1. Paik-1 Inverse-Square Law Experiment in Space: Search for Extra Dimensions Ho Jung Paik, Violeta Prieto, M. Vol Moody University of Maryland and Donald M. Strayer Jet Propulsion Laboratory Quantum to Cosmos, Warrenton, Virginia May 21-24, 2006

2. Paik-2 Gravity-Only Extra Dimensions? In string theories, the extra dimensions must be compactified. Gravity may escape into n gravity-only extra dimensions. For n = 2, the law of gravity changes from 1/r 2 to 1/r 4, as r is reduced to below R 2, the radius of compactification. For r > R i, If extra dimensions are compactified on an n-torus,  = 2n. For two large extra dimensions of similar size,  = 4, R 1  R 2  1 mm (Arkani- Hamed, Dimopoulos and Dvali, 1998).

3. Paik-3 Gauss’s Law Test at 1 m Principle:  (r) =  N (r) +  Y (r) = – (GM/r) [1 +  exp (-r/ )]   2  N = –  g = 4  G  = 0, where  = 0,  2  Y = – (GM/r) (  / 2 ) exp (-r/ ) Source: 1500-kg lead (Pb) pendulum Detector: 3-axis gravity gradiometer (null detector) (Paik, 1979) Gauss’s Law Detector

4. Paik-4 Result of 1-m Test Moody & Paik, PRL 70, 1195 (1993) 3-axis SGG developed at UM

5. Paik-5 Null Test at 100  m Principle:  N is constant on either side of an infinite plane slab, independent of position. Source: Ta (  = 16.6 g cm  3 ) disk of large diameter (null source). Detector:1-axis SGG formed by two thin Ta disks, located at 150  m from the source. Frequency discrimination: As the source is driven at f s, the differential signal appears at 2f s.  This greatly reduces mechanical and magnetic cross talk.

6. Paik-6 Exploded View of the Experiment

7. Paik-7 Experimental Hardware (1) with Nb shield Interior Exterior Source mass Test mass

8. Paik-8 Experimental Hardware (2) Apparatus integrated with the cryostat

9. Paik-9 Superconducting Circuits

10. Paik-10 Cryostat and Platform Control Experiment is cooled to <2 K by pumping on liquid helium through a capillary (not shown). Experiment is suspended with the sensitive axes horizontal to eliminate the gravity bias. Source-induced linear acceleration of the platform is reduced by 10 3 by stiffening horizontal suspension. Source-induced tilt of the platform is reduced by 10 2 by feeding back the tilt-meter output to the voice-coil actuators.

11. Paik-11 Expected Signal The violation signal (2.6  10  14 m s  2 rms) appears at almost purely 2f s. The Newtonian error due to the finite diameter is negligible.

12. Paik-12 Metrology Errors Azimuthal density and thickness variations of the source are averaged out by repeating the experiment with the source mass rotated. Test mass density and thickness variations contribute second-order errors. Radial thickness variation of the source is the limiting error source. SourceAllowedError  10 –16 m s –2 Baseline 25  m 0.02 Source mass suspension spring 0.06 absolute thickness 10  m 0.016 density fluctuations10 –4 0.01 thickness variation 10  m 13 radial taper 10  m 0.41 bowing (static) 10  m 0.004 bowing (dynamic) 4.6 Test masses suspension spring 0.06  m 0.80 radial misalignment 50  m < 0.01 Total error14

13. Paik-13 Direct Vibration Coupling The source motion induces a platform displacement x p = 1.8  10  9 m and tilt  p = 3  10  6 rad. The platform displacement causes a linear acceleration  2 x p and an angular acceleration through mismatches in horizontal springs. The tilt modulates g E and produces a linear acceleration  p g E and an angular acceleration  2  p. The tilt is reduced (by 10 2 ) by feedback.  Residual linear acceleration couples through CM rejection error (10  6 ), axis misalignment (10  6 ), and nonlinearity of the detector.  Residual angular acceleration couples through sensitive axes misconcentricity (0.05 mm) and nonlinearity of the detector.  Residual angular velocity results in a centrifugal acceleration at 2f s, which couples through the finite baseline (0.20 mm).

14. Paik-14 Other Errors Seismic noise: The signal frequency is chosen (f = 2f s = 0.1 Hz) as a compromise between the seismic noise and the SQUID noise. The seismic noise is rejected by adjusting persistent currents in the sensing and alignment circuits.  Linear and angular accelerations are rejected to 10  6 and 5  10  5 m, respectively. Magnetic cross talk: The source is driven at f/2.  This frequency discrimination, combined with a superconducting shield, provides over 200-dB isolation. Temperature noise: Measured and compensated by a factor of 10 2.

15. Paik-15 Error Budget Error SourceError  10 –15 m s –2 Metrology1.4 Random (  =10 6 s) intrinsic8.4 temperature2.4 seismic0.7 Source dynamic17.4 Gravity noise< 0.1 Magnetic coupling< 1 Electrostatic forces< 0.1 Total19.5 The dominant error source is the source-driven tilt, which produces linear acceleration that couples through the nonlinearity of the detector. The second largest error source is the intrinsic instrument noise due to the stiff suspension of the test masses. Both of these limitations come from the Earth’s gravity.

16. Paik-16 Sensitivity Goal This experiment is expected to improve  by  10 2 at = 10~100  m. The experiment will probe extra dimensions down to R 2  15  m.

17. Paik-17 ISLES (Inverse-Square Law Experiment in Space) Test masses of nearly ideal geometry can be levitated magnetically.  Softer suspension gives much higher sensitivity. The g E related errors (such as source- induced tilt) disappear. Source mass can be fabricated out of crystalline material, polished optically flat, and then coated with Nb.  Improved metrology error. More than 2 orders of magnitude improvement in sensitivity is expected over the ground experiment.

18. Paik-18 Expected Resolution of ISLES ISLES will probe extra dimensions down to R 2  4  m. ISLES will be sensitive enough to detect the axion with the highest allowed strength.