Search for Lorentz Violation in a Short-Range Gravity Experiment Parameter Spaces and Motivation Experimental Approach and Overview 2002 Data Set and Results Lorentz Violation Analysis Estimated Sensitivity to Spin-Dependent Forces Outlook Simon Kelly, Evan Weisman, Dan Bennett, Trevor Leslie, Andrew Peckat Indiana University, Bloomington Josh Long

r m1m1 m2m2 mBmB Yukawa Interaction  = strength relative to gravity Optimized for Inverse-Square Law Test

r m1m1 m2m2 mBmB Yukawa Interaction  = strength relative to gravity Power Law m1m1 m2m2 m=0 r 0 = experimental scale set limits on  n for n = Optimized for Inverse-Square Law Test

Search for Lorentz Violation Source: A. Kostelecký, Scientific American, September 2004, 93. Test for sidereal variation in force signal:

Search for Lorentz Violation 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 (2006). V. A. Kostelecký, PRD (2004). 20 coefficients controlling L.V. Estimated sensitivities: – 10 -4

Short Range Limits and Predictions Colorado: J. Long et al., Nature (2003) Experimental limits: Theoretical predictions: Limits still allow forces 1 million times stronger than gravity at 5 microns Moduli, dilatons: new particles motivated by string models Vacuum energy: prediction from new field which also keeps cosmological constant small Irvine, Washington = classical torsion pendulum experiments Stanford = AFM-type experiment “Large” extra dimensions Stanford: A. Geraci et al., PRD (2008) Washington: D. Kapner et al., PRL (2007)

Challenge: Scaling with Size of Apparatus m 1,  1 r m 2,  2 r ~ 2r Background Forces: ~ r - 2 (electrostatics), ~ r - 4 (magnetic dipoles, Casimir) r = 100  m  F ≈ N  1 =  2 = 20 g/cm 3, r = 10 cm  F ≈ N

Experimental Approach Source and Detector OscillatorsShield for Background Suppression ~ 5 cm Planar Geometry - null for 1/r 2 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

Central apparatus Scale: 1 cm 3 detector mass shield source mass PZT bimorph transducer amp box tilt stage vibration isolation stacks Figure: Bryan Christie ( for Scientific American (August 2000) Vibration isolation stacks: Brass disks connected by fine wires; make set of soft springs which attenuate at ~10 10 at 1 kHz (reason for using 1 kHz) Readout: capacitive transducer, JFET and lock-in amplifiers Vacuum system: torr

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

Central Apparatus ~50 cm Inverted micrometer stages for full XYZ positioning Torque rods for micrometer stage control Vacuum system base plate

Force Measurement Data – hours on-resonance data collected over 5 days with interleaved diagnostic data On-resonance: Detector thermal motion and amplifier noise Off-resonance: amplifier noise (“zero”) Results: Nature 421, 922–925 (2003 )

Means are consistent with zero force off-resonance on-resonance V on -V off = -0.44±0.82  V Corresponds to F = -1.2 ±2.2 fN force on detector

Current Status and Projected Sensitivity IUCF: 1 day integration time, 50 micron gap, 300 K Lower: 1 day integration time, 50 micron gap, 4.2 K, factor 50 Q improvement Summer: ~ 2-5 x detector thermal noise, resonant, weak vertical gap dependence – “Long-range” capacitive coupling Present: ~ No signal above thermal noise (50 um gap, 2000 s integration) Signals in 2010 data Thinner shield 60  m thick sapphire plate replaced by 10  m stretched copper membrane Compliance ~5x better than needed to suppress electrostatic force Minimum gap reduced from 105  m (2003) to 48  m.

