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A New Laboratory Test of the Equivalence Principle

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. Roland E ö tvös 1922, 5 10 -9 Robert Dicke 1964, 1 10 -11

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A New Laboratory Test of the Equivalence Principle

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  1. 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

  2. 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.

  3. 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.

  4. 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

  5. Gen-I TMA Φ = 44.5 mm h = 36.5 mm

  6. Stabilized Laser Frequency Shifter (ADM) Phase Modulator L ~ fm VCO VFS Frequency Counter Int (Hopping) Controller Analog Output TFG, Classic Realization Tracking Frequency laser Gauge: loop closed by Pound-Drever-Hall locking.

  7. Measurement Precision TFG early results: Nov 1991 σ(length) < 2 pm, 1 min < τ < 400 min 10 pm 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 pm 1 s 10,000 s

  8. ~ Tunable Laser Phase Modulator L VFS Reference Laser fm Int Frequency Counter Analog Output Hopping Controller New TFG

  9. + + - - ~ 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

  10. Drive: 0.1 V rms, 10 – 20 kHz Sensitivity: < 8 nm @ 1 s. Electrode gaps: 1 mm (nominal)

  11. 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.

  12. 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 > 40 Hz. * Corporate donation.

  14. A B B A 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.

  15. 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.

  16. 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.

  17. 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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