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A New Laboratory Test of the Equivalence
Principle

• R.D. Reasenberg and J.D. Phillips
• Smithsonian Astrophysical Observatory
• Harvard-Smithsonian Center for Astrophysics

APS Meeting, Jacksonville Florida, 14 April 2007
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Roland Eötvös 1922, 5 10-9 Robert Dicke 1964, 1
10-11 Vladimere Braginsky 1972, 1 10-12 Eric
Adelberger today
Torsion balances are exquisitely sensitive force
detectors. Solar and horizontal gravity down by
10-3. Depends on mechanical behavior of stressed
fiber.
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Alternative Galilean test.

• Faller and Niebauer at JILA s (?g) / g 5
  10-10
• Limited by systematic error associated with
  lateral separation of falling masses in separate
  chambers.

4
POEM Chamber Optics, Gen-I
Key Technologies Laser gauge Capacitance
gauge Motion system.
POEM long-term goal s(?) 5 10-14 requires
second pair of TMA
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Gen-I TMA F 44.5 mm h 36.5 mm
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TFG, Classic Realization
Tracking Frequency laser Gauge loop closed by
Pound-Drever-Hall locking.
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Measurement Precision
TFG early results Nov 1991 s(length) lt 2 pm, 1
min lt t lt 400 min
10 pm
For 1 pm _at_ 1 s, Q 0.8 s, R 0.3, s(?) 1.1
10-11, single toss. s(?g)/g 5 10-14 gt 5.1 104
tosses (22 hours )
1 pm
1 s
10,000 s
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New TFG
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POEM Capacitance Gauges
Collaboration with Winfield Hill, Rowland
Institute at Harvard
Vacuum
TMA
Correlator s/w in PC f1, f2, , f5
ADC 24 bit 100 kHz
Estimates of 5 positions (x, y top and bottom
z) per TMA, at 1 kHz
Cal.
f1
Moving
Static
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Drive 0.1 V rms, 10 20 kHz Sensitivity lt
8 nm _at_ 1 s. Electrode gaps 1 mm (nominal)
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Motion System Requirements

• Follow free-falling TMA.
• Rapid reversal of motion at bottom.
• Minimize shock, vibration energy loss.
• Lateral velocity deviation lt 10 µm/s.
• Simplify Coriolis correction.
• Smooth transition through zero-g to launch TMA.
• Structural resonances high.
• Avoid interaction with motion servo.

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Present Motion System

• Slide (commercial).
• Follow nominal trajectory.
• Torsion bar bouncer.
• Store and return energy.
• Do no harm. (Cause no shock.)
• Horizontal cable hit by moving system.
• Soft onset of force on moving system, from
  geometry.
• Effective mass of cable, 0.05 kg (chamber, 40 kg).

13
New Motion System

• Granite beam as way for air bearings. ordered
• Porous graphite air bearings. stock items
• Aluminum box to hold bearings. parts ordered
• HEIDENHAIN linear position encoder.
• Aerotech motor controller.
• Massive steel base. designed
• Mechanical modes gt 40 Hz.
• Corporate donation.

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Systematic Error, I

• Earths gravity gradient.
• ?g / g 1.6 10-7 (for ?h 0.5 m)
• Goal (TMA) s (?g) / g 1.5 10-14
• gt require s(?h) lt 0.05 µm.
• Second pair of TMA.
• Absolute distance measurement.
• Top-bottom interchange.
• Requires breaking vacuum gt
• separate runs 1 or 2 days apart.

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Systematic Error, II

• Gravity gradient due to local mass (parked cars).
• SUV assumed 2000 kg, on street, 9 m from TMA.
• On street closest to TMA gt 9 10-12 g
  (top-bottom).
• Second pair of TMA.
• SUV, worst location (26 deg) gt 6.2 10-14 g
  (double diff.)
• Inventory of cars during night.
• Model using estimated masses.
• Frequent left-right interchanges of TMA, if
  needed.
• TMA separation (70 mm) ? seating error (ltlt 0.1
  mm).
• Would address all variabilities in local gravity.

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Systematic Error, III

• Coriolis force and transverse velocity.
• Capacitance gauge measures velocity.
• Require ve-w be measured to 33 nm/s bias lt 0.25
  nm/s.
• Air slide reduces vibration gt reduced transverse
  velocity, and thus dynamic range requirement.
• Rotation of TMA around horizontal axis.
• Vertical offset, optical reference point from CM,
  
• ez2 µm 1 mrad/s rotation da210-13 g
• Measure rotation with capacitance gauge and
  calibrate ez by inducing fast rotation via high
  voltage on capacitance gauge electrodes.
• Correction to 0.510-14 g.

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More Information

• www.cfa.harvard.edu/poem
• reasenberg_at_cfa.harvard.edu
• 617-495-7108
• jphillips_at_cfa.harvard.edu
• 617-495-7360