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

Experimental Approach

• Limitation: Scaling with size of apparatus

• Our approach

• Major components

Signal force = GMm/r2 ~ length4

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 OscillatorDetector OscillatorTransducer and AmplifierElectrostatic ShieldVibration IsolationVacuum System and Translators, later Cryostat

Planar Geometry

Source and Detector Oscillators

Shield for Background Suppression

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 cm3

Sensitivity

FY (t) Gsd Ad2 exp( d(t ) / )[1 exp( ts / )][1 exp( td / )]

• Signal

Force on detector due to Yukawa interaction with source:

• Thermal Noise

• Setting SNR = 1 yields

SF 4kT m

Q

~1

Gsd2 Ad

kTmQ

~ 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)

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 ~ V4 for shield bias > 1V

Observed Signal and Backgrounds

• Background Sources:

• Magnetic Forces - External Fields

- Eddy Currents: F ~ 2B2 or F ~ 2B B

Susceptibility: F~2B2

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)

- B2 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

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

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

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)

“Large” gaps> 10 m(ElectrostaticBackground)

“Small” gaps< P

Casimir Bkgd.(IsoelectronicTechniques)

“Intermediate”

Range P < < 10 m

Shield CasimirBackground?

sampleisotope

1isotope

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

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

Ratio of Yukawa to Casimir ForcesTitle: Graph5 Creator: PSCRIPT.DRV Version 4.0 Preview: This EPS picture was not saved with a preview (TIFF or PICT) included in it Comment: This EPS picture will print to a postscript printer but not to other types of printers

• 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)

Purdue: E. Fischbach, 36th Rencontres de Moriond, 22 January 2001

Dedicated Sub-m Experiment Limits

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