Backaction suppression in levitated optomechanics using reflective boundaries

We show theoretically that the noise due to laser induced backaction acting on a small nanosphere levitated in a standing-wave trap can be considerably reduced by utilising a suitable reflective boundary. We examine the spherical mirror geometry as a case study of this backaction suppression effect, discussing the theoretical and experimental constraints. We study the effects of laser recoil directly, by analysing optical force fluctuations acting on a dipolar particle trapped at the centre of a spherical mirror. We also compute the corresponding measurement imprecision in an interferometric, shot-noise-limited position measurement, using the formalism of Fisher information flow. Our results show that the standing-wave trapping field is necessary for backaction suppression in three dimensions, and they satisfy the Heisenberg limit of detection.