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Register a new userPrecision and Casimir Force Measurements in Superfluid and Vacuum with Silicon Nitride Membranes
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Authors
Steve Lamoreaux
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The recent discovery that silicon nitride membranes can be used as extremely high Q mechanical resonators makes possible a number of novel experiments, which include improved long range vacuum Casimir force measurements, and measurments of the properties of liquid helium below the lambda point. It is noted that in the thermal correction to the Casimir force, the phase velocity of the excitations does not enter, with the force per unit area between parallel plates depending only on the temperature and distance between the plates. Thus it appears as possible to measure the phonon analog of the finite temperature Casimir force in liquid helium.
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We report on measurements of forces acting between two conducting surfaces in a spherical-plane configuration in the 35 nm-1 micrometer separation range. The measurements are obtained by performing electrostatic calibrations followed by a residual analysis after subtracting the electrostatic-dependent component. We find in all runs optimal fitting of the calibrations for exponents smaller than the one predicted by electrostatics for an ideal sphere-plane geometry. We also find that the external bias potential necessary to minimize the electrostatic contribution depends on the sphere-plane distance. In spite of these anomalies, by implementing a parametrixation-dependent subtraction of the electrostatic contribution we have found evidence for short-distance attractive forces of magnitude comparable to the expected Casimir-Lifshitz force. We finally discuss the relevance of our findings in the more general context of Casimir-Lifshitz force measurements, with particular regard to the critical issues of the electrical and geometrical characterization of the involved surfaces.
We present Casimir force measurements in a sphere-plate configuration that consists of a high quality nanomembrane resonator and a millimeter sized gold coated sphere. The nanomembrane is fabricated from stoichiometric silicon nitride metallized with gold. A Kelvin probe method is used in situ to image the surface potentials to minimize the distance-dependent residual force. Resonance-enhanced frequency-domain measurements of the nanomembrane motion allow for very high resolution measurements of the Casimir force gradient (down to a force gradient sensitivity of 3 uN/m). Using this technique, the Casimir force in the range of 100 nm to 2 um is accurately measured. Experimental data thus obtained indicate that the device system in the measured range is best described with the Drude model.
We present calculations of contact potential surface patch effects that simplify previous treatments. It is shown that, because of the linearity of Laplaces equation, the presence of patch potentials does not affect an electrostatic calibration (of force and/or distance) of a two-plate Casimir measurement apparatus. Using models that include long-range variations in the contact potential across the plate surfaces, a number of experimental observations can be reproduced and explained. For these models, numerical calculations show that if a voltage is applied between the plates which minimizes the force, a residual electrostatic force persists, and that the minimizing potential varies with distance. The residual force can be described by a fit to a simple two-parameter function involving the minimizing potential and its variation with distance. We show the origin of this residual force by use of a simple parallel capacitor model. Finally, the implications of a residual force that varies in a manner different from 1/d on the accuracy of previous Casimir measurements is discussed.
We have measured the optical and mechanical loss of commercial silicon nitride membranes. We find that 50 nm-thick, 1 mm^2 membranes have mechanical Q > 10^6 at 293 K, and Q > 10^7 at 300 mK, well above what has been observed in devices with comparable dimensions. The near-IR optical loss at 293 K is less than 2E-4. This combination of properties make these membranes attractive candidates for studying quantum effects in optomechanical systems.
We calculate the Casimir force between two parallel ideal metal plates when there is an intervening chiral medium present. Making use of methods of quantum statistical mechanics we show how the force can be found in a simple and compact way. The expression for the force is in agreement with that obtained recently by Q.-D. Jiang and F. Wilczek [Phys. Rev. B {bf 99}, 125403 (2019)], in their case with the use of Green function methods.
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