Title: Single-beam dielectric-microsphere trapping with optical heterodyne detection,
Abstract: A technique to levitate and measure the three-dimensional position of
micrometer-sized dielectric spheres with heterodyne detection is presented. The
two radial degrees of freedom are measured by interfering light transmitted
through the microsphere with a reference wavefront, while the axial degree of
freedom is measured from the phase of the light reflected from the surface of
the microsphere. This method pairs the simplicity and accessibility of single
beam optical traps to a measurement of displacement that is intrinsically
calibrated by the wavelength of the trapping light and has exceptional immunity
to stray light. A theoretical shot noise limit of
$1.3\times10^{-13}\,\text{m}/\sqrt{\text{Hz}}$ for the radial degrees of
freedom, and $3.0\times10^{-15} \, \text{m}/\sqrt{\text{Hz}}$ for the axial
degree of freedom can be obtained in the system described. The measured
acceleration noise in the radial direction is $7.5\times10^{-5} \,
(\text{m/s}^2)/\sqrt{\text{Hz}}$.