Quantum Theory of Light Interaction with a Dielectric Sphere: Towards 3D Ground-State Cooling

We theoretically analyze the motional quantum dynamics of a levitated dielectric sphere interacting with the quantum electromagnetic field beyond the point-dipole approximation. To this end, we derive a Hamiltonian describing the fundamental coupling between photons and center-of-mass phonons, including Stokes and anti-Stokes processes, and the coupling rates for a dielectric sphere of arbitrary refractive index and size. We then derive the laser recoil heating rates and the information radiation patterns (the angular distribution of the scattered light that carries information about the center-of-mass motion) and show how to evaluate them efficiently in the presence of a focused laser beam, either in a running or a standing-wave configuration. This information is crucial to implement active feedback cooling of optically levitated dielectric spheres beyond the point-dipole approximation. Our results predict several experimentally feasible configurations and parameter regimes where optical detection and active feedback can simultaneously cool to the ground state the three-dimensional center-of-mass motion of dielectric spheres in the micrometer regime. Scaling up the mass of the dielectric particles that can be cooled to the center-of-mass ground state is not only relevant for testing quantum mechanics at large scales but also for current experimental efforts that search for new physics (e.g. dark matter) using optically levitated sensors.