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

04/22/23 Reasenberg & Phillips Quantum to Cosmos 1 of 26

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


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.


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, ??


Gen-I TMA

Φ = 44.5 mm

h = 36.5 mm


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.


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


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.


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.


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.


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)


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


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.


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) .


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.


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.


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.


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


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)


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).


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.


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.


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.


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.


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.


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.


More Information

• www.cfa.harvard.edu/poem

• [email protected]• 617-495-7108

• [email protected]• 617-495-7360

http://www.cfa.harvard.edu/poem

mailto:[email protected]

mailto:[email protected]


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)


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.


Classic TFG Performance


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


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.


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.

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

Documents