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A novel experimental approach for the measure of the Casimir effect at large distances

A novel experimental approach for the measure of the Casimir effect at large distances. Giovanni Carugno INFN Padova, Italy. P. Antonini 1 , G. Bressi 2 , G. Carugno 1 , G. Galeazzi 3,4 , G. Messineo 3 , G. Ruoso 4 1 INFN sez. di Padova, Italy 2 INFN sez. di Pavia, Italy

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A novel experimental approach for the measure of the Casimir effect at large distances

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  1. A novel experimental approach for the measure of the Casimir effect at large distances Giovanni Carugno INFN Padova, Italy. P. Antonini1, G. Bressi2, G. Carugno1, G. Galeazzi3,4, G. Messineo3, G. Ruoso4 1INFN sez. di Padova, Italy 2INFN sez. di Pavia, Italy 3Dipartimento di Fisica, Università di Padova, Italy 4INFN Legnaro, Italy.

  2. Contents • The Casimir effect • Experimental Status Before 1998 OUR APPROACH • Old Setup: Results and Problems • New Experimental Setup • Preliminary Results

  3. The uncertainty principle allows for fluctuations of • fields and non-zero energy in the ground state of • systems with finite and infinite degrees of freedom • QUANTUM VACUUM • Observable effects well tested at the microscopic level • Lamb shift and (g-2)e (low energy) • radiative corrections in electroweak physics (high energy) • Not adequately tested instead at the macroscopic level • These tests are also important due to the expected • contribution to the cosmological constant • (Zeldovich, Weinberg)

  4. Vacuum fluctuations of the electromagnetic field result in radiation pressure on macroscopic bodies They are also expected to be isotropic unless some modes of the vacuum field are inhibited by properly chosen boundary conditions Simpler situation: two indefinite,parallel,conducting, and uncharged plates spaced by a distance d d Only stationary modes inside the cavity are allowed

  5. The energy of this configuration is calculable by summing over all the mode contributions after regularization (high-frequency cut-off) Attractive zero-point radiation pressure Casimir 1948 • Very idealized situation • Indefinite planes finite size • Parallel planes unparallel • flatness roughness • conducting plasma frequency • no background forces residual charges • zero temperature black-body radiation • Difficult experimental task: • one attempt in the original configuration plus • many experiments relaxing some of the constraints above

  6. ... to give the feeling: for two opposing surfaces of area S the force is given by: at a separation d = 1 mm, the force for a 1 cm2 plates is FC ~ 10-7 N

  7. First (and unique) experimental attempt Sparnaay[Physica 24, 751 (1958)] “The obtained results do not contradict Casimir’s theoretical prediction…” 100% errors and also repulsive forces • Important landmark but non conclusive • Some other important results obtained for different but • related configurations: • dielectric surfaces • plane-spherical geometry

  8. Casimir-van der Waals forces between dielectrics Tabor,Winterton, and Israelachvili Nature, 219,1120 (1968), Proc. Roy. Soc. A, 331, 19 (1972) Cylindrical surfaces of mica • Sharp transition from the van der Waals force to its retarded component found at 12 nm • Three relaxed hypothesis: • non parallel configuration • dielectric properties • static charges not under control

  9. Casimir force in a plane-spherical geometry van Blokland and Overbeek, J.Chem.Soc.Faraday Trans. I 74, 2637 (1978) Lens (radius of curvature R) and a flat plate coated with chromium vs. • Versions of this experiment implemented more recently • Lamoreaux [PRL 78, 5 (1997)] • Mohideen and Roy [PRL 81, 45 (1998)] • Chan et al [Science 291, 1941 (2001) ]

  10. CASIMIRO experiment: experimental set-up • Plane parallelgeometry • Silicon plates with a 50 nm chromium deposit • Apparatus inside Scanning Electron Microscope (SEM) • (pressure ~ 10-5 mbar) • Mechanical decoupling between resonator and source • SEM sitting on antivibration table • System of actuators for parallelization • Fiber-optic interferometer transducer • SEM for final cleaning and parallelism monitoring • Mechanical feedthroughs allow correct positioning of • the apparatus in the electron beam • Source approach to the cantilever using a linear PZT

