Transcript A Laboratory Test of the Equivalence Principle as Prolog to a Spaceborne Experiment Robert D.

A Laboratory Test of the
Equivalence Principle as Prolog to
a Spaceborne Experiment
Robert D. Reasenberg and James D. Phillips
Smithsonian Astrophysical Observatory
Harvard-Smithsonian Center for Astrophysics
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Motivation for
Testing the Equivalence Principle
can be found at this conference.
• Central to the present accepted theory of gravity.
– Some theorists argue it is the place to look for a
breakdown of general relativity.
• The evidence that leads to dark energy may be
telling us that we need a new gravity theory.
• Attempts to create a quantum theory of gravity show
a failure of the equivalence principle.
• Gravity is the least well tested force.
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POEM Gen-I:
Chamber Optics
and Slide
Photodetector &
Amplifier
Vacuum
Chamber
A
Beamsplitter
(injectorextractor)
Compensator
Key Technologies:
Cart
Laser gauge;
Capacitance gauge;
Track
Test Mass
Assembly
Motion system.
B
Gen-I, Gen-II, Gen-III, ??
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Quad Cell
Modulated Light Entering Chamber
(from beam launcher)
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Gen-I TMA
Φ = 44.5 mm
h = 36.5 mm
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A Vacuum Chamber in Free Fall?
• Advantages
– No mechanisms or motors in vacuum or power shafts
passing through the wall to operate on each toss, at high
speed and at sub-mm accuracy.
• Laser gauge and capacitance gauge components must move with
the TMA.
– Chamber is relatively small.
• Disadvantages
– Massive object (ca. 50 kg) moves at up to 5 m/s, but must
have low vibration level and rapid change of direction.
– A vacuum pump must ride with chamber.
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Second Pair of TMA, Gen-II
• Cancellation of gravity gradient.
• Δg / g = 1.6 10-7 (for Δh = 0.5 m)
– Local sources vary.
A B
• Requires absolute distance.
– dg/dz = 3 10-7 g / m.
– TMA is 30% test mass.
– Science goal (Gen-III):
σ (Δg) / g = 5 × 10-14
– Measurement goal = 1.5 10-14
=> Δh-error < 0.05 μm.
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B A
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Interchanges, Gen-III
• Gen-III goal: σ (Δg) / g = 5 × 10-14
– Requires control of systematic error.
• Gen-III introduces interchanges to cancel systematic
errors.
– Robotic left-right.
• Perhaps every 10 minutes.
– Manual top-bottom.
• Requires braking vacuum => separate runs 1 or 2 days apart.
– Manual interchange of test substance between TMA.
• One interchange per experiment – if needed.
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Principal Systematic Error Sources, I
• Earth’s gravity gradient.
– Absolute distance measurement.
– Top-bottom interchange.
– Second pair of TMA.
• Coriolis force and transverse velocity.
– Capacitance gauge measures velocity.
– Air slide reduces vibration => reduced transverse velocity.
• Gravity gradient due to local mass (parked cars).
– Second pair of TMA.
– Frequent left-right interchanges of TMA.
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Principal Systematic Error Sources, II
• Rotation of TMA around horizontal axis.
– Measured with capacitance gauge and calibrated by
inducing fast rotation with high voltage on capacitance
gauge electrodes.
• Misalignment of measurement beam WRT cavity.
– Measure beam position.
– Measured TMA position with capacitance gauge.
– Measure effect by exaggerated beam tilt.
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Why the Tracking Frequency
Laser Gauge?
No other laser gauge will do.
• When we started working on POINTS, there
was no adequate laser gauge.
– We needed 2 pm in 1 minute to 1 hour.
– We found only one serious contender, the standard
heterodyne gauge.
• For POEM, we need 1 pm in 1 s.
– We would like 0.1 pm in 1 s!
