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PASI- Frontiers on Casimir Physics Ushuaia, Argentina, 10/7/2012
Casimir force measurements using mechanical transducers: sensitivity, noise and background
Ricardo S. DeccaDepartment of Physics, IUPUI
PASI- Frontiers on Casimir Physics Ushuaia, Argentina, 10/7/2012
• Dominant electronic force at small (~ 1 nm) separations
• Non-retarded: van der Waals
• Retarded: Casimir
Attractive interaction
4480z
hcPC
z
k
EBE
BE
,
222
2
1 0||0 0|(|0 ½
0 0||0 0||0
k
No mode restriction on the outside
PASI- Frontiers on Casimir Physics Ushuaia, Argentina, 10/7/2012
In principle, a simple task
• System to measure the interaction -Mechanical oscillators with soft springs. -It actually is a transducer, and either a deflection (linear or angular) or a frequency shift is measured. -A calibration against a known interaction is needed. An electrostatic interaction between the bodies is used. -It needs to be free of systematic effects. But nobody succeeds. • System to measure the separation between bodies -Two-color interferometer yields absolute positioning. -One point needs to be obtained in a different way. • Characterization of the system and samples -Measurement of all parameters involved. -Minimization of backgrounds. -Characterization of the materials used
• Comparison with theory
400 600 800 10000
50
100
150
200
250
PC (
mP
a)
z (nm)
R = 300 m R = 150 m
PASI- Frontiers on Casimir Physics Ushuaia, Argentina, 10/7/2012
Collaborators
Funding
Daniel López Argonne National LabEphraim Fischbasch Purdue UniversityDennis E. Krause Wabash College and Purdue UniversityValdimir M. Mostepanenko Noncommercial Partnership “Scientific Instruments”, RussiaGalina L. Klimchitskaya North-West Technical University, Russia
Jing Ding, Brad Chen IUPUIEdwin Tham, Hua Xing
Vladimir Aksyuk CNST/Univ. of MarylandDiego Dalvit Los Alamos National LabPeter Milonni Los Alamos National LabFrancesco Intravaia Los Alamos National LabPaul Davids Sandia National LabIl Woong Jung Argonne National Lab
NSF, DOE, LANL, DARPA
PASI- Frontiers on Casimir Physics Ushuaia, Argentina, 10/7/2012
Outline
1.- Review of experimental results
2.- Characteristics of a system
3.- Measurement of the interaction 4.-Measurement of the separation
5.- Sample preparation, and characterization 6.- Comparison with theory
7.- Effects of environment
8.- Low temperature measurements
9.- Potential approaches to get better results? 10.- Summary
400 600 800 10000
50
100
150
200
250
PC (
mP
a)
z (nm)
R = 300 m R = 150 m
PASI- Frontiers on Casimir Physics Ushuaia, Argentina, 10/7/2012
Review of experimental results
Observation of the thermal Casimir forceA. O. Sushkov, W. J. Kim, D. A. R. Dalvit & S. K. LamoreauxNature Physics 7, 230–233 (2011)
PASI- Frontiers on Casimir Physics Ushuaia, Argentina, 10/7/2012
Roberto Onofrio's group at Dartmouth College
G. Bressi, G. Carugno, R. Onofrio, G. Ruoso, "Measurement of the Casimir force between Parallel Metallic Surfaces", Phys. Rev. Lett. 88 041804 (2002)
Review of experimental results
PASI- Frontiers on Casimir Physics Ushuaia, Argentina, 10/7/2012
A. Roy, C.Y. Lin and U. Mohideen, "Improved precision measurement of the Casimir force," Physical Review D, Rapid Communication, Vol. 60, pp.111101-05 (1999).
Review of experimental results
PASI- Frontiers on Casimir Physics Ushuaia, Argentina, 10/7/2012
Review of experimental setups
Measurement of dispersive forces between evaporated metal surfaces in the range below 100 nm P.J. van Zwol, G. Palasantzas, M. van de Schootbrugge, J. Th. M. De Hosson
PASI- Frontiers on Casimir Physics Ushuaia, Argentina, 10/7/2012
D. Chavan, G. Gruca, S. de Man, M. Slaman, J. H. Rector, K. Heeck, and D. Iannuzzi, Ferrule-top atomic force microscope, Rev. Sci. Instrum. 81, 123702
Review of experimental results
PASI- Frontiers on Casimir Physics Ushuaia, Argentina, 10/7/2012
Review of experimental results
PASI- Frontiers on Casimir Physics Ushuaia, Argentina, 10/7/2012
Quantum Mechanical Actuation of Microelectromechanical Systems by the Casimir Force; Chan, Aksyuk, Kleiman, Bishop, CapassoScience 291, 1941
Nonlinear Micromechanical Casimir Oscillator;
Phys. Rev. Lett. 87, 211801
Review of experimental results
PASI- Frontiers on Casimir Physics Ushuaia, Argentina, 10/7/2012
Effect of hydrogen-switchable mirrors on the Casimir forceIannuzzi, Lisanti, and CapassoProc. Nat. Acad. of Sci. 101, 4019
Review of experimental results
PASI- Frontiers on Casimir Physics Ushuaia, Argentina, 10/7/2012
More yet!
