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 × 10 −13 m/ √ Hz for the radial degrees of freedom, and 3.0 × 10 −15 m/ √ 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 × 10 −5 (m/s 2 )/ √ Hz.

Precision Mass and Density Measurement of Individual Optically Levitated Microspheres

“…The case of zero optical power cannot be directly measured, as there is a minimum power necessary both to constrain the MS to the optical axis, and to generate sufficient back-reflected light to measure the axial position via the methods described in Refs. [20,29]. The technique described is applicable only to single-beam traps [29], as its extension to systems with more than one beam requires care to account for the contributions of auxiliary beams to the total optical levitation force.…”

“…The optical trap used here is described in Refs. [20,29]. Silica MSs obtained from the Stöber process [30,31] with diameter of approximately 4.7-µm are loaded into the trap by ejection from a vibrating glass slide placed above it.…”

Three-dimensional force-field microscopy with optically levitated microspheres

“…The optical trap used here is almost identical to that described in Ref. [24]. The optical system is shown schematically in Fig.…”

“…The optical readout system used in the feedback for the three DOFs closely follows Ref. [24] with significant improvements made to the electronics. The single-beam configuration of the ap- paratus is ideal for the application described here, as it allows optimal access to the MS from all directions in the horizontal plane.…”

“…The single-beam configuration of the ap- paratus is ideal for the application described here, as it allows optimal access to the MS from all directions in the horizontal plane. The current noise level on the motion of the MSs is dominated by effects [24] other than the residual vacuum, which is limited at 10 −6 mbar by the out-gassing of a number of translation stages.…”