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

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/r2 to 1/r4, as r is reduced to below R2, the radius of compactification.

• For r > Ri,

If extra dimensions are compactified on an n-torus, = 2n.

• For two large extra dimensions of similar size, = 4, R1 R2 1 mm (Arkani-Hamed, Dimopoulos and Dvali, 1998).

jRrr

GMr /e1)(

Paik-3

Gauss’s Law Test at 1 m

• Principle: (r) = N(r) + Y(r) = – (GM/r) [1 + exp (-r/)]

2 N = – g = 4G = 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

Paik-4

Result of 1-m Test

Moody & Paik, PRL 70, 1195 (1993)

• 3-axis SGG developed at UM

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 cm3) 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 fs, the differential signal appears at 2fs.

This greatly reduces mechanical and magnetic cross talk.

Paik-6

Exploded View of the Experiment

Source Mass

Temperature SensingCoil

Cover Plate

Test Mass

Source Driving Coil

ShieldTensioningScrew

Alignment Coil

S/C Shield

SensingCoil

Paik-7

Experimental Hardware (1)

with Nb shieldInterior

Exterior

Source mass

Test mass

Paik-8

Experimental Hardware (2)

Apparatus integrated with the cryostat

Paik-9

Superconducting Circuits

(b) Temperature sensing circuit(a) DM sensing circuit

(c) Source driving circuit

3

DM

1

iScost

1

2

T

Paik-10

Cryostat and Platform Control

LASER

TURNTABLE

Photodiode

LiquidHelium

Voice CoilActuator

Mumetal(2-Wall)

Rubber Tube

Micrometer

Instrument

Mirror

• 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 103 by stiffening horizontal suspension.

• Source-induced tilt of the platform is reduced by 102 by feeding back the tilt-meter output to the voice-coil actuators.

Paik-11

Expected Signal

• The violation signal (2.6 1014 m s2 rms) appears at almost purely 2fs.

• The Newtonian error due to the finite diameter is negligible.

-80 -40 0 40 80

Source Mass Position (m)

0

1

2

3

4

5

6

7

8

Acc

eler

atio

n (

10-1

4 m s

-2)

Yukawa( = 10-3)

Newtonianx 10

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.

Source Allowed Error 10–16 m s–2

Baseline 25 m 0.02

Source mass    

suspension spring    0.06

absolute thickness 10 m 0.016

density fluctuations 10–4  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 error 14

Paik-13

Direct Vibration Coupling

• The source motion induces a platform displacement xp = 1.8 109 m and tilt p = 3 106 rad.

• The platform displacement causes a linear acceleration 2xp and an angular acceleration through mismatches in horizontal springs.

• The tilt modulates gE and produces a linear acceleration pgE and an angular acceleration 2p.

• The tilt is reduced (by 102) by feedback.

Residual linear acceleration couples through CM rejection error (106), axis misalignment (106), 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 2fs, which couples through the finite baseline (0.20 mm).

Paik-14

Other Errors

Seismic noise:

• The signal frequency is chosen (f = 2fs = 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 106 and 5 105 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 102.

Paik-15

Error Budget

Error Source Error

10–15 m s–2

Metrology 1.4

Random ( =106 s)

intrinsic 8.4

temperature 2.4

seismic 0.7

Source dynamic 17.4

Gravity noise < 0.1

Magnetic coupling < 1

Electrostatic forces < 0.1

Total 19.5

• 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.

Paik-16

Sensitivity Goal

• This experiment is expected to improve by 102 at = 10~100 m.

• The experiment will probe extra dimensions down to R2 15 m.

10-5 10-4 10-32 5 2 5 2 5

RANGE (m)

10-4

10-2

100

102

104

106

CO

UP

LIN

G |

|

Axion

String Theory

UM predicted

Long et al. (2003)

Hoyle et al.

(2004)

Chiaverini

et al. (2003)

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 gE 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.

TESTMASS 1

TESTMASS 2

SOURCEMASS

S/CSHIELD

6.3

cm

Paik-18

Expected Resolution of ISLES

• ISLES will probe extra dimensions down to R2 4 m.

• ISLES will be sensitive enough to detect the axion with the highest allowed strength.

10-5 10-4 10-33 5 2 5 2 5

RANGE (m)

10-6

10-4

10-2

100

102

CO

UP

LIN

G |

|

Axion

Hoyle et al. (2004)

ISLES

String Theory

Ground

Long et al. (2003)