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Progress of a High-Frequency Gravitational Experiment Below 50 Microns Josh Long, Sean Lewis Indiana University Experimental approach and overview Minimum test mass separation Observed signals and current sensitivity (300 K) Recent improvements Projected sensitivity (4 K)

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Experimental Approach Source and Detector OscillatorsShield for Background Suppression ~ 5 cm Planar Geometry Resonant detector with source mass driven on resonance 1 kHz operational frequency - simple, stiff vibration isolation Stiff conducting shield for background suppression Double-rectangular torsional detector: high Q, low thermal noise

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Central Apparatus Scale: 1 cm 3 detector mass shield source mass PZT bimorph transducer amp box tilt stage vibration isolation stacks Figure: Bryan Christie (www.bryanchristie.com) for Scientific American (August 2000) “Taber” vibration isolation stacks: Brass disks hanging from fine wires; make set of soft springs which attenuate at ~10 10 at 1 kHz Installed in 75 liter vacuum bell jar (10 -7 torr) for further suppression of acoustic forces Capacitive probe above large detector rectangle connects to JFET, Lock-in amplifiers READOUT

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Interaction Region: Two Improvements ~1 cm 60 m Au-plated sapphire shield: replace with 10 m stretched Cu membrane (shorter ranges possible) Develop higher-Q (more sensitive) detector mass

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Vibration Isolation and Position Control ~50 cm Inverted micrometer stages for full XYZ positioning Torque rods for micrometer stage control Vacuum system base plate

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Leveling and Minimum Test Mass Gap Reciprocity of source mass piezo drive allows for use as a touch sensor Surface tilt mapped by repeated touch-offs, map determines adjustment Flatness < 6 m peak-to-peak variation observed on opposing surfaces Minimum Separation Measured: Opposing surfaces of test masses brought into contact above shield Test masses touched off on opposite sides of shield at same x,y positions Initial Result: 48 micron minimum gap with metal film shield (previous: 106 m)

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Sensitivity: increase Q and statistics, decrease T Signal Force on detector due to Yukawa interaction with source: Thermal Noise Setting SNR = 1 yields ~ 3 x 10 -15 N rms (for = 1, = 50 m) ~ 3 x 10 -15 N rms (300 K, Q = 5 x10 4, 1 day average) ~ 7 x 10 -17 N rms (4 K, Q = 5 x10 5, 1 day average)

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Current Status and Projected Sensitivity Recent signals: Repaired Vibration isolation system Fall 2008: ~ 5 x detector thermal noise, resonant, but independent of test mass position -- vibration Spring 2009: ~ 2-10 x detector thermal noise, non-resonant – unstable electronic pick-up (ground loop?) Replacing single-ended capacitive transducer amplifier with differential, defining single system ground point IUCF: 1 day integration time, 50 micron gap, 300 K

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Readout – To be replaced with differential design Sensitive to ≈ 100 fm thermal oscillations Interleave on resonance, off resonance runs Typical session: 8hrs with 50% duty cycle

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MaterialQ @ 300 KQ @ 77 KQ @ 4 K Si6 x 10 3 1 x 10 5 8 x 10 5 W (as machined)5 x 10 3 ?? W (1600 K anneal)*2.5 x 10 4 ?? W (2700 K anneal)2.8 x 10 4 ?? Projected Improvement at Cryogenic Temperatures Available Detector Mass Prototypes * Used for published experiment ~ (T/Q) 1/2 improves by few % at 300 K, ~ 100 at 4 K if tungsten behaves as silicon Factor ~ 50 improvement in tungsten Q at 4 K observed with 1 kHz cylindrical oscillators [W. Duffy, J. Appl. Phys. 72 (1992) 5628] Cryogenic measurements of detector mass mechanical properties underway

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Projected Sensitivity – Cryogenic Upper: 1 day integration time, 50 micron gap, 300 K Lower: 1 day integration time, 50 micron gap, 4.2 K, factor 50 Q improvement

