a laboratory test of the equivalence principle as prolog to a spaceborne experiment

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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 forTesting the Equivalence Principle

• 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.

can be found at this conference.

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Photodetector &AmplifierVacuumChamber

Cart

Beamsplitter(injector-extractor)

Modulated Light Entering Chamber(from beam launcher)

Track

Compensator

Quad Cell

A

B

Test MassAssembly

POEM Gen-I:Chamber Optics and Slide

Key Technologies:

Laser gauge;

Capacitance gauge;

Motion system.

Gen-I, Gen-II, Gen-III, ??

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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.

• 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.

A

B

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 DiagramClassic Realization

Tracking Frequency laser Gauge: loop closed by Pound-Drever-Hall locking.

Stabilized Laser

Frequency Shifter (ADM)

Phase Modulator L

VFS

Interferometer(Hopping) Controller

VCO

Frequency Counter

Analog Output

~fm

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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

OutTMA ADC

24 bit100 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

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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)

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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 Rlever

2).

• 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.– 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).– 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

• reasenberg@cfa.harvard.edu• 617-495-7108

• jphillips@cfa.harvard.edu• 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.