Lateral Casimir effect
Measurements on corrugated samples Phase-change materials
Indium-Tin Oxide (ITO)
Review of experimental results
PASI- Frontiers on Casimir Physics Ushuaia, Argentina, 10/7/2012
- Base pressure: ~ 1x10-7 Torr- Mounted in an active damping control air table- Passive magnetic damping on floating system
- 5 axis (xyz, rock and tilt) stepper motor drive- 3 axis (xyz, not seen) closed loop 70 micron range piezo stage- Two color interferometer integrated into the system for continuous absolute position measurement- Total position stability control better than 0.2 nm
Characteristics of a system
PASI- Frontiers on Casimir Physics Ushuaia, Argentina, 10/7/2012
Characteristics of a system
df
Qffiff
f
Soo
o
rms
0
2
22
2
2
ff
f oo
o
r
curr
Qffff
Qff
dfZ
kTQf
RkT
ZQ
SNR
2222
2
44
Nl
Ewts 48
3
PASI- Frontiers on Casimir Physics Ushuaia, Argentina, 10/7/2012
Characteristics of a system
Not considering intrinsic losses Newell(1986)
Optimal strategy: Decrease a, increase Q, work at fo, and low T
PASI- Frontiers on Casimir Physics Ushuaia, Argentina, 10/7/2012
Characteristics of a system
What is t? Noise (thermal, vibrational, 1/f), actual forces (known and unknown: Electrostatic, patch effects, Casimir, gravitational, …)
702 702.5 703 703.5 704 704.5 7050
0.2
0.4
0.6
0.8
1
Noise
Noise
702 702.5 703 703.5 704 704.5 7050.01
0.1
1
f(Hz)
PASI- Frontiers on Casimir Physics Ushuaia, Argentina, 10/7/2012
bzzzz goimetal Lately, we have changed the setup: the sphere is on the oscillator, the plate is on top.
-Different sample (nanostructured), cannot be made on the oscillator’s plate.-Larger sample, requires different deposition.
Characteristics of a system
PASI- Frontiers on Casimir Physics Ushuaia, Argentina, 10/7/2012
703.4 703.6 703.8 704.0 704.20.0
0.2
0.4
0.6
0.8
1.0
No
rma
lize
d a
mp
litu
de
Freq (Hz)
Hzrad10 9
HzfNFF
b
AQ
Tk
bF
elth
el
o
B
4~1
41
22
2
400 600 800 10001E-15
1E-14
1E-13
1E-12
1E-11
F N
/Hz1/
2Freq (Hz)
elF
thF
Characteristics of a system
PASI- Frontiers on Casimir Physics Ushuaia, Argentina, 10/7/2012
Measurement of the interaction
z
F
I
b C
oor 2
222 1
CC
CC PRz
FERF
22
PASI- Frontiers on Casimir Physics Ushuaia, Argentina, 10/7/2012
z
F
I
b C
oor 2
222 1
CC
CC PRz
FERF
22
0 200 400 600 800712.80
712.85
712.90
712.95
713.00
713.05
713.10
713.15
713.20
f r (H
z)
t (s)
z= 550 nmfo=713.250 Hz
Determined by:-Looking into the response of the oscillator in the thermal bath.Or-Inducing a time dependent separation between the plate and the sphere (preferred).
