Quantum Fluctuation Forces between Optically Trapped Nanospheres*

We present an analysis of the quantum fluctuation forces between two dielectric nanospheres trapped via optical tweezers. We develop a full quantum description of the radiative forces between the two nanospheres using an open quantum system master equation approach. Considering their mutual interaction mediated via the classical trapping field and the quantum fluctuations of the electromagnetic field, an analysis of the three separate contributions to the total potential – the Casimir-Polder potential, the classical trap potential and the optical binding potential – is presented. The total potential is subsequently studied as a function of various parameters, such as the tweezer field intensity and phase, demonstrating that, for appropriate sets of parameters, there exists a mutual bound state of the two nanospheres which can be ~200 K deep. Furthermore, we utilize the master equation approach to study the decoherence and dissipation of the quantized centre of mass of the nanospheres, focusing in particular on the interplay between fluctuation fields and the external drive. Our results are pertinent to ongoing experiments with trapped nanospheres in the macroscopic quantum regime and for exploring quantum thermodynamic phenomena.