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 (2006). V. A. Kostelecký, PRD (2004). 20 coefficients controlling L.V. Estimated sensitivities: – 10 -4

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 (off-resonance, diagnostic data in between) Plots: Average signal over 3 consecutive sets (best for viewing time distribution) with 1  error, vs mean time of the sets

Calculation of the Fitting Function = coefficients of Lorentz violation in the SME standard lab frame (x L = South, y L = East, z L = vertical) [1] Q. G. Bailey and V. A. Kostelecký, PRD (2006). LV force function [1]:

Calculation of the Fitting Function = 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] Q. G. Bailey and V. A. Kostelecký, PRD (2006). LV force function [1]:

Calculation of the Fitting Function = 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 [2] V. A. Kostelecký and M. Mewes, PRD (2002). [1] Q. G. Bailey and V. A. Kostelecký, PRD (2006). LV force function [1]: Transform to sun-centered frame [2]: ignore boost (  );  = colatitude = 0.87 = sidereal frequency

Calculation of the Fitting Function = 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 [2] V. A. Kostelecký and M. Mewes, PRD (2002). [1] Q. G. Bailey and V. A. Kostelecký, PRD (2006). LV force function [1]: Transform to sun-centered frame [2]: Detector has distributed mass: ignore boost (  );  = colatitude = 0.87 = sidereal frequency

Calculation of the Fitting Function = 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 [2] V. A. Kostelecký and M. Mewes, PRD (2002). [1] Q. G. Bailey and V. A. Kostelecký, PRD (2006). LV force function [1]: Transform to sun-centered frame [2]: Detector has distributed mass: ignore boost (  );  = colatitude = 0.87 mode shape from finite element model = sidereal frequency

Results Compare: Chung, Chu, et al., PRD : S JK < 1 x (atom interferometer sensitive to  g/g ~ 1 x ) D. Bennett, V. Skavysh, J. Long, Proc. 5 th CPT conference C , S  functions of detector geometry, s JK Fit: Force:

r m1m1 m2m2 mBmB monopole-monopole Spin – Dependent Interactions g s1 g s2

r m1m1 m2m2 mBmB monopole-monopole monopole-dipole Spin – Dependent Interactions r eN mBmB g s1 g s2 gsgs i5gpi5gp Example: axion

Spin – Dependent Interactions G. Hammond et al., PRL 98 (2007) Spherical superconducting torsion balance (U. Birmingham) Dy 6 Fe 23 test mass Assume 1% of attained spin densities 100  m thick Magnetic shield Also 100  m thick  metal?

Spin – Dependent Interactions

Summary High-frequency experiment test mass separation now below 50 microns Sensitive to forces 1000 times gravitational strength at 10 microns Preliminary results ~ few weeks if no new backgrounds 4 K experiment with gravitational sensitivity at 20 microns goal for future (2- 4 years?) Spin-mass experiment with same technique: ~ 14 orders of magnitude more sensitivity than current experiments (if backgrounds controllable…) Null geometry limits sensitivity of short-range experiment to Lorentz Violating effects in pure gravity sector of SME to s ~ 10 4 Scale-dependent predictions are difficult

Supplemental slides

Experiment is short-range (~ 50  m), high-frequency (1 kHz) version of Cavendish Experiment source mass detector mass

Experiment is short-range (~ 50  m), high-frequency (1 kHz) version of Cavendish Experiment Pb test masses (  = kg/m 3 ): large = 20 cm diam., small = 5 cm diam source mass detector mass

Experiment is short-range (~ 50  m), high-frequency (1 kHz) version of Cavendish Experiment G = 6.76 x m 3 kg -1 s CODATA: G = 6.673(10) x m 3 kg -1 s -2 Pb test masses (  = kg/m 3 ): large = 20 cm diam., small = 5 cm diam source mass detector mass

Classes of Laboratory-Scale Tests (sample) (Precision) Measurements of G NEWTON Equivalence Principle Tests Tests of the Inverse Square Law Cavendish (1798, few %) Luther, Towler (1982,.1%) Gundlach, Merkowitz (2000,.01%) Eötvös ( ) Eöt-Wash (~1990-present) Dicke (1960s) Long (1976) Newman ( ) Composition-dependence, < few % of F G Precision F G, null tests, large effects >> F G

Limits from 1 mm to 1 light year From: E. Fischbach and C. Talmadge, The Search for Non-Newtonian Gravity (Springer-Verlag, 1999)  mm

