Three-dimensional force-field microscopy with optically levitated microspheres

Abstract

We report on the use of 4.7-µm-diameter, optically levitated, charged microspheres to image the three-dimensional force field produced by charge distributions on an Au-coated, microfabricated Si beam in vacuum. An upward-propagating, single-beam optical trap, combined with an interferometric imaging technique, provides optimal access to the microspheres for microscopy. In this demonstration, the Au-coated surface of the Si beam can be brought as close as ∼10 µm from the center of the microsphere while forces are simultaneously measured along all three orthogonal axes, fully mapping the vector force field over a total volume of ∼10 6 µm 3 . We report a force sensitivity of (2.5 ± 1.0) × 10 −17 N/ √ Hz, in each of the three degrees of freedom, with a linear response to up to ∼10 −13 N. While we discuss the case of mapping static electric fields using charged microspheres, it is expected that the technique can be extended to other force fields, using microspheres with different properties.

Absolute pressure and gas species identification with an optically levitated rotor

“…An optical system, detailed in Refs. [28,31], is used to measure the MS's three translational DOFs and provide stabilizing feedback under high vacuum conditions. Polarization-sensitive optics, described in Refs.…”

“…The torsional drag on the MS can be measured by analyzing the rotational dynamics of the trapped MS. While silica MSs commonly used in optical levitation experiments [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33] can be electrically neutralized [21,23,26,[28][29][30][31][32][33], they have been shown to have residual electric dipole moments [21,23]. Rotation can then be induced by applying torque with an electric field, while being measured optically, as described in Ref.…”

Measurement of the Newtonian constant of gravitation G by precision displacement sensors

“…Be- cause the kinetic energy scales ∼ f 2 , increasing the number of source masses by a factor of n reduces the total kinetic energy to 1/n. An advantage specific to opticallylevitated microspheres is the force measurement is performed three-dimensionally [39]. This allows the use of F y , which potentially helps increasing the precision of the measurement and discriminating background.…”

“…Another method, which is more suitable for opticallylevitated spheres than gravitational wave detectors, is to apply the force through electric field. Because the force sensitivity of the system is ∼ 10 −17 N or less [37,39], the system is sensitive to the change of the amount of charge q by the elementary charge e. This allows exact determination of the charge on the test mass, and all uncertainty of the force F = qE applied by an external electric field E comes from that of electric field. As there exists some DC power supply whose relative stability is in the order of 1 ppm, it can be possible to have force calibration with a precision below 10 −5 .…”

Strong mechanical squeezing for a levitated particle by coherent scattering

“…Introduction.-Cavity optomechanics [1], in which optical fields interact with mechanical elements via radiation pressure, has a tremendous potential for sensing of weak forces [2][3][4] and testing fundamental physical theories [5,6]. Particularly levitated nanoparticles [7][8][9] represent-owing to lack of clamping lossesan interesting platform for metrology [10][11][12], thermodynamics [13,14], and probing the quantum-classical boundary [15,16] or other fundamental theories [17,18]. Experimental techniques for cooling [19][20][21][22][23] and thermal squeezing [24] of their center-of-mass motion, as well as for controlling their rotations [25,26] and libration [27,28], have been firmly established.…”