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Summary High-frequency experiment test mass separation now below 50 microns Sensitive to forces 1000 times gravitational strength at 10 microns Preliminary results ~ several months 4 K experiment with gravitational sensitivity at 20 microns possible goal for future (2-4 years?) Postdoctoral Position Available http://www.iucf.indiana.edu/jobs/#job94 Apply at: http://www.iucf.indiana.edu/u/jcl/personal/research.htm More information at:

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(Supplemental Slides)

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Stretched membrane shield installed Conducting planes surround both test masses on 5 sides (get rid of copper tape) Surface variations: 5 m peaks 0.7 m rms variations (should be sufficient for ~ 30 m experiment) Shield clamp Tensioning screw Macor standoff minimum gap = 48 microns

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Installation at IUCF Hollow riser for magnetic isolation Central apparatus (previous slide) behind brass mesh shield Diffusion pump P ~ 10 -7 torr LN 2 - trapped diffusion pump mounts below plate Vacuum System

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m D Calibration with Thermal Noise Free thermal oscillations: Damped, driven oscillations on resonance: where k z z T, z D, , T, Q from data, For distributed oscillator sampled at r, mode shape from computer model Measured force: Detector Model:

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Consistency checks Additional runs: Larger test mass gap Source over opposite side of detector (and shield) Reduced overlap F electrostatic ~ r –4, F pressure ~ F magnetic ~ r –2,F vibrational ~ (constant) Shield response No resonant signal observed Expected backgrounds from ambient fields: ES Background = Signal with applied V × (V ambient / V applied ) 4 = 10 -10 V Magnetic Background = Signal with applied B × (B ambient / B applied ) 2 = 10 -7 V All < thermal noise (10 -6 V)

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Systematic Errors (m)

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New Analysis - Search for Lorentz Violation (2002 Data) Source: A. Kostelecký, Scientific American, September 2004, 93. Test for sidereal variation in force signal: Standard Model Extension (SME) Recently expanded to gravitational sector Action: Q. G. Bailey and V. A. Kostelecký, PRD 74 045001 (2006). V. A. Kostelecký, PRD 69 105009 (2004). 20 coefficients controlling L.V. Estimated sensitivities: 10 -15 – 10 -4

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First Look at 2002 Data as Function of Time 22 hrs of data accumulated over 5 days (August 2002) On-resonance (signal) data accumulated in 12 minute sets at 1 Hz every 30 minutes (off-resonance, diagnostic data in between) Plots: Average signal over 3 consecutive sets (best for viewing time distribution) with 1s error, vs mean time of the sets

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Calculation of the Fitting Function William Jensen Fit net signal to [1]: = sidereal angular frequency of Earth = time measured in Sun-centered celestial equatorial frame [1] C i = linear combinations of s (celestial frame) and theoretical LV force in lab frame LV Gravitational potential [2] = coefficients of Lorentz violation in the SME standard lab frame (x L = South, y L = East, z L = vertical) Force misaligned relative to, but 1/r 2 behavior preserved [1] V. A. Kostelecký and M. Mewes, PRD 66 056005 (2002). [2] Q. G. Bailey and V. A. Kostelecký, PRD 74 045001 (2006).

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Lab Frame Coefficient Sensitivity Estimate Lab frame result (“signal”): s 12, s 13 terms: ~ 10 -2 x diagonal terms Very sensitive to numerical integration input parameters (~ 10 6 Monte Carlo trials) Thermal Noise ~ 2 x 10 -14 N rms (300 K, 30 minute average) Approximate SNR = F LV / F T

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excluded allowed s 11 s 22 Lab Frame Coefficient Sensitivity Estimate (diagonal elements only) Approximate allowed/excluded regions shown assuming no evidence of sidereal variation s 11 = s 22 = 0 s 33 = ± 20 F LV = s 11 F 11 + s 22 F 22 – s 33 F 33

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