Measurement of the interaction
PASI- Frontiers on Casimir Physics Ushuaia, Argentina, 10/7/2012
Measurement of the interaction
z
F
I
b C
oor 2
222 1
C
CCC PR
z
FERF
22
Errors Minimum values
Frequency: 6 mHz ~28 mHz (at 750 nm)b2/I: 0.0005 mg-1 1.2432 mg-1
R: 0.2 mm 150 mm
400 600 800 10000
50
100
150
200
250
PC (
mP
a)
z (nm)
R = 300 m R = 150 m
100 200 300 400 500 600 700 800
-2
0
2
4
6
8
10
P (
mP
a)
z (nm)
PASI- Frontiers on Casimir Physics Ushuaia, Argentina, 10/7/2012
Measurement of the separation
bzzzz goimetal
zg = (2172.8 ± 0.1) nm, interferometer
zi = ~(10000.0s ± 0.2) absolute interferometer
zo = (8162.3 ± 0.5) nm, electrostatic calibration
b = (207 ± 2) mm, optical microscope
Q = ~(1.000 ± 0.001) mrad
zg
zo is determined using a known interaction
zi, Q are measured for each position
PASI- Frontiers on Casimir Physics Ushuaia, Argentina, 10/7/2012
Electrostatic force calibration
-15 -10 -5 0 5 10 15 20 250.0
0.2
0.4
0.6
0.8
1.0
(
rad
)
V (mV)
z = 3 mz = 5 m
3.00 3.25 3.50 3.75 4.00 4.25 4.50 4.75 5.00
100
125
150
175
200
225
250
275
300
325
350
Fe (
pN
)
zmetal
(m)
V = 0.35 V
V = 0.27 V
R
zzu
zz
RAVV
nu
nunuVVF
metal
i
metaliiAuo
nAuoe
)(1
)()(2
~sinh
cothcoth)(2
1
0
2
2
metalz
Measurement of the separation
PASI- Frontiers on Casimir Physics Ushuaia, Argentina, 10/7/2012
Electrostatic force calibration
-15 -10 -5 0 5 10 15 20 250.0
0.2
0.4
0.6
0.8
1.0
(
rad
)
VAu
(mV)
z = 3 mz = 5 m
z = 3.5 m
Measurement of the separation
PASI- Frontiers on Casimir Physics Ushuaia, Argentina, 10/7/2012
Electrostatic force calibration
0 1000 2000 3000 400010
12
14
16
18
20
Vo (
mV
)
z (nm)
Vo is constant as a function of separation…
… and time
0 10000 20000 3000010
11
12
13
14
15
16
17
18
19
20
Vo (
mV
)
t (s)
Otherwise, Vo needs to be determined at each point
10 x 10 grid, 5 mm pitch
Measurement of the separation
PASI- Frontiers on Casimir Physics Ushuaia, Argentina, 10/7/2012
Electrostatic force calibration
R
zzu
zz
RAVV
nu
nunuVVF
metal
i
metaliiAuo
nAuoe
)(1
)()(2
~sinh
cothcoth)(2
1
0
2
2
-After measuring the deflection (expressed as force here), we adjust for the unknown separation.-The figure shows the DFe for the optimal and oneoff by 1.5 nm
z
Measurement of the separation
PASI- Frontiers on Casimir Physics Ushuaia, Argentina, 10/7/2012
-Problems in lack of parallelism (curvature of wavefronts) are compensated when subtracting the two phases
-Gouy phase effect is ~ , and gives an error much smaller than the random one
(Yang et al., Opt. Lett. 27, 77 (2005) Interferometer
fNA
fG arctan)(
lLC =(1240 +/- D) nm (low coherence),
lCW 1550 nm (high coherence) in
x
Mirror (v ~ 10 mm/s)
Dx = zi
Readout
Measurement of the separation
PASI- Frontiers on Casimir Physics Ushuaia, Argentina, 10/7/2012
lLC =(1240 +/- D) nm (low coherence),
lCW 1550 nm (high coherence) input
x
Mirror (v ~ 10 mm/s)
Dx = zi
Readout(independent at each wavelength)
-Phases obtained doing a Hilbert transform of the amplitude-Changes in D (about 2 nm) give different curves. Intersections provide Dx-Quite insensitive to jitter. Only 2DDx’/(lCW)2 Instead of 2Dx’/lCW
(Yang et al., Opt. Lett. 27, 77 (2005)
)2(mod)()(
int4
21
54
xxS
SSz
DDphase
phasefringeCW
i
CWLCD
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
1.5
D
= 1.7 nm = -2.1 nm
0 2 4 6 8 10 12 14 16 18 20 22 24-1
0
1
2
3
4
5
6
7
CW
x (m)
Interferometer
zi1 2 3 4 5
Det
ecto
r si
gn
al
t (s)
Measurement of the separation
PASI- Frontiers on Casimir Physics Ushuaia, Argentina, 10/7/2012
Sample preparation and characterization
-Au on the sapphire sphere is deposited by thermal evaporation.
-Au on the oscillator is also deposited by thermal evaporation but on large samples it is deposited by electroplating (on Si[111])
-Samples are characterized by measuring resistance as a function of temperature, AFM measurements and also ellipsometry in the electrodeposited sample.
-The sample to be used is mounted as quickly as possible into the system, baked to ~ 60 oC for ½ hour (not the oscillator)
(10x10 mm2)~ 20 nmpp
PASI- Frontiers on Casimir Physics Ushuaia, Argentina, 10/7/2012
Sample characterization
PASI- Frontiers on Casimir Physics Ushuaia, Argentina, 10/7/2012
2/32 )(
4)(
pp
T
TT
eV)1.09.8( p
-r vs T and spectroscopic ellipsometry (190 nm to 830 nm) used to determine optical properties.