  11. The Cavity Resonant cantilever: 1.9 cm x 1.2 mm x 47 mm m = 11 mg resonant frequency = 138.275 Hz Source (Crossed with cantilever): 1.9 cm x 1.2 mm x 0.5 mm Surfaces roughness ~ 10 nm Useful area S = 1.2 x 1.2 mm2 Picture at SEM: field of view 3 mm x 2.3 mm

  12. Overall view of apparatus with various motion controls

  13. Detailed view of resonator, source and fiber optic end

  14. Measurement procedure • Pre-vacuum steps: • careful cleaning of surfaces • parallelization using optical microscope • Setting up of the gap (in vacuum): • identification and removal of possible dust particles • fine parallelization using ac bridge • Measurement of the working parameters: • calibration using several bias voltages in the gap • rough evaluation of residual offset voltage V0 • in the gap • Measurement of the Casimir force: • counterbias -V0 in the gap to prevent attachment • of the surfaces at small distance • measurement of the residual force vs gap separation

  15. Cleaning procedure • apparatus under laminar air flow • pre-cleaning in air with solvents • microbroom under SEM

  16. Parallelization procedure • in air pre-parallelization with optical microscope • in vacuum first refinement using SEM imaging • a “gondola” for monitoring the third dimension • AC capacitive bridge • final parallelization studying C(d) and • maximization of C for d fixed • parasitic capacitances give an offset of 8.5 pF The two plates touch each other at a C = 22 ± 0.4 pF, corresponding to an average gap separation of ~ 0.4 mm The estimated deviation from parallelism is 20 nm over 1.2 mm distance (angular deviation ~ 3 10-5 rad)

  17. Measurement technique • Monitor the motion of the cantilever to detect the changes induced by the facing surface (source) • heterodyne technique (Onofrio&Carugno, PLA 95) • frequency-shift technique (Bressi et al., CQG 01) • homodyne technique (Long et al., NPB 99) • Detection is made by using a fiber optic interferometer • (D. Rugar et al., Appl. Phys. Lett. 1989) Diode laser: 20 mW @ 780 nm Sensitivity ~ 5 10-11 m Hz-1/2

  18. Frequency shift technique Measurement of the frequency of the first torsional mode of the cantilever by means of an FFT of the interferometer signal cantilever size 2 cm x 5 mm x 100 mm A power-law static force F(d0) = C / d0n exerted between source and cantilever, spaced by d0, gives • n=2 Coulomb force • n=4 Casimir force

  19. Frequency shift technique Coulomb Force: Casimir Force: From the electrostatic calibration it is possible to measure the ratio S / meffto be used for the Casimir force measurement

  20. Electrostatic calibration Several bias voltage V for different gap separations d0: Va=0V Vb=1V Vc=2V Vd=3V d0 10 mm 15 mm 20 mm

  21. Electrostatic calibration Quick determination of the residual voltage in the gap: static measurement of cantilever bending Bending @ 8 mm gap meff = (0.30  0.05) m0 V0 = -(68.6  2.2) mV

  22. The measurement Use the linear PZT to approach the source to the cantilever Study resonance nr vs d • I)Large bias voltages in the gap for precise determination • of working parameters • Cel from which one extract S / meff • rest position of source (VPZT = 0) • correct determination of V0 • These measurement are performed at separation larger than • ~ 3 mm, for smaller gaps the cantilever collapse on the source • II)Counterbias in the gap Vc-V0 ~ 0 V • allows for small distances, down to 0.5 mm, since there • is an almost complete cancellation of electrostatic force

