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Short-range gravity test with a micro-cantilever

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. Measurement with Microcantilevers. Amplitude:. A. w. w 0.

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Short-range gravity test with a micro-cantilever

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  1. 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

  2. Measurement with Microcantilevers Amplitude: A w w0 F l w t Actual Cantilever w= 50 m d = 0.3 m l = 250 m K ~ 0.006 N/m Q ~ 80,000 f ~ 300 Hz l w Human hair 3300 Å-thick silicon cantilevers

  3. Fundamental Limit:Thermal Noise  k ~ 0.006 N/m Q ~ 80,000 f0 ~ 300 Hz T ~ 10 K b ~ 0.001 - 0.0001 s-1 Fmin ~ 1 aN Minimum measurable force:

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

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

  6. Experimental Probe

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

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

  9. Varying Equilibrium Position (current on) 200µm 200µm Magnitude, phase of signal vary with equilibrium position. Magnetic period of 200 µm. Gravity period would be 100mm Earth Field Maximum magnetic force Minimum magnetic force 200 µm Magnetic Force (10-15 N) Phase (Rad)

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

  11. Magnetic calibration Use a permanent magnetic moment on test mass, but block the Earth’s B-field mu-metal shield encloses cryostat SEM/FIB view 12 mm squares of Co/Pt bilayer film m ~ 10-13 J/T 250x attenuation transverse and 160x longitudinal at 1’ from base

  12. Latest Data 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 p) Current on Current off y

  13. Experimental constraints Phys. Rev. D 78, 022002 (2008)

  14. Next generation experiment • rotary drive preliminary results…more soon D. Weld et.al, PRD 77,062006 (2008) • Separation between masses ~25 microns • Larger area  • Sensitivity should be 10-100x improved

  15. Shorter-range experiments • Atomic BEC sensor • Optically-levitated microspheres S. Dimopoulos and A. A. Geraci., Phys.Rev.D68, 124021 (2003) A. A. Geraci, S.B. Papp, and J. Kitching, Phys. Rev. Lett. 105, 101101 (2010)

  16. Shorter-range experiments • Atomic BEC sensor • Optically-levitated microspheres S. Dimopoulos and A. A. Geraci., Phys.Rev.D68, 124021 (2003) A. A. Geraci, S.B. Papp, and J. Kitching, Phys. Rev. Lett. 105, 101101 (2010) Looking for new students/postdocs!!!

  17. 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 • 2nd generation cantilever experiment 10-100x more sensitive

  18. Stanford Gravity Group Andy Aharon John David Sylvia

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

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

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

  22. Averaging Data Data Analysis Method for Small Bandwidth 1. Time of data files longer than ringdown time t 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 Signal µ time-1/2 Force(N) artificial signal Averaging time (s) Averaging time (s)

  23. Mechanical Backgrounds Piezo Nonlinearity Ideal Bimorph 3% Nonlinearity • 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 F0~300 Hz slow

  24. 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

  25. Monte-carlo analysis <a> 95% confidence exclusion

  26. Monte-carlo analysis l = 10 mm l = 4 mm l = 6 mm l = 18 mm l = 34 mm <a> 95% confidence exclusion

  27. Error budget

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