling for optically levitated nanoparticles promising strong, versatile
interactions with light and between nanoparticles. We show that it allows
efficient deterministic generation of Gaussian entanglement between two
particles in separate tweezers. A combination of red- and blue-detuned tweezers
brings a mechanical Bogoliubov mode to its ground state. An additional,
dispersively coupled cavity mode can reduce noise in the orthogonal mode,
resulting in strong entanglement as quantified by the logarithmic negativity
and verifiable with the Duan criterion for realistic experimental parameters.
Such an important resource for quantum sensing and quantum simulations is
pivotal for current experiments and presents an important step towards
optomechanics with multiple particles in the quantum regime.
