sao 1 of 17 a new laboratory test of the equivalence principle r.d. reasenberg and j.d. phillips...
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SAO 1 of 17
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
SAO 2 of 17
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.
SAO 3 of 17
Alternative: Galilean test.• Faller and Niebauer at JILA: σ (Δg) / g = 5 × 10-10
• Limited by systematic error associated with lateral separation of falling masses in separate chambers.
SAO 4 of 17
POEM Chamber Optics, Gen-I
Key Technologies:
Laser gauge;
Capacitance gauge;
Motion system.
POEM long-term goal:
σ(η) = 5 10-14
requires second pair of TMA
SAO 5 of 17
Gen-I TMA
Φ = 44.5 mm
h = 36.5 mm
SAO 6 of 17
TFG, Classic Realization
Stabilized Laser
Frequency Shifter (ADM)
Phase Modulator
L
VFS
Int
(Hopping) Controller
VCO
Frequency Counter
Analog Output
~fm
Tracking Frequency laser Gauge: loop closed by Pound-Drever-Hall locking.
SAO 7 of 17
Measurement Precision
TFG early results: Nov 1991
σ(length) < 2 pm, 1 min < τ < 400 min0 0 0
2
( )( )acc T K
Q T
12 5 27K
( ) /( 2)acc R g
For 1 pm @ 1 s, Q = 0.8 s, R = 0.3,
σ(η) = 1.1 10-11, single toss.
σ(Δg)/g = 5 10-14 => 5.1 104 tosses
(22 hours ) 1 s 10,000 s
1 pm
10 pm
SAO 8 of 17
New TFG
Tunable Laser
Phase Modulator LVFS
Int
Hopping Controller
~
Frequency Counter
Analog Output
Reference Laser
fm
SAO 9 of 17
POEM Capacitance Gauges
TMA ADC24 bit
100 kHz
Cal.
Correlators/w in PCf1, f2, …, f5
+-
+-
~ f1
Vacuum
Moving Static
Estimates of 5 positions (x, y: top and bottom & z) per TMA, at 1 kHz
Collaboration with Winfield Hill, Rowland Institute at Harvard
SAO 10 of 17
TMA, exclusive of feet.
Drive plates, 3 of 5 sets.
Pick-up ring.
Drive: 0.1 V rms, 10 – 20 kHz
Sensitivity: < 8 nm @ 1 s.
Electrode gaps: 1 mm (nominal)
SAO 11 of 17
Motion System Requirements
• Follow free-falling TMA.• Rapid reversal of motion at bottom.
– Minimize shock, vibration & energy loss.
• Lateral velocity deviation < 10 μm/s.– Simplify Coriolis correction.
• Smooth transition through zero-g to launch TMA.• Structural resonances high.
– Avoid interaction with motion servo.
SAO 12 of 17
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).
SAO 13 of 17
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 > 40 Hz.
* Corporate donation.
SAO 14 of 17
Systematic Error, I
• Earth’s gravity gradient.– Δg / g = 1.6 10-7 (for Δh = 0.5 m)
• Goal (TMA): σ (Δg) / g = 1.5 × 10-14
• => require σ(Δh) < 0.05 μm.
– Second pair of TMA. – Absolute distance measurement.– Top-bottom interchange.
• Requires breaking vacuum =>
separate runs 1 or 2 days apart.
A
B
B
A
SAO 15 of 17
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 => 9 10-12 g (top-bottom).
– Second pair of TMA.• SUV, worst location (26 deg) => 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 (<< 0.1 mm).
Would address all variabilities in local gravity.
SAO 16 of 17
Systematic Error, III
• Coriolis force and transverse velocity.– Capacitance gauge measures velocity.
• Require ve-w be measured to 33 nm/s [bias < 0.25 nm/s].
• Air slide reduces vibration => reduced transverse velocity, and thus dynamic range requirement.
• Rotation of TMA around horizontal axis.– Vertical offset, optical reference point from CM,
εz=2 μm; 1 mrad/s rotation: δa=2×10-13 g
– Measure rotation with capacitance gauge and calibrate εz by inducing fast rotation via high voltage on capacitance gauge electrodes.
– Correction to 0.5×10-14 g.
SAO 17 of 17
More Information
• www.cfa.harvard.edu/poem
• 617-495-7108
• 617-495-7360