Gauge-mediated model: supersymmetry broken at TeV,  Down, Strange, Gluon Moduli with ~  m [S. Dimopoulos and G. Giudice, Phys. Lett. B 379, 105 (1996)] Compactification model: supersymmetry broken at weak scale (~ 1 TeV)  Radius Modulus with  ~ 1/3 [I. Antoniadis, S. Dimopoulos, and G. Dvali, Nuc. Phys. B 516 (1998) 70] Yukawa corrections with  ~ 4 E.G. Floratos and G. K. Leontaris, Phys. Lett. B 465 (1999) 95; A. Kehagias and K. Sfestos, Phys. Lett. B 472 (2000) Moduli Gravitationally-coupled light scalars in string theories. Comprehensive Reviews N. Arkani-Hamed, S. Dimopoulos, G. Dvali, Phys. Lett. B 429 (1998) 263 E. G. Adelberger, B. R. Heckel, A. E. Nelson, Ann. Rev. Nucl. Part. Sci. 53 (2003) 77 Compact Extra Dimensions Solution to Hierarchy Problem: Weakness of gravity due to n “large” extra dimensions in which only gravitons propagate. Size R of extra dimensions related to unification scale M* by: M* ~ 1 TeV  R ~ 1 mm for n = 2 Theoretical Motivations J. Hewett, M. Spiropulu, Ann. Rev. Nucl. Part. Sci. 52 (2002) 397 Exotic Boson Exchange Forces

Cosmological Constant (  ) problem Axions and other light pseudoscalars Effective field theories + observed smallness of L implies new quanta [S. R. Beane, Gen. Rel. Grav. 29 (1997) 945.] New quanta comprised of light gravitational strings [R. Sundrum, JHEP 9907 (1999) 001] [Moody and Wilczek, Phys Rev. D 30 (1984) 130; P. Barbieri, A. Romanino, A. Strumina, Phys. Lett. B 387 (1996) 310; Fischbach and D. Krause, Phys. Rev. Lett. 82 (1999) 4753.] Theoretical Motivations Dilaton Scalar in string models, coupling to nucleons with  up to ~ 10 4 or greater [D. B. Kaplan, M. B. Wise, J. High Energy Phys (2000) 037] Boson Exchange Forces (cont.)

“Large” Extra Dimensions Strong, Weak, EM force confined to 3 dimensions Gravity spreads out into n extra dimensions of size R, appears diluted Gravity unifies with EW force (M* ~ 1 TeV) if n = 2, R ~ 1 mm Infinite dimension compact dimension R n = 3, R ~ 1 nm

55  m minimum gap 10  m BeCu membrane (not shown) Eot-Wash Torsion Pendulum Experiment D. Kapner, E. Adelberger et al., PRL (2007) tungsten fiber detector mass (Mo) source mass disks (Mo, Ta) mirror for optical readout

55  m minimum gap 10  m BeCu membrane (not shown) Eot-Wash Torsion Pendulum Experiment D. Kapner, E. Adelberger et al., PRL (2007) tungsten fiber detector mass (Mo) source mass disks (Mo, Ta) mirror for optical readout Limits: Scenarios with  ≥ 1 excluded at 95% CL for ≥ 56  m ADD Model (2 equal-sized extra dimensions compactified on a torus): R < 56  m  M* ≥ 3.2 TeV Largest extra dimension: R < 44  m Torque and residuals vs. gap

Installation at IU – operational since 2008 Hollow riser for magnetic isolation Central apparatus (previous slide) behind brass mesh shield Diffusion pump P ~ torr LN 2 - trapped diffusion pump mounts below plate Vacuum System

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

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 N rms (for  = 1, = 50  m) ~ 3 x N rms (300 K, Q = 5 x10 4, 1 day average) ~ 7 x N rms (4 K, Q = 5 x10 5, 1 day average)

Background Forces Electrostatic Acoustic Magnetic (contaminants, eddy currents) Vibrations Suppress with stiff conducting shields Suppress with stiff shields, high vacuum Use non-magnetic materials Shielding and insulating (plated) test masses Filter with passive vibration isolation Non-resonant actuation Thermal Suppress with low temperature, high mechanical quality (Q) test mass

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:

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 = V Magnetic Background = Signal with applied B × (B ambient / B applied ) 2 = V All < thermal noise (10 -6 V)

