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EXPLORATION OF THE QUANTUM VACUUM USING THE CASIMIR FORCE

EXPLORATION OF THE QUANTUM VACUUM USING THE CASIMIR FORCE. UMAR MOHIDEEN Dept. of Physics, Univ. of California-Riverside, CA. From Quantum Electrodynamics:. n k = number of real photons in mode k. k = p /L, 2 p /L,……. Zero point energy. If k cut off = Compton wavelength of electron

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EXPLORATION OF THE QUANTUM VACUUM USING THE CASIMIR FORCE

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  1. EXPLORATION OF THE QUANTUM VACUUM USING THE CASIMIR FORCE UMAR MOHIDEEN Dept. of Physics, Univ. of California-Riverside, CA

  2. From Quantum Electrodynamics: nk= number of real photons in mode k k= p/L, 2p/L,……. Zero point energy If kcut off= Compton wavelength of electron Uo ~ 1015 g/cc ~ Nuclear Density Feynman “Path Integral.. Weinberg ’89 Millonni >> Mass Density of Universe Gravitational Problems!!! Uo cancelled by supersymmetric Zero point Energies???

  3. Casimir wanted a direct check of Experiment (Simple Explanation) U1 U2 U2 < U1 Attractive Casimir Force Subtleties Ignored: 1. Surrounding vacuum 2. is infinite

  4. Uobox Uobox + Plates Casimir Energy= ’ -  Use exponential cutoffs and let size of box go to  Usually referred to as regularization CASIMIR EXPERIMENT (COMPLETE THEORY)

  5. Millennium Evenings Millennium Council Science in the Next Millennium Remarks by Stephen Hawking March 6th 1998 Stephen Hawking explaining the infinities in the Casimir force to then President Clinton: “There is a well defined way in which one can subtract one infinity from the other and get a finite answer. Both the government tax revenue It is a bit like the American budget. and its expenditure, are very large sums, almost infinite. Yet,……………… If one is careful one can subtract one from another and get small surplus atleast until the next election.”

  6. Casimir Force If z= 1 micron , Area= 1 cm2 Force ~ 10-7 Newtons

  7. Perfectly reflecting shell Repulsive Electrostatic Energy = Attractive Casimir Energy a Unfortunately Casimir Force on Spherical Shell is REPULSIVE T. Boyer ‘68 C= - 0.09 Casimirs Model for the Electron Fine Structure Constant!!

  8. SOME EXAMPLES OF SHAPE DEPENDNENCES Repulsive force for spheres Boxes REPEL & ATTRACT c Repel for 0.4 < c/a <3.48 a Torus REPEL & ATTRACT a c Casimir force criticaly depends on Boundary Geometry !!!!!

  9. Zero point energy Generalization Casimir Effect is the modification of vacuum energy density with boundaries U1 U2 U2 < U1 Attractive Casimir Force

  10. IMPORTANCE OF THE CASIMIR EFFECT 1. General to all force fields (Eg. photons in E.M, gluons in StrongForce) 2. Impacts many branches of Physics (Eg. Quantum Field Theory, Cosmology, Condensed Matter Phy. Atomic Physics) 3. Unique Shape dependences (Eg. Attractive or Repulsive force) 4. Macroscopic Quantum Effect (Eg. Correllations at large distances) 5. Places Strongest Constraints on limits to hypothetical forces (Eg. Supersymmetry, Supergravity, Unified Gauge theories)

  11. _ _ + + Interaction Energy = - a = polarizability of atom van der Waals Force [1873] Attraction between neutral atoms Neutral Atoms have Fluctuating Dipole Moment induced by zero point photons London (1930) Casimir and Polder (1948) d Casimir Force is long range van der Waals No way to get Shape Dependences

  12. Casimir Force Measurements (Metallic Surfaces): 1. M.J. Sparnaay, Physica, 24, (1958). 2. P.H.G.M. van Blokland and J.T.G. Overbeek, J. Chem. Soc. Faraday Trans., 74, (1978). 3. S.K. Lamoreaux, Phys. Rev. Lett., 78, (1997). 4. U. Mohideen and A. Roy, Phys. Rev. Lett., 81, (1998). 5. A. Roy, C.Y. Lin, and U. Mohideen, Phys. Rev. D, 60, (1999). 6. B.W. Harris, F. Chen and U. Mohideen, Phys. Rev. A, 62, (2000). 7. H.B. Chan, F. Capasso et. al , Science, 291 (2001), Phys. Rev. Lett., 87 (2001). 8. G. Bressi, G. Carugno, R. Onofrio and G. Russo, Phys. Rev. Lett., 88 (2002). Shape Dependences: 1. A. Roy and U. Mohideen, Phys. Rev. Lett., 82, (1999). Lateral Casimir Force: 1. F. Chen, U. Mohideen, G.L.Klimchitskaya and V.M.Mostepanenko, Phys. Rev. Lett., 88 (2002).