– We also need absolute distance to 0.01 μm
(differential, averaged over an experiment)
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TFG Block Diagram
Classic Realization
Stabilized
Laser
VFS
Frequency Shifter
(ADM)
L
VCO
Frequency
Counter
Analog
Output
Phase
Modulator
fm ~
Interferometer
(Hopping)
Controller
Tracking Frequency laser Gauge: loop closed by Pound-Drever-Hall locking.
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4 TFG Advantages
• Intrinsically free of the cyclic bias characteristic of
heterodyne laser gauges.
• Able to operate in a cavity for increased sensitivity.
• Absolute distance available at little additional cost.
• Able to suppress polarization errors (nm scale or
much smaller with a cat’s eye) and, when used in a
cavity, to suppress alignment errors.
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TFG Precision
• Shot noise limit, HeNe power of 1 μW, 1 s.
– Michelson intrinsic precision: 0.06 pm.
– Similar for heterodyne gauge.
• Current TFG limitation is “technical noise.”
– σ < 10 pm on 0.1 s samples. (12/02) .
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TFG Absolute Distance
• Fringe spacing in optical frequency, Φ = c/(2L).
• Measure Φ, get L with no ambiguity length.
– Measure optical frequency before and after a hop
of K fringes to get ΔF. K>1 increases precision.
– L = K c / (2 ΔF)
• Precision degraded by η = ΔF / F.
• Either use two lasers to read simultaneously or
hop fast to avoid errors due to fluctuating path.
– TFG does hop fast (50 kHz demonstrated), unlike most
narrow-linewidth laser systems.
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How Large Can η Be?
• Using HeNe & an ADM, 500 MHz / 470 THz = 10-6.
• Using a semiconductor laser, the frequency counter
limit yields 2 GHz / 200 THz = 10-5.
– This yields wave count => connect to phase measurement.
• Using a series of markers.
– Assume the DFB laser we are using.
– 60 GHz / 200 THz = 3 10-4.
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Coriolis
• Coriolis acceleration.
– Vertical Coriolis acceleration: ac = 2 ve-w |ω| cos(latitude).
– Earth rotation: |ω| = 7.292 10-5 /s.
– Require ve-w be measured to 33 nm/s [bias < 0.25 nm/s].
• Add capacitance gauge.
– Collaboration with W. Hill (Rowland Institute at Harvard).
– 5 degrees of freedom for each of 4 TMA.
– TMA free floating and minimal drive signal.
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POEM Capacitance Gauges
Collaboration with Winfield Hill, Rowland Institute at Harvard
Vacuum
TMA
+
-
Cal.
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ADC
Correlator
24 bit
100 kHz
s/w in PC
f1, f2, …, f5
Estimates of 5 positions
(x, y: top and bottom & z)
per TMA, at 1 kHz
+
-
~ f
1
Out
Moving
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Static
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TMA, exclusive of feet.
Drive:
0.1 V rms, 10 – 20 kHz
Drive plates, 3 of 5 sets.
Sensitivity:
< 8 nm @ 1 s.
Pick-up ring.
Electrode gaps:
1 mm (nominal)
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Motion System
• Slide (commercial now).
– Follow nominal trajectory.
– Low vibration motion.
• 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).
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Torsion Bar Bouncer
• Torsion bar with lever holds each end of cable.
– Bar working size, 74 x 1 inch.
– 4340 steel, heat treated. (Racing car industry)
– Made possible by moving-chamber approach
• Internal modes of torsion bar (cf. coil springs).
– F > 1 kHz.
– Small moment of inertia (vs Mchamber Rlever2).
• Status: working well – alone and with motor.
– Replaces system with ¼ inch cable running over pulleys.
This had too much friction.
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Present Slide
• Anorad slide including linear motor,
Renishaw gauge, and track rollers
running on small rails.
• TMA must be launched vertically.
• Vibration at micron level (mostly
100 – 200 Hz).
– Transverse velocity  3 mm / s
• Long-standing plan:
Use air-bearing slide.
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Laser Gauge : Progress & Status
• HeNe TFG works in moving system.
• Two-channel frequency counter built.
– Contiguous measurements – no dead time.
– Precise synchronization.
