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)

Experimental Approach

Source and Detector Oscillators Shield 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

Central ApparatusScale:1 cm3

detector massshield

source massPZT bimorph

transduceramp box

tilt stage

vibrationisolationstacks

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 ~1010 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

Interaction Region: Two Improvements

~1 cm

60 mm Au-plated sapphire shield: replace with 10 mm stretched Cu membrane (shorter ranges possible)

Develop higher-Q (more sensitive) detector mass

Vibration Isolation and Position Control

~50 cm

Inverted micrometer stages for full XYZ positioning

Torque rods for micrometer stage control

Vacuum system base plate

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 mm 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 mm)

Sensitivity: increase Q and statistics, decrease T

)]/exp(1)][/exp(1)[/)(exp(2)( 2 dsddsY tttdAGtF

• Signal

Force on detector due to Yukawa interaction with source:

• Thermal Noise

• Setting SNR = 1 yields

kTDFT

4 Q

mD

QkTm

AG dds2

1~

~ 3 x 10-15 N rms (for = 1, = 50 mm)

~ 3 x 10-15 N rms (300 K, Q = 5 x104, 1 day average)~ 7 x 10-17 N rms (4 K, Q = 5 x105, 1 day average)

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

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

Material Q @ 300 K Q @ 77 K Q @ 4 KSi 6 x 103 1 x 105 8 x 105

W (as machined) 5 x 103 ? ?

W (1600 K anneal)* 2.5 x 104 ? ?

W (2700 K anneal) 2.8 x 104 ? ?

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

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

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:

(Supplemental Slides)

Stretched membrane shield installed

• Conducting planes surround both test masses on 5 sides (get rid of copper tape)

• Surface variations:

5 mm peaks

0.7 mm rms variations (should be sufficient for ~ 30 mm experiment)

Shield clamp

Tensioning screw

Macor standoff

minimum gap = 48 microns

Installation at IUCF

• Hollow riser for magnetic isolation

Central apparatus (previous slide) behind brass mesh shield

Diffusion pump

• P ~ 10-7 torr

• LN2 - trapped diffusion pump mounts below plate

Vacuum System

m

D

Calibration with Thermal Noise

Free thermal oscillations:12kBT

12m 2zT (rms)

2

Damped, driven oscillations on resonance:

FD m 2

QzD Q

mDwherek

FD zDzT(rms)

mkBTQ

z

zT, zD, , T, Q from data,

For distributed oscillator sampled at r, m z

2dV

z(r ) 2mode shape fromcomputer model

Measured force:

Detector Model:

zDzT (rms)

VDVT (rms)

Consistency checksAdditional runs:

Larger test mass gap

Source over opposite side of detector (and shield)

Reduced overlap

Felectrostatic ~ r –4,• Fpressure ~ Fmagnetic ~ r –2, Fvibrational ~ (constant)• Shield response

No resonant signal observed

Expected backgrounds from ambient fields:

ES Background = Signal with applied V × (Vambient/ Vapplied)4 = 10-10 V

Magnetic Background = Signal with applied B × (Bambient/ Bapplied)2 = 10-7 V

All < thermal noise (10-6 V)

Systematic Errors

(m) (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 74 045001 (2006).

V. A. Kostelecký, PRD 69 105009 (2004).

MATTERLVGR SSSS

),,( mm tsufSLV

20 coefficients controlling L.V.

Estimated sensitivities: 10-15 – 10-4

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

Calculation of the Fitting FunctionWilliam Jensen

Fit net signal to [1]:

)2cos()2sin()cos()sin( 54321 tCtCtCtCCFLV

= sidereal angular frequency of Earth

= time measured in Sun-centered celestial equatorial frame [1]t

Ci = linear combinations of sm (celestial frame) and theoretical LV force in lab frame

LV Gravitational potential [2]

ˆ ˆˆ ˆ1 2

1 2

1 ˆ ˆ1 ,2

i k ikGdm dmdV x x sx x

ˆjks = coefficients of Lorentz violation in the SME standard lab frame

(xL = South, yL = East, zL = vertical)

Force misaligned relative to , but 1/r2 behavior preserved21 xxr

[1] V. A. Kostelecký and M. Mewes, PRD 66

056005 (2002).[2] Q. G. Bailey and V. A. Kostelecký, PRD 74

045001 (2006).

Lab Frame Coefficient Sensitivity Estimate

Lab frame result (“signal”):

2316331622161116 )N102.4()N104.9()N107.8()N107.8( ssssFLV

s12, s13 terms:

~ 10-2 x diagonal terms

Very sensitive to numerical integration input parameters (~ 106 Monte Carlo trials)

Thermal Noise

4 ,BT

k TDF

mDQ

~ 2 x 10-14 N rms (300 K, 30 minute average)

Approximate SNR = FLV / FT

excluded

excluded

allowed

allowed

s11

s22

Lab Frame Coefficient Sensitivity Estimate(diagonal elements only)

11 22 33, , 1.s s s SNR

Surfaces: relationship between and when

33s

Approximate allowed/excluded regions shown assuming no evidence of sidereal variation

s11= s22 = 0 s33 = ± 20

FLV = s11F11 + s22F22 – s33F33