  Recent experiments demonstrate highly tunable non-reciprocal coupling between
levitated nanoparticles due to optical binding [Rieser et al., Science 377, 987
(2022)]. In view of recent experiments cooling nanoparticles to the quantum
regime, we here develop the quantum theory of small dielectric objects
interacting via the forces and torques induced by scattered tweezer photons.
The interaction is fundamentally non-hermitian and accompanied by correlated
quantum noise. We present the corresponding Markovian quantum master equation,
show how to reach non-reciprocal and unidirectional coupling, and identify
unique quantum signatures of optical binding. Our work provides the theoretical
tools for exploring and exploiting the rich quantum physics of non-reciprocally
coupled nanoparticle arrays.
