Transcript A magnetic force calibration for the Stanford (1st Gen) short

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
F   Kx
F
l
t
w
0 
K
m
Q
 0 f 0



Actual Cantilever
Amplitude:
w= 50 m
d = 0.3 m
l = 250 m
A
0
A( f )  Adc
l
f0
2

w
K ~ 0.006 N/m
Q ~ 80,000
f ~ 300 Hz
2
f0 f 2
( f0  f ) 
Q2
2
2 2
Human hair
3300 Å-thick silicon cantilevers
Fundamental Limit:Thermal Noise
Minimum measurable force:
1/ 2
Fmin

k ~ 0.006 N/m
Q ~ 80,000
f0 ~ 300 Hz
T ~ 10 K
b ~ 0.001 - 0.0001 s-1

4kkB Tb 
 

 Q 0 
Fmin ~ 1 aN
Experimental Setup
Fiber
Test mass
Cantilever
With conducting
surfaces
Drive mass
motion
Silicon nitride
shield (cutaway)
Cantilever resonance (f0): ~300 Hz
Drive frequency(f0/3): ~100Hz
Piezo Actuator
(±130 µm at f0/3 or f0/4)
Min. Drive mass/Test mass
separation: ~20 m (edge-edge
distance)
Magnetic version
Spatially alternating
magnetic field
created above drive
mass, B ~ 1mG/mA
Magnetic film on
test mass
B
Current
B
Au wires in
bulk silicon
motion
Experimental Probe
Overall Experimental Setup
Signal from
interferometer
Analog to
Digital
converter
Computer
storage
Exchange
gas space
Piezoelectric
Actuator drive
LHe space
Analysis
Vacuum
can
voltage
Actuator
Cantilever
time
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
Varying Equilibrium Position (current on)
Magnitude, phase of signal vary with equilibrium position.
Magnetic period of 200 µm. Gravity period would be 100m
200µm
Earth Field
Maximum magnetic force
Minimum magnetic force
200µm
Phase (Rad)
Magnetic Force (10-15 N)
200 µm
Magnetic Test Mass - Susceptibility Scan
200 µm
200 µm
4 periods
Idm=0
Force (N)
Phase
Idm >0
2 periods
Force (N)
Phase
Equilibrium Position (CPS Units)
Magnetic calibration
Use a permanent magnetic moment on test mass, but block
the Earth’s B-field
SEM/FIB view
u-metal
shield
encloses
cryostat
12 m squares of
Co/Pt bilayer film
m ~ 10-13 J/T
250x attenuation transverse and
160x longitudinal
at 1’ from base
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 )
Current on
Current off
y
Experimental constraints
m1m 2
V  G
(1 er /  )
r

Phys. Rev. D 78, 022002 (2008)
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
Shorter-range experiments
• Atomic BEC sensor
S. Dimopoulos and A. A. Geraci., Phys.Rev.D 68, 124021 (2003)
• Optically-levitated microspheres
A. A. Geraci, S.B. Papp, and J. Kitching, Phys. Rev. Lett. 105, 101101 (2010)
Shorter-range experiments
• Atomic BEC sensor
S. Dimopoulos and A. A. Geraci., Phys.Rev.D 68, 124021 (2003)
• Optically-levitated microspheres
A. A. Geraci, S.B. Papp, and J. Kitching, Phys. Rev. Lett. 105, 101101 (2010)
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
• 2nd generation cantilever experiment 10100x more sensitive
Stanford Gravity Group
Andy
David
Sylvia
Aharon
John
Buried Drive Mass
Lead to meander
Lead to ground plane
Actuator ground plane
Gold
Al2O3
Quartz
Thin Si
(not
shown)
Gold and Si bars
ADVANTAGES:
• No periodic electrostatic/Casimir coupling
• Presents very flat surface of drive mass to the test mass

Feedback Cooling
Intf
Preamp
BP
filter
•Adjust phase for negative velocity
feedback
•Adjust gain to reduce Q
•Advantage: experiment easier
Variable
Phase
Shifter
Piezo
Stack
•Disadvantage: Voltage SNR
decreases
Variable
Gain
x  Acos(t)
Fourier Amplitude (m)
d2x
dx
m
 c
 kx
dt
dt
Q, T reduced ~ 10x
1/ 2


4kk
T
1/ 2
S1/F 2   B   4kB T 
 Q 0 
Adjusting phase
of feedback so
that Q is
reduced and
frequency
unchanged
Open loop

Ffeedback  GA cos(t   )
Freq (Hz)
Averaging Data: Example
Interferometer signal over one period of bimorph
Drive signal over same period of bimorph
Interferometer signal after averaging
FFT
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
Force(N)
Measured Thermal Noise
Signal time-1/2
Signal Above
Thermal Noise
artificial signal
Averaging time (s)
Averaging time (s)
Mechanical Backgrounds
• Other masses
– Large masses in exp.
environment
– (Relatively) high frequency
prevents coupling
F0~300 Hz
slow
• Vibration isolation
Piezo Nonlinearity
Ideal
Bimorph
– 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
3% Nonlinearity
Monte Carlo simulation
Vary all relevant statistical and systematic errors- compare FEA simulation with data
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 analysis
<>
95% confidence exclusion
Monte-carlo analysis
 = 10 m
 = 4 m
 = 18 m
<>
95% confidence exclusion
 = 6 m
 = 34 m
Error budget