Systematic Errors (m)

New detector prototypes have been fabricated 200  m thick tungsten sheet (high density) Fabricated by wire EDM First generation: Annealed at 1600 K in helium atmosphere New oscillators: Annealed at 2700 K; expect larger crystals, higher Q

New detector surface (200 x magnification) 1000 x showing 90  m crystal (previous maximum = 15  m) 2700 K annealing leads to much larger crystals Higher T anneals had expected material effect, but mechanical properties still unknown…

New detectors and projected sensitivity K Si6 x x 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 x 10 5 (94 K) ? Data of W. Duffy (~ 3 cm diameter, 1 kHz cylindrical torsional oscillators): K W (as machined)2 x x x 10 5 W (2023 K anneal)2 x x x 10 7 J. Appl. Phys. 72 (1992) 5628 Available prototypes * Used for published experiment  ~ (T/Q) 1/2 improves by ~ 50 at 4 K if no further secondary re-crystallization enhancement…

Stretched membrane shield – 1 st prototype Copper- beryllium alloy stretched over frame Ten microns thick Hyperbolic shape for uniform distribution of tension 5  m peaks, 0.7  m rms variations (sufficient for ~ 30  m experiment) resonant signals with weak vertical gap dependence – “leakage”

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

Stretched membrane shield – 2nd prototype Stretch in “longitudinal” direction - Greater area clamped around perimeter Much greater coverage of front and sides no precision metrology; installed immediately

Stanford Microcantilever Experiment – Generation II figures courtesy of David M. Weld Masses modulated on spinning rotor Larger area drive and test masses for increased sensitivity Drive mass mounted in gas bearing

Limits and Projections – 1 µm – 1 m R. Newman, Space Sci. Rev. 148 (2009) 175

P OUT P IN d N/m 2 at 100  m 10 N/m 2 at 100 nm Casimir Effect

Limits to 1 nm and Revised Predictions Predictions: S. Dimopoulos, A. A. Geraci Phys. Rev. D. 68 (2003) Limits: E. Fischbach et al., PRD 64 (2001) ; R. S. Decca et al., Ann. Phys. 318 (2005) 37

“Large” gaps > 10  m (Electrostatic Background) “Small” gaps < P Casimir Bkgd. (Other ideas…) “Intermediate” Range P < < 10  m Shield Casimir Background?

Casimir Background Shielding Effect calculated using finite thickness corrections in: A. Lambrecht and S. Reynaud Eur. Phys. J. D 8 (2000) 309 Compared with Yukawa forces (  = 1, = D) for same geometry

Indiana – Purdue “Isoelectronic” Experiment R. S. Decca, et al., Phys. Rev. Lett. 94 (2005) AuGe Au Oscillator (Si) Al 2 O nm 200 nm ( P = 135 nm) Gap ~ 100 – 500 nm probe motion ~1 mm

Proposed Experiments using BEC Probes S. Dimopoulos, A. A. Geraci Phys. Rev. D. 68 (2003) Conducting probe replaced with dielectric ( 87 Rb BEC with n ~ /cm 3 ;  ~ 1)  Increased sensitivity (reduction in Casimir background) by ~ 10 3 near 1  m JILA BEC Experiment: Casimir-Polder effect measured for 87 Rb BEC suspended 6-12  m above dielectric surfaces  Yukawa constraints derived D. M. Harber, E. A. Cornell et al. cond-mat/ BEC clouds trapped at (anti)nodes: 100  m acquire differential phase shift due to distance dependence of interaction potential with surface shift due to Yukawa potential will change with lateral position of source mass

Limits and Projections – Sub-micron

Indiana – Purdue “Isoelectronic” Experiment R. S. Decca, et al., Phys. Rev. Lett. 94 (2005) AuGe Au Oscillator (Si) Al 2 O nm 200 nm ( P = 135 nm) Gap ~ 100 – 500 nm probe motion ~1 mm Au Ge oscillator Au Average force difference vs gap (each point ~ 40 min avg) Signal: Casimir force difference from “step:” 0.1 nm  F C ~ 15 fN at 200 nm gap