Short-range gravity test with a micro-cantilever Andy Geraci (NIST  U. Nevada, Reno) Aharon Kapitulnik John Chiaverini (MIT Lincoln Lab) Sylvia Smullin (Etalim, Inc.) David Weld (MIT) Rencontres de Moriond, La Thuile, 2011

l t w F A  00 Amplitude: Human hair 3300 Å-thick silicon cantilevers Measurement with Microcantilevers l w Actual Cantilever w= 50  m d = 0.3  m l = 250  m K ~ N/m Q ~ 80,000 f ~ 300 Hz

Fundamental Limit:Thermal Noise k ~ N/m Q ~ 80,000 f 0 ~ 300 Hz T ~ 10 K b ~ s -1  F min ~ 1 aN Minimum measurable force:

Test mass Cantilever Silicon nitride shield (cutaway) Fiber Drive mass Cantilever resonance (f 0 ): ~300 Hz Drive frequency(f 0 /3): ~100Hz Experimental Setup Piezo Actuator (±130 µm at f0/3 or f0/4) motion With conducting surfaces Min. Drive mass/Test mass separation: ~20  m (edge-edge distance)

Magnetic version Magnetic film on test mass Au wires in bulk silicon Current Spatially alternating magnetic field created above drive mass, B ~ 1mG/mA B B motion 1 mm

Experimental Probe

Exchange gas space LHe space Vacuum can Piezoelectric Actuator drive Computer storage Analog to Digital converter Signal from interferometer time voltage Actuator Cantilever Analysis Overall Experimental Setup

Spatial Lock-in Analysis Measure force as a function of equilibrium-position of oscillation Magnitude and phase of magnetic or gravitational force vary in a predictable way Exploit geometry to distinguish coupling between drive mass and test mass from other backgrounds

Varying Equilibrium Position (current on) Magnitude, phase of signal vary with equilibrium position. Magnetic period of 200 µm. Gravity period would be 100  m 200 µm Magnetic Force ( N) Phase (Rad) 200µm Maximum magnetic forceMinimum magnetic force Earth Field

Magnetic Test Mass - Susceptibility Scan I dm =0 I dm >0 Force (N) Phase Equilibrium Position (CPS Units) 4 periods 2 periods 200 µm

Magnetic calibration Use a permanent magnetic moment on test mass, but block the Earth’s B-field  u-metal shield encloses cryostat SEM/FIB view 12  m squares of Co/Pt bilayer film m ~ J/T 250x attenuation transverse and 160x longitudinal at 1’ from base

Latest Data Current on Current off Take gravity data as a function of y, and magnetic data at each point -For each gravity point, do magnetic scan to determine position relative to closest magnetic minimum  can combine many days data! -Expected phase known (mod  ) y

Experimental constraints Phys. Rev. D 78, (2008)

Next generation experiment rotary drive preliminary results…more soon Separation between masses ~25 microns Larger area  Sensitivity should be x improved D. Weld et.al, PRD 77, (2008)

Shorter-range experiments Atomic BEC sensor Optically-levitated microspheres A. A. Geraci, S.B. Papp, and J. Kitching, Phys. Rev. Lett. 105, (2010) S. Dimopoulos and A. A. Geraci., Phys.Rev.D 68, (2003)

Shorter-range experiments Atomic BEC sensor Optically-levitated microspheres A. A. Geraci, S.B. Papp, and J. Kitching, Phys. Rev. Lett. 105, (2010) S. Dimopoulos and A. A. Geraci., Phys.Rev.D 68, (2003) Looking for new students/postdocs!!!

Conclusion Notable experimental progress over past few years Stanford experiment has improved bounds at ~20 microns by > 4 orders of magnitude Still rich possibilities for new physics below 1mm 2 nd generation cantilever experiment x more sensitive

Stanford Gravity Group David Sylvia Andy JohnAharon

Buried Drive Mass Lead to meander Lead to ground plane Actuator ground plane Thin Si (not shown) Gold Quartz Al2O3 ADVANTAGES : No periodic electrostatic/Casimir coupling Presents very flat surface of drive mass to the test mass Gold and Si bars

Feedback Cooling Variable Phase Shifter Intf BP filter Variable Gain Preamp Piezo Stack Open loop Freq (Hz) Fourier Amplitude (m) Q, T reduced ~ 10x Adjusting phase of feedback so that Q is reduced and frequency unchanged Adjust phase for negative velocity feedback Adjust gain to reduce Q Advantage: experiment easier Disadvantage: Voltage SNR decreases

Interferometer signal over one period of bimorph Drive signal over same period of bimorph Interferometer signal after averaging Averaging Data: Example FFT

Averaging Data Data Analysis Method for Small Bandwidth 1. Time of data files longer than ringdown time  of cantilever 2. FFT each file 3. Average between files 4. Compare to thermal noise Force (N) vs. Averaging Time (sec) Compared to Theoretical Thermal Noise Measured Thermal Noise Signal Above Thermal Noise artificial signal Signal  time -1/2 Force(N) Averaging time (s)

Other masses –Large masses in exp. environment –(Relatively) high frequency prevents coupling Vibration isolation –Cryostat is hung from ceiling on ~1 Hz springs –High Q can lead to vibrational excitation due to piezo nonlinearity –Two stages (2.2 Hz springs/pendula) isolate actuator Piezo Nonlinearity Bimorph 3% Nonlinearity Ideal F 0 ~300 Hz slow Mechanical Backgrounds

Uncertainty in position and tilt Z-separation: 27–31 ± 3  m  yz: 2 ± 5  m across width  xz: 3 ± 5  m across length Monte Carlo simulation Vary all relevant statistical and systematic errors- compare FEA simulation with data

Monte-carlo analysis <><> 95% confidence exclusion

Monte-carlo analysis <><> 95% confidence exclusion = 4  m = 6  m = 34  m = 18  m = 10  m

Error budget