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

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

3 Casimir wanted a direct check of Experiment (Simple Explanation) U1U1U1U1 U2U2 U 2 < U 1 Attractive Casimir Force Subtleties Ignored: 1. Surrounding vacuum 2. is infinite

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

5 Millennium Evenings Millennium Council Stephen Hawking explaining the infinities in the Casimir force to then President Clinton: Science in the Next Millennium Remarks by Stephen Hawking March 6 th 1998 “There is a well defined way in which one can subtract one infinity from the other and get a finite answer. It is a bit like the American budget. Both the government tax revenue 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 cm 2 Force ~ Newtons

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

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

9 Generalization Zero point energy U1U1U1U1 U2U2 U 2 < U 1 Attractive Casimir Force Casimir Effect is the modification of vacuum energy density with boundaries

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. Cosmology, Condensed Matter Phy. Atomic Physics) 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) (Eg. Supersymmetry, Supergravity, Unified Gauge theories)

11 van der Waals Force [1873] Attraction between neutral atoms Neutral Atoms have Fluctuating Dipole Moment induced by zero point photons + _ + _ d London (1930) Casimir and Polder (1948) Interaction Energy = -  = polarizability of atom 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 CASIMIR FORCE: z < 1µm Finite Conductivity Correction : R>>z Skin depth  nm ;  p =plasma frequency  p=100nm) Lifshitz Formula:

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

15 EXPERIMENT

16

17 INSTRUMENT USED: ATOMIC FORCE MICROSCOPE Room Temperature 10 mTorr vacuum

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

19 ELECTROSTATIC CALIBRATION OF CANTILEVER V 1 = voltage on plate (±0.4 to ±3) V 2 = Residual voltage on sphere (Systematic) V 2 =3mV measured from electrostaric force for ±V 1 Where  cosh -1 (1+z/R) V

20 Raw data from one force scan

21 Raw data from one force scan

22 Raw data from one force scan Apply to horizontal axis: z=z 0 + z piezo -F photodiode signal * m 1. z 0 = Surface separation on contact 2. m= rate of change in distance due to cantilever tilt Apply to vertical axis F casimir =F measured - F electrostatic

23 ELECTROSTATIC MEASUREMENT CONTACT SEPARATION Repeat for other plate voltages Average Contact Separation z 0 =32.7  0.8 nm z 0 =31.7nm Theory Plate Voltage=0.256 V

24 Measurement of the Tilt Correction Factor ‘m’

25 Measurement of the Tilt Correction Factor ‘m’

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

27 Average Casimir Force from 30 scans

28 ERROR BUDGET

29 MEASURES OF PRECISION We generate the complete function & no fitting parameters Distances between 60nm 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

30 APPLICATIONS OF THE CASIMIR FORCE

31 ELECTROSTATIC FORCE VS. CASIMIR FORCE FOR PARALLEL PLATES V applied =0.25 V

32 spher e Si substrate spher e Si substrate Bell Labs MEMS Actuator Capasso et al Science, 291 (2001)

33 SHAPE DEPENDENCE OF CASIMIR FORCE

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

35 CASIMIR FORCE FOR A PERIODICALLY CORRUGATED SURFACE Period= 1.1  m Amplitude=60nm Radius of Sphere=100  m Perturbative Theory: Start w/ flat plate z---->z+Asin(2  x/ )

36 Experimental Schematic for Casimir Force from Corrugated Plate

37 PERTURBATIVE THEORY Total Casimir Force= F c x Conductivity Corrections Casimir force between large sphere and grating: Trivial Theory **Ignores diffraction Effects

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

39 DEMONSTRATION OF THE LATERAL CASIMIR FORCE

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

41 Force Force

42 Force Force

43 Force Force

44 Force=0 Force=0

45 Force Force

46 Force Force

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

48 EXPERIMENTAL SETUP

49 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 A 1,2 =Amplitude of corrugation  corrugation period

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

51 DYNAMIC CASIMIR EFFECT Creation of Real Photons from vacuum by Mechanical Motion -Fulling-Davies-Unruh-Hawking Radiation Velocity and angle dependent damping Golestanian and Kardar PRL (1997)  Very hard to do Hawking ’73 Unruh ’76 Fulling & Davies ‘76 Jaekel & Reynaud,93 Barton & Eberlein ‘93

52 CONCLUSIONS 1. Measured the Normal Casimir Force to a precision of 1-2% 2. Demonstrated Simple Shape Dependences 3. Measured the Material Dependences 4. Demonstrated the Lateral Casimir Force Future 1. Improve the precision by ~10 2 -set theoretical constraints on hypothetical forces 2. Measure the Temperature Effect on the Casimir Force -effect of real photons 3. Measure for more complex shape dependences -Optimize the lateral Casimir force -Look for the repulsive Casimir force

53 Acknowledgements: B. Benson A. Roy C.Y. Lin B.W. Harris F. Chen Theory: V.M. Mostepanenko G.L. Klimchitskaya