1. Gravitational Experiment Below 1 Millimeter and Search for Compact Extra Dimensions Josh Long, Allison Churnside, John C. Price Department of Physics, University of Colorado, Boulder Introduction Experimental Approach and Overview Force Measurements and Backgrounds Current Sensitivity Outlook Support: NSF

2. Experimental Approach Limitation: Scaling with size of apparatus Our approach Major components Signal force = GMm/r 2 ~ length 4 Background Forces ~ gap -2 (electrostatics), gap -4 (Casimir, magnetic dipoles) Planar geometry for largest possible signal Use high frequency (1 kHz) for easy vibration isolation Final version is cryogenic, but no superconductivity, superfluidity, etc. Source Mass Oscillator Detector Oscillator Transducer and Amplifier Electrostatic Shield Vibration Isolation Vacuum System and Translators, later Cryostat

3. Planar Geometry Source and Detector Oscillators Shield for Background Suppression

4. Overview 3 independent vibration isolation stacks X-Y-Z translation of source and detector stacks 3 tilt stages Electrostatic shields around source mass stack and transducer Scale: 1 cm 3

5. Sensitivity Signal Force on detector due to Yukawa interaction with source: Thermal Noise Setting SNR = 1 yields ~ 2 x 10 -14 N rms (for  = 1, = 100  m) ~ 4 x 10 -14 N rms (300 K, 1000 s average) ~ 7 x 10 -16 N rms (4 K, 1000 s average)

6. Observed Signal and Backgrounds Room temperature version operational since 4/00 10/00 upgrade: Observe resonant signal ~ 10 -13 N (10x T-noise for  = 1/2 hr) Vibrations Residual Gas - Filter with multi-stage passive isolation stacks - Observed signal only present when test masses overlap - Suppress with stiff shield - Signal is pressure independent from 5x10 -8 torr to 1x10 -6 torr - F ~ P above 1x10 -6 (unshielded) Weak gap dependence over large range (120  m - 2.5 mm) Background Sources: Electrostatic forces from surface potentials - Suppress with stiff shield (conducting, grounded) - Signal reducible by factor of 3 with applied biases of 0.1 - 1.0 V on shield or detector (net potential between test masses not known) - F ~ V 4 for shield bias > 1V

7. Observed Signal and Backgrounds Background Sources: Magnetic Forces - External Fields - Eddy Currents: F ~  2 B 2 or F ~  2 B  B Susceptibility: F~  2 B 2 These effects are 10 -13 -10 -12 N for B ~ 1 G,  B ~ 1 G/m - Avoid with non-magnetic materials, reduce with external coils - Signal reducible by factor of 4 with applied B (|B| near test masses ~ 5 G, large uncertainty) - B 2 behavior observed for larger (10-30 G) applied field Magnetic Forces - Contamination - Single, micron - sized Fe particles on test masses produce F ~ 10 -14 N - Expect much stronger gap dependence - In-situ imaging if necessary

8. Sensitivity as of April 2001 Based on signal ~ 10x T-noise for  = 1/2 hr, no applied fields or potentials

9. Projected Limits from 1  m to 1 cm Padova: G. Ruoso, 9th Marcel Grossmann Conference (Rome, 2-8 July 2000) Stanford: A. Kapitulnik, Beyond 4D Conference (ITCP Trieste, 2-6 July 2000); http://www.ictp.trieste.it/~highener/beyond4d.html

10. Existing Limits to 1 nm Lamoreaux analysis: M. Bordag et al., quant-ph/0106045 (sub. Phys Rep.) Derjaguin, Riverside, Ederth: Casimir Force measurements analyzed in: E. Fischbach et al., hep-ph/0106331 (sub. Phys Rev. D)

11. “Large” gaps  > 10  m (Electrostatic Background) “Small” gaps  < P Casimir Bkgd. (Isoelectronic Techniques) “Intermediate ” Range P < < 10  m Shield Casimir Background?

12. sample isotope 1 isotope 2  s (drive)  p (response) probe cantilever Nanometer Range Experiment: Iso-electronic Effect E. Fischbach et al., hep-ph/0106331 (sub. Phys. Rev. D) Casimir effect determined by electronic properties New effects (and mass-coupled): electronic + nuclear Sample: alternating strips of different isotopes of same element (or Au, Cu) Search for small changes in cantilever amplitude as sample is scanned

13. Casimir Background Shielding Calculate this effect using: A. Lambrecht and S. Reynaud Eur. Phys. J. D 8 (2000) 309 Compared with Yukawa forces (  = 1, = D) for same geometry

14. Ratio of Yukawa to Casimir Forces Shielding turns on at D~ P = 1.4 x 10 -7 m (Gold probe and sample) Yukawa signal > Casimir background at D =  ~ 3  m Joshua C. Long, Allison B. Churnside, John C. Price, hep-ph/0009062, to appear in the Proceedings of the Ninth Marcel Grossmann Conference (Rome, 2-8 July 2000)

15. Purdue: E. Fischbach, 36th Rencontres de Moriond, 22 January 2001 Dedicated Sub-  m Experiment Limits

16. Summary and Outlook New experiments have explored 4 new square decades in (  ) parameter space in past year, more results imminent Much new theoretical interest Our 300 K experiment now at sensitivity of current best limit at 100 microns; ultimate sensitivity (2-3 more decades) in reach 4K experiment will reach gravitational strength down to 50  m if backgrounds can be suppressed Scanning Force Microscopy techniques: ~ 10 additional decades below 1  m may be possible in next few years