Transcript Document

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
Planar Geometry
Resonant detector with source mass driven on resonance
1 kHz operational frequency - simple, stiff vibration isolation
Double-rectangular torsional detector: high Q, low thermal noise
Stiff conducting shield for background suppression
~ 5 cm
Source and Detector Oscillators
Shield for Background Suppression
Central Apparatus
“Taber” vibration
isolation stacks:
Brass disks hanging
from fine wires; make
set of soft springs
which attenuate at
~1010 at 1 kHz
Scale:
1 cm3
vibration
isolation
stacks
tilt stage
Installed in 75 liter
vacuum bell jar (10-7
torr) for further
suppression of
acoustic forces
transducer
amp box
detector mass
READOUT
shield
source mass
PZT bimorph
Capacitive probe
above large detector
rectangle connects to
JFET, Lock-in
amplifiers
Figure: Bryan Christie (www.bryanchristie.com) for Scientific American (August 2000)
Interaction Region: Two Improvements
60 mm Au-plated
sapphire shield:
replace with 10 mm
stretched Cu
membrane (shorter
ranges possible)
Develop higher-Q
(more sensitive)
~1 cm
detector mass
Vibration Isolation
and Position Control
Inverted micrometer stages for
full XYZ positioning
~50 cm
Vacuum
system
base
plate
Torque rods for micrometer stage control
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
• Signal
Force on detector due to Yukawa interaction with source:
FY (t )  2Gs d Ad 2 exp(d (t ) /  )[1 exp(ts /  )][1 exp(td /  )]
~ 3 x 10-15 N rms (for  = 1,  = 50 mm)
• Thermal Noise
FT 
4kTD

D
m
Q
~ 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)
• Setting SNR = 1 yields
~
1
kTm
G s  d 2 Ad
Q
Current Status and Projected Sensitivity
Recent signals:
Fall 2008: ~ 5 x detector thermal
noise, resonant, but independent
of test mass position -- vibration
Repaired Vibration isolation
system
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
Projected Improvement at Cryogenic Temperatures
Available Detector Mass Prototypes
Material
Q @ 300 K
Q @ 77 K
Q@4K
Si
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
?
?
*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
Apply at:
http://www.iucf.indiana.edu/jobs/#job94
More information at:
http://www.iucf.indiana.edu/u/jcl/personal/research.htm
(Supplemental Slides)
Stretched membrane shield installed
• Surface variations:
5 mm peaks
0.7 mm rms
variations (should
be sufficient for ~
30 mm experiment)
Shield clamp
Tensioning
Macor
screw
standoff
• Conducting
planes surround
both test masses
on 5 sides (get
rid of copper
tape)
minimum gap =
48 microns
Installation at IUCF
Central apparatus
(previous slide)
Vacuum System
behind brass
mesh shield
• Hollow riser for magnetic
isolation
• LN2 - trapped diffusion
pump mounts below plate
• P ~ 10-7 torr
Diffusion
pump
Calibration with Thermal Noise
Free thermal oscillations:
1
1
2 2
kB T  m zT (rms )
2
2
Detector Model:
Damped, driven oscillations on resonance:
D
m 2
FD  
zD
Q
k
m
z
where
m
Q
D
zD  mkBT
 Measured force: FD  
zT(rms )
Q
zT, zD, , T, Q from data,
zD
zT (rms )

VD
VT (rms )
2
For distributed oscillator sampled at r,
m
  z dV
z(r )
2
mode shape from
computer model
Consistency checks
Additional runs:
Larger test mass gap
Source over opposite side of detector (and shield)
Reduced overlap
• Fpressure ~ Fmagnetic ~ r –2,
Felectrostatic ~ r –4, Fvibrational ~ (constant)
• Shield response
No resonant signal observed
Expected backgrounds from ambient fields:
Magnetic Background = Signal with applied B × (Bambient/ Bapplied)2 = 10-7 V
ES Background = Signal with applied V × (Vambient/ Vapplied)4 = 10-10 V
All < thermal noise (10-6 V)
Systematic Errors
(m)
(m)
New Analysis - Search for Lorentz Violation (2002 Data)
Test for sidereal variation in force signal:
Standard Model Extension (SME)
Recently expanded to gravitational
sector
V. A. Kostelecký, PRD 69 105009 (2004).
Q. G. Bailey and V. A. Kostelecký, PRD 74
045001 (2006).
Action:
S  SGR  S LV  SMATTER
m
S LV  f (u
,
s m, t
)
20 coefficients controlling L.V.
Estimated sensitivities: 10-15 – 10-4
Source: A. Kostelecký, Scientific American,
September 2004, 93.
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 Function
William Jensen
Fit net signal to [1]:
FLV  C1  C2 sin(t )  C3 cos(t )  C4 sin(2t )  C5 cos(2t )
 = sidereal angular frequency of Earth
t = time measured in Sun-centered celestial equatorial frame [1]
Ci = linear combinations of sm (celestial frame) and theoretical LV force in lab frame
LV Gravitational potential [2]
dV 
Gdm1dm2  1 iˆ kˆ ikˆˆ 
1  xˆ xˆ s  ,
x1  x2  2

Force misaligned relative to
s
ˆjkˆ
= coefficients of Lorentz violation in
the SME standard lab frame
  
r  x1  x2 ,
(xL = South, yL = East, zL = vertical)
but 1/r2 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).
Lab Frame Coefficient Sensitivity Estimate
Lab frame result (“signal”):
FLV  (8.7 1016 N)s 11  (8.7 1016 N)s 22  (9.4 1016 N)s 33  (4.2 1016 N)s 23
s12, s13 terms:
~ 10-2 x diagonal terms
Very sensitive to numerical integration input parameters (~ 106 Monte Carlo trials)
Thermal Noise
FT 
4kBTD

,
D
m
Q
~ 2 x 10-14 N rms (300 K, 30 minute average)
Approximate SNR = FLV / FT
Lab Frame Coefficient Sensitivity Estimate
(diagonal elements only)
Surfaces: relationship
between s 11 , s 22 , and s 33 when SNR  1.
Approximate allowed/excluded
regions shown assuming no
evidence of sidereal variation
excluded
allowed
s11= s22 = 0  s33 = ± 20
s 33
allowed
excluded
FLV = s11F11 + s22F22 – s33F33
s22
s11