  13. R>>z R z CASIMIR FORCE: z < 1µm Finite Conductivity Correction: Skin depth d=16nm ; wp=plasma frequency (lp=100nm) Lifshitz Formula:

  14. Roughness Correction Amplitude A = 1nm (measured with AFM) <<1% effect Finite Temperature Correction (T=300oK): <<1% effect

  15. EXPERIMENT

  16. INSTRUMENT USED: ATOMIC FORCE MICROSCOPE Room Temperature 10 mTorr vacuum

  17. 200 micron Polystyrene Sphere on AFM Cantilever Gold coating = 85.6±0.6nm

  18. ELECTROSTATIC CALIBRATION OF CANTILEVER V Where =cosh-1(1+z/R) V1= voltage on plate (±0.4 to ±3) V2= Residual voltage on sphere (Systematic) V2=3mV measured from electrostaric force for ±V1

  19. Raw data from one force scan

  20. Raw data from one force scan

  21. Raw data from one force scan Apply to horizontal axis: z=z0+ zpiezo-Fphotodiode signal * m 1. z0 = Surface separation on contact 2. m= rate of change in distance due to cantilever tilt Apply to vertical axis Fcasimir=Fmeasured - Felectrostatic

  22. Plate Voltage=0.256 V Theory z0=31.7nm ELECTROSTATIC MEASUREMENT CONTACT SEPARATION Repeat for other plate voltages Average Contact Separation z0=32.70.8 nm

  23. Measurement of the Tilt Correction Factor ‘m’

  24. Measurement of the Tilt Correction Factor ‘m’

  25. Measurement of the Tilt Correction Factor ‘m’ m=8.9±0.3 nm per unit signal

  26. Average Casimir Force from 30 scans

  27. ERROR BUDGET

  28. MEASURES OF PRECISION We generate the complete function & no fitting parameters Distances between 60nm - 350 nm Corresponding forces 500pN - 3pN Number of Data point N = 2583 Number of Scans = 30 Around 60nm separation 1.Experimental Uncertainty= 19pN/30 =3.5 pN < 1% of the measured force 2. Average Standard Deviation from Theory < 1% of the measured force 3. For 95% confidence level based on random + systematic error get 2% precision

  29. APPLICATIONS OF THE CASIMIR FORCE

  30. ELECTROSTATIC FORCE VS. CASIMIR FORCE FOR PARALLEL PLATES Vapplied=0.25 V

  31. Bell Labs MEMS Actuator Capasso et al Science, 291 (2001) sphere sphere Si substrate Si substrate

  32. SHAPE DEPENDENCE OF CASIMIR FORCE

  33. a SOME EXAMPLES Repulsive force for spheres Boxes REPEL & ATTRACT c Repel for 0.4 < c/a <3.48 a Torus REPEL & ATTRACT Casimir force depends on Boundary Geometry c

  34. CASIMIR FORCE FOR A PERIODICALLY CORRUGATED SURFACE Period= 1.1 mm Amplitude=60nm Radius of Sphere=100mm Perturbative Theory: Start w/ flat plate z---->z+Asin(2px/l)

  35. Experimental Schematic for Casimir Force from Corrugated Plate

  36. PERTURBATIVE THEORY Casimir force between large sphere and grating: Trivial Theory Total Casimir Force= Fc x Conductivity Corrections **Ignores diffraction Effects

  37. Roy and UM PRL, 82 (1999) Comparison of Casimir Force between Flat plate and Sphere w/ Corrugated plate and Sphere Trivial Perturbation Theory Fails Casimir Force depends Non-Trivially on the Boundary Klimchitskaya, Zanette and Caride, (2001) Emig, Hanke and Kardar (2001)

  38. DEMONSTRATION OF THE LATERAL CASIMIR FORCE

  39. Casimir Force From Two Corrugated Surfaces 1. Break right-left symmetry---->lateral forces 2. Change orientation angle--->Torque Golestanian and Kardar PRL (1997) Nussinov et al PRA (2002) 3. Probably the best hope of observing the dynamic Casimir effect in a table top experiment

  40. Force Force

  41. Force Force

  42. Force Force

  43. Force=0 Force=0

  44. Force Force

  45. Force Force

  46. How to make to alligned corrugations with periods of 1 micron ? AFM Cantilever Press Gold Sphere Indium Corrugated plate

  47. EXPERIMENTAL SETUP

  48. MEASURED LATERAL CASIMIR FORCE VS DISPLACEMENT Two surfaces separated by z= 221±2 nm Chen, U.M, G.L.K V.M.M, PRL, 89, 2002 R= radius of the sphere A1,2=Amplitude of corrugation D= corrugation period

  49. MEASURED LATERAL CASIMIR FORCE VS. SURFACE SEPARATION Chen, U.M, G.L.K V.M.M, PRL, 89, 2002 Slope = 4.1 ± 0.2

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