(Jim MacArthur, Harvard-Physics Electronics Shop)
• Developing TFG using semiconductor lasers.
–
–
–
–
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DFB lasers at 1550 nm communications band.
Lasers locked to reference cavity.
Improved electronics being developed by contractor.
On path to space-based application.
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Capacitance Gauge: Progress & Status
• Architecture long established.
• Electrode assemblies in hand – preliminary version.
• All electronic components designed and in various
stages of fabrication at Rowland Institute.
– Packaging to be finalized soon.
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Motion System: Progress & Status
• Torsion-bar bouncer has high mechanical efficiency.
– Motor servo can be (and has been) tuned less
aggressively =>lower noise yet still follows trajectory to
10s of μm.
• Vibration measured in present slide – too high.
• Next step, air-bearing slide to replace wheels and
track (as long planned).
–
–
–
–
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Use granite beam and porous graphite bearings.
Preliminary designs completed – no serious problems.
Found vendors: meet requirements at reasonable price.
Have hardware to make clean dry compressed air.
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POEM Summary
• The SAO Principle of Equivalence Measurement is a Galilean
test of the WEP.
• The goal for the Gen-III version of the experiment is
σ (Δg) / g = 5 × 10-14 for several pairs of substances.
• All Gen-I components are working and being tuned or
modified for better performance; some components, originally
described as part of Gen-II, are started.
– Capacitance gauge (nearly finished).
– Air slide (preliminary design).
• The measurement system is being designed both for the
control of systematic error and, where applicable, to be easily
translated to be space-based.
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More Information
• www.cfa.harvard.edu/poem
• [email protected]
• 617-495-7108
• [email protected]
• 617-495-7360
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Principal Approaches Today
• Torsion balance tests.
– Sensitive to sun's gravity or horizontal component of
earth's gravity. Also, other distant matter.
– Best results: σ (Δg) / g = 4 × 10-13.
• Adelberger et al. 2001. (confusion about factor of 3)
• Galilean tests (dropping).
– Sensitive to full vertical gravity of earth.
– Niebauer et al. (Faller) 1987, σ (Δg) / g = 5 × 10-10.
– Best results: σ (Δg) / g = 10-10 (Dittus 2001, 109 m tower,
σ (Δg) / g = 10-12, projected).
– Works (better) in space: our long-term goal.
– POEM (σ (Δg) / g = 5 × 10-14, projected)
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Heterodyne Gauge
• Cyclic bias due to polarization leakage.
– Multiple averaging reduces bias to 0.15 pm in few min.
[Gursel, SPIE 2200, pp. 27-34, 1994].
– Abandoned by SIM in favor of concentric beams.
– Variant without polarization: 3 pm in 1 sec.
[Gursel, priv. comm. 2002].
• Absolute distance possible.
– Requires either a second laser or a tunable laser.
• Complexity.
• Not able to operate in a cavity.
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Classic TFG Performance
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POEM Smooth Motion Problem
• Coriolis acceleration.
– Require ve-w be measured to 33 nm/s [bias < 0.25 nm/s].
• Capacitance gauge.
– Dynamic range limit: 4 104. (engineering judgment)
• Maximum transverse velocity for TMA.
– (0.25 nm/s) (4 104) = 0.01 mm/s
• Transverse velocity limit.
– Vvertical = 5 m/s => slope error < 2 10-6.
hard but possible
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Straight Rails for Air Slide
• Keeping the slope error < 2 10-6 is well within the
capability of today’s optical fabrication techniques.
– Could do better, even if we needed general non-flat shape.
$(0.3 – 3) 105
• It is just within the capability of the precision granite
industry.
– $(4 - 7) 103
• Active system could compensate for irregular
surface of rails, if needed.
– E.g., PZT at each bearing and (averaged) inertial sensors.
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Motion System, Cont.
• Identified replacement motor controller that will
permit still lower noise level.
– Eliminates 5 μm encoder discretization.
– More flexible and transparent control model.
– Not known to be needed.
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