Three-dimensional force-field microscopy with optically levitated microspheres

Abstract

We report on the use of 4.7-$\mu$m-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 $\sim 10\mu$m 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 $\sim 10^6\mu$m${}^3$. We report a force sensitivity of $(2.5\pm 1.0)\times 10^{-17}N/\sqrt{\mathrm{Hz}}$, in each of the three degrees of freedom, with a linear response to up to $\sim 10^{-13}\mathrm{N}$. 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.

arXiv comment7 pages, 7 figures

References in corpus (25)

• Sub-Kelvin Parametric Feedback Cooling of a Laser-Trapped Nanoparticle
• Cavity optomechanics using an optically levitated nanosphere
• Heating of trapped ions from the quantum ground state
• Millikelvin cooling of an optically trapped microsphere in vacuum
• Optical microrheology using rotating laser-trapped particles
• Zeptonewton force sensing with nanospheres in an optical lattice
• Direct Measurement of Photon Recoil from a Levitated Nanoparticle
• Cavity cooling a single charged nanoparticle
• Short-range force detection using optically-cooled levitated microspheres
• New Experimental Constraints on Non-Newtonian Forces below 100 microns
• Torsional optomechanics of a levitated nonspherical nanoparticle
• Search for Millicharged Particles Using Optically Levitated Microspheres
• Attonewton force detection using microspheres in a dual-beam optical trap in high vacuum
• Optomechanics of Levitated Dielectric Particles
• Nonlinear dynamics and millikelvin cavity-cooling of levitated nanoparticles
• Cavity cooling of free silicon nanoparticles in high-vacuum
• Optical levitation of 10 nanogram spheres with nano-$g$ acceleration sensitivity
• Search for Screened Interactions Associated with Dark Energy Below the 100 $\mu \mathrm{m}$ Length Scale
• Force sensing with an optically levitated charged nanoparticle
• Parametric Feedback Cooling of Levitated Optomechanics in a Parabolic Mirror Trap
• Optical Rotation of Levitated Spheres in High Vacuum
• Probing the Casimir force with optical tweezers
• The effect of patch potentials in Casimir force measurements determined by heterodyne Kelvin probe force microscopy
• Single-beam dielectric-microsphere trapping with optical heterodyne detection
• Direct measurement of short-range forces with a levitated nanoparticle

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