Single-beam dielectric-microsphere trapping with optical heterodyne detection

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 $7.5\times10^{-5} \, (\text{m/s}^2)/\sqrt{\text{Hz}}$.