A Laboratory Test of the Equivalence Principle as Prolog to a Spaceborne Experiment

1. 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 Reasenberg & Phillips Quantum to Cosmos

2. Motivation forTesting 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. Reasenberg & Phillips Quantum to Cosmos

3. POEM Gen-I:Chamber Opticsand Slide Key Technologies: Laser gauge; Capacitance gauge; Motion system. Gen-I, Gen-II, Gen-III, ?? Reasenberg & Phillips Quantum to Cosmos

4. Gen-I TMA Φ = 44.5 mm h = 36.5 mm Reasenberg & Phillips Quantum to Cosmos

5. 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. Reasenberg & Phillips Quantum to Cosmos

6. A B B A 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. Reasenberg & Phillips Quantum to Cosmos

7. 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. Reasenberg & Phillips Quantum to Cosmos

8. 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. Reasenberg & Phillips Quantum to Cosmos

9. 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. Reasenberg & Phillips Quantum to Cosmos

10. 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) Reasenberg & Phillips Quantum to Cosmos

11. ~ fm Stabilized Laser Frequency Shifter (ADM) Phase Modulator L VCO VFS Frequency Counter Interferometer (Hopping) Controller Analog Output TFG Block DiagramClassic Realization Tracking Frequency laser Gauge: loop closed by Pound-Drever-Hall locking. Reasenberg & Phillips Quantum to Cosmos

12. 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. Reasenberg & Phillips Quantum to Cosmos

13. 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) . Reasenberg & Phillips Quantum to Cosmos

14. 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. Reasenberg & Phillips Quantum to Cosmos

15. 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. Reasenberg & Phillips Quantum to Cosmos

16. 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. Reasenberg & Phillips Quantum to Cosmos

17. + + - - ~ 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 Out Estimates of 5 positions (x, y: top and bottom & z) per TMA, at 1 kHz Cal. f1 Moving Static Reasenberg & Phillips Quantum to Cosmos

18. Drive: 0.1 V rms, 10 – 20 kHz Sensitivity: < 8 nm @ 1 s. Electrode gaps: 1 mm (nominal) Reasenberg & Phillips Quantum to Cosmos

19. 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). Reasenberg & Phillips Quantum to Cosmos

20. 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. Reasenberg & Phillips Quantum to Cosmos

21. 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. Reasenberg & Phillips Quantum to Cosmos

22. 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. Reasenberg & Phillips Quantum to Cosmos

23. 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. Reasenberg & Phillips Quantum to Cosmos

24. 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. Reasenberg & Phillips Quantum to Cosmos

25. 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. Reasenberg & Phillips Quantum to Cosmos

26. More Information • www.cfa.harvard.edu/poem • reasenberg@cfa.harvard.edu • 617-495-7108 • jphillips@cfa.harvard.edu • 617-495-7360 Reasenberg & Phillips Quantum to Cosmos

27. 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) Reasenberg & Phillips Quantum to Cosmos

28. 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. Reasenberg & Phillips Quantum to Cosmos

29. Classic TFG Performance Reasenberg & Phillips Quantum to Cosmos

30. 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 Reasenberg & Phillips Quantum to Cosmos

31. 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. Reasenberg & Phillips Quantum to Cosmos

32. 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. Reasenberg & Phillips Quantum to Cosmos