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The Casimir effect Physics 250 Spring 2006 Dr Budker Eric Corsini

The Casimir effect Physics 250 Spring 2006 Dr Budker Eric Corsini. Casimir Patron Saint of Poland and Lithuania (March 4 th ). Hendrik Casimir (1909-2000) Dutch theoretical physicist Predicted the “force from nowhere” in 1948. Abstract The Casimir Force.

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The Casimir effect Physics 250 Spring 2006 Dr Budker Eric Corsini

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  1. The Casimir effect Physics 250 Spring 2006Dr BudkerEric Corsini Casimir Patron Saint of Poland and Lithuania (March 4th) Hendrik Casimir (1909-2000) Dutch theoretical physicist Predicted the “force from nowhere” in 1948

  2. AbstractThe Casimir Force • The Casimir Force was first predicted by Dutch theoretical physicist Hendrik Casimir and was first effectively measured by Steve Lamoreaux in 1995. • The boundary conditions imposed on the electromagnetic fields by metallic surfaces lead to a spatial redistribution of the zero-point energy mode density with respect to free space, creating a spatial gradient of the zero-point energy density and hence a net force between the metals. That force is the most significant force between neutral objects for distances <100nm • Because of that dependence on boundary conditions, the Casimir Force spatial dependence and sign can be controlled by tailoring the shape of the interacting surfaces. • In this presentation I briefly review the formalism pertaining to the zero point energy and summarize the recent experiment By Bell and Lucent labs, investigating the effect of the Casimir Force on a dynamic system.

  3. Origin of the Casimir forceThe short answer • The vacuum cannot have absolute zero energy  that would violate Heisenberg uncertainty principle.

  4. The long answer  “green” book approach • We show a 1-1 relationship: SHO ↔ E&M Field • Maxwell + Coulomb gauge (.A=0) (no local current/charge) • General sol to wave equation  • Then

  5. Consider the SHO • Note: • Then there is a 1-1 relation • If we set αoto be such that • Then, per mode ω we have:

  6. We can then apply the SHO mechanics to the E&M field • Eigenstates |n> • Eigenvalues En = ħω(n+1/2) • In particular Eo= ħω/2 ≠ 0 for mode ω • However

  7. But we are only concerned in the difference in energy density • Between two conducting parallel plates only virtual photons whose wavelengths fit a whole number of times between the plates contribute to the vacuum energy  there is a force drawing the plates together.

  8. Notes • Bosons  attractive Casimir force • Fermions  repulsive Casimir force • With supersymmetry there is a fermion for each Boson  no Casimir effect. • Hence if supersymmetry exists it must be a broken symmetry

  9. Casimir ForceFrom theory to experiment • Predicted by Dutch physicist Hendrick Casimir in 1948. • First attempt to measure the Casimir Force: 1958 by M.J.Sparnaay - Used the attraction between a pair of parallel plates. - But irreducible systematic errors  measurements had a 100% uncertainty, (but it fit the expectations) • Sparnaay gave three guidelines; - The plates should be free of any dust or debris, with as little surface roughness as possible - Static electrical charges should be removed (electrostatic force can easily swamp the weak Casimir attraction). - The plates should not have different surface potentials - Ref: "Measurements of Attractive Forces Between Flat Plates“ (Sparnaay, 1958) Physica, 24 751-764 • 2nd attempt and first successful results: 1996 by Steven Lamoreaux: - In agreement with theory to within uncertainty of 5%. • Several other successful experiments since.

  10. Steven Lamoreaux’ experimental set up • Steve Lamoreaux (University of Washington – Seattle) • Measured the Casimir force between a 4 cm diameter spherical lens and an optical quartz plate about 2.5 cm across, both coated with copper and gold. The lens and plate were connected to a torsion pendulum.

  11. There are only a few dozen published experimental measurements of the Casimir force • But there are more than 1000 theoretical papers • And citations of Casimir’s 1948 paper are growing exponentially.

  12. Effects of edgesshape of decay function is strongly dependent on size and separation of surfacesref:http://images.google.com/imgres?imgurl=http://www.sr.bham.ac.uk/yr4pasr/project/casimir/currentthumb.jpg&imgrefurl=http://www.sr.bham.ac.uk/yr4pasr/project/casimir/&h=275&w=275&sz=41&tbnid=Buy2QDUNZEvi6M:&tbnh=109&tbnw=109&hl=en&start=20&prev=/images%3Fq%3Dcasimir%2Beffect%26svnum%3D10%26hl%3Den%26lr%3D%26sa%3DG Dist > 25µm: dome shape The Casimir force occurs when virtual photons are restricted. The force is reduced where virtual photons are diffracted into the gap between the plates Unshaded areas correspond to higher Casimir forces Casimir force is decreased at the edges of the plates

  13. The Casimir force: FCon Microelectromechanical systems (MEMS)(PRL: H. B. Chan et al – Bell Lab & Lucent Tech –Published Oct 2001) • Prior experiments have focused on static FC and adhesion FC • This experiment investigates the dynamic effect of FC: • A Hooke’s law spring provides the restoring force • FC between a movable plate and a fixed sphere provides the anharmonic force • For z>dCRITICAL system is bistable • PE has a local + global minima • FC makes the shape of local min anharmonic • Note: chosing a sphere as one of the surfaces avoids alignment problems Mock set up K= 0.019 Nm-1 Sphere radius = 100μm dEQUILIBRIUM = 40nm

  14. The actual set up • Oscillator: 3.5-mm-thick, 500-mm2, gold plated (on top), polysilicon plate • Room temp – 1 milli Torr • A driving voltage VAC excites the torsional mode of oscillation (VDC1: bias) • Vdc: bias to one of the two electrodes under the plate to linearize the voltage dependence of the driving torque • VDC2: detection electrode • Note: amplitude increases with VAC = 35.4μV to 72.5 μV Torsional Spring constant: k=2.1 10-8 Nrad-1 Fund res. Freq. = 2753.47 Hz I = 7.1 10-17 kgm2 System behaves linearly w/o sphere

  15. Due to FC z (equil dist sph-plate w/o FC) Due to Electrostatic force Add a gold plated polystyrene sphere radius = 200μm • Equation of motion  Freq shift ~ FC gradient (FC’)

  16. FC anharmonic behavior • I: Sphere far away  normal resonnance • Sphere is moved closer to plate I  IV • Res. freq shifts as per model  • At close distance  hysteresis occurs ie: amplitude A has up to 3 roots:

  17. Depends on history • Or we can keep a constant excitation freq (2748Hz), vary sphere-plate distance, and measure amplitude. Freq < resonant freq Freq > resonant freq

  18. Is repulsive Casimir force physical ? • Plate-plate: attractive • Sphere-plate: attractive • Concave surface – concave surface: can be repulsive or attractive depending on separation  pendulum • Plate-plate with specific dielectric properties can be repulsive  nanotech applications

  19. References • Nonlinear Micromechanical Casimir Oscillator [PRL: published 31 October 2001 H. B. Chan,* V. A. Aksyuk, R. N. Kleiman, D. J. Bishop, and Federico Capasso† Bell Laboratories, Lucent Technologies, Murray Hill, New Jersey 07974 • Physics World article (Sept 2002) – Author:Astrid Lambrecht • REPORTS ON PROGRESS IN PHYSICS Rep. Prog. Phys. 68 (2005) 201–236 Steven Lamoreaux

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