  23. Determination of absolute distance and bias offset A globalfit for external bias voltages Vc = [-205.8, -137.2, + 68.6] mV gives: Dn2offset = (6 ± 1) Hz2 d0 = - (3.30 ± 0.32) 10-7 m Cel = (4.24 ± 0.11) 10-13 Hz2 m3 V-2 V0 = (60.2 ± 1.7) mV

  24. Measurements at small distances Residuals after subtraction of the electrostatic contribution

  25. Summary and outlook • Five years of figthing against several issues: • one for all: dust • Many changes along the way: • Use of STM technique as first trasducer • use of SEM • fiber optic interferometer • different type of resonator materials (tungsten, platinum) • different thicknesses of resonator (47 mm - 200 mm) • several detection technique employed • microbroom • continuous reduction of useful area to avoid dust issue

  26. ....and after all this effort: On June 21, 2001 Kcmeas = (1.22 ± 0.18) 10-27 N m2 Kcth = 1.3 10-27 N m2 Next steps? Corrections: • finite conductivity • surface roughness • finite temperature Better limits on gravitational like forces (?) General reference Bordag, Mohideen, Mostepanenko, Phys. Rep. 353, 1 (2001)

  27. Motivations for new Tests of Casimir force • The Casimir force is not measured at distances larger than 1 mm with accuracy; • Thermal contribution to the Casimir force not measured up to now;

  28. Finite temperature correction For finite temperatures the appropriate state of the field is the thermal state with mean number of photons n(w), for each field mode of frequency w. (Bordag, Mohideen,Mostepanenko, Phys. Rep. 353 (2001), 1.) The influence of thermal field fluctuations on Casimir force are important for distances of the order of:

  29. The detection scheme Eq. of motion: If the force has the form: Then: Modulate position of the source: With the homodyne amplitude modulation technique the force component at the driving frequency is: The Casimir coefficient is obtained comparing The electrostatic calibrations and the force measurement:

  30. New experimental setup Here a LCR meter or a voltage supply can be connected. The voltage is needed to counterbias the built-in voltage. Vibration isolation 2 stage , Lab. Class 10000 (coarse) Interferometer Vibration isolation (fine)

  31. Resonator and source Resonators: • Several resonators tested; • Area = 1 cm2, planarity 100-200 nm; • Mass: between 2 and 7 x 10-2 mg; • Elastic constant: about 15 N/m; • The back side is reflective, as part of the interferometer. Source: • Planarity: 419 nm; • mass: 2.5 mg; • driven by piezoelectric actuator.

  32. Calibrations [1] Varying the absolute distance one gets the relative distance (also with measurements of capacity as function of distance. Modulating the position of the source at 5-7 Hz, Changing either voltage applied or Distance source – resonator. • Were used to find: • the built-in voltage; • the distance source-resonator; • the resonance frequency; • the elastic constant; • the angle between the plates. Varying Vbias one gets the built-in voltage

  33. Calibrations [2] • A control of the built-in voltage at level of 1 mV corresponds to the Casimir force at 5.5 mm, 1.4 x 10-10N; > the built in voltage must be controlled under 1 mV level. This is one of the most challenging issues. Maximum distance at which the Casimir force can be detected: about 6 mm with this setup. If the two plates are parallel within a few 10 mrad, the systematic error is within a few percent. An angle of 10-5 rad results in an error of 10%. Bordag et al., Physics Reports 353 (2001),1.

  34. Results • F = 10-10 N, corresponds to the Casimir force at 6 mm for S = 1 cm2; • Built-in voltage controlled at 1 mV; • Minimum distance 7 mm (not close enough, yet); • dmax = 6 mm, the maximum distance between the plates at which the setup is sensitive to the Casimir force.

  35. Summary • An experimental setup for the measurement of the Casimir force at large distances; • two parallel plates, 1 cm2; • experimental goal: measurement in the range 3 – 6 mm; • minimal distance reached so far: 7 mm; • sensitive to force at the level 10-10 N. DURO LAVORO E UN PO’ DI FORTUNA

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