-Both methods indicate a rather good Au sample
Sample characterization
PASI- Frontiers on Casimir Physics Ushuaia, Argentina, 10/7/2012
100 1000-60
-50
-40
-30
-20
-10
0
10
RE
(nm)
10 100 1000-2
0
2
4
6
8
10
IM
(nm)-Measured real and imaginary parts of the dielectric functions (red circles) are similar to published values (Palik, black squares)
-It was checked that either can be used, given the same results.
Sample characterization
PASI- Frontiers on Casimir Physics Ushuaia, Argentina, 10/7/2012
022
)(''21)( dx
x
xxi
1E12 1E13 1E14 1E15 1E16 1E17 1E18 1E191
10
100
1000
10000
100000
1000000
1E7
1E15 1E16 1E17 1E18 1E190.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
" (
i)
(rad/s)
"(
i)
(rad/s)
Sample characterization
PASI- Frontiers on Casimir Physics Ushuaia, Argentina, 10/7/2012
200 300 400 500 600 7000.0
0.2
0.4
0.6
0.8
1.0
1.2
200 300 400 500 600 700-0.005
-0.004
-0.003
-0.002
-0.001
0.000
0.001
0.002
0.003
0.004
0.005
0.006
|PC|
(Pa)
zmetal
(nm)
(a) (b)
PC (
Pa)
zmetal
(nm)
Both samples on the left panel. Difference between them on the right one
Sample characterization
PASI- Frontiers on Casimir Physics Ushuaia, Argentina, 10/7/2012
vi: Fraction of the sample at separation zi
)(zPvP CSi
iC
Roughness corrections
Roughness corrections are ~0.5% to the Casimir interaction at 160 nm
Comparison with theory
PASI- Frontiers on Casimir Physics Ushuaia, Argentina, 10/7/2012
Finite conductivity and finite temperature
Comparison with theory
2222 4
c
Tlkkq B
l
PASI- Frontiers on Casimir Physics Ushuaia, Argentina, 10/7/2012
Comparison with theory
Bentsen et al., J. Phys. A (2005)
2
2
2
1)(
)(1)(
p
p
i
PASI- Frontiers on Casimir Physics Ushuaia, Argentina, 10/7/2012
- Dark grey, Drude model approach-Light grey, plasma model approach
PRD 75, 077101
Comparison with theory
PASI- Frontiers on Casimir Physics Ushuaia, Argentina, 10/7/2012
Effects of environment: Vo
For the residual effects of the patch potentials, it has been noted that their influence does not average to 0, since . Hence in the effective area of separation, there could be a residual electrostatic force. For the size of our sphere, at large separations, we do not see it.
Is it possible for it to be there at short separations?
Why do we see Vo constant? (Many others don’t)
We can give an answer to the first question:
2)( crystalpatch VVE
200 300 400 500 600 700
0
1
2
3
4
5
6
7
8
PC (
mP
a)
zmetal
(nm)
(V - Vo) = 5 mV
R
zzu
zz
RAVV
nu
nunuVVF
metal
i
metaliiAuo
nAuoe
)(1
)()(2
~sinh
cothcoth)(2
1
0
2
2
0 1000 2000 3000 400014.0
14.5
15.0
15.5
16.0
16.5
17.0
Vo (
mV
)
zmetal
(nm)
(a)
PASI- Frontiers on Casimir Physics Ushuaia, Argentina, 10/7/2012
Effects of environment: Vo
The capacitance is measured as arising from a contribution from the sphere and the plate plus a small, constant parasitic capacitance.
PASI- Frontiers on Casimir Physics Ushuaia, Argentina, 10/7/2012
Low temperature measurement
Setup schematic
LHe can
Springs
Low pressure He can
Magnet
Experimental space(with positioning stage)
Also at T = 0K dissipation will be reduced
PASI- Frontiers on Casimir Physics Ushuaia, Argentina, 10/7/2012
Low temperature measurement
Characterization
0 200 400 600 800 1000730
740
750
760
770
780
790
1.5 K 4.2 K 77 K
z = 550 nm
f r (H
z)
t (s)
When compared with previous measurements, the error in frequency is ~ 30 times larger at 1.5 K and ~ 40 times larger at 4.2 K and 77 K, yielding anincreased error in PC
lLC =(1240 +/- D) nm
lCW 1550 nm
x
Dx = zi
Readout
Measured error is ~ 5 nm.
Mechanical vibrations
And problems with the interferometer
PASI- Frontiers on Casimir Physics Ushuaia, Argentina, 10/7/2012
702 702.5 703 703.5 704 704.5 7050.01
0.1
1Room temperature
Frequency shifts, Q increases,
77K
f(Hz)
f(Hz)732 732.5 733 733.5 734 734.5 735
0.01
0.1
1
… Noise increases!
Low temperature measurement
PASI- Frontiers on Casimir Physics Ushuaia, Argentina, 10/7/2012
100 200 300 400 500 600 700 8000.0
0.2
0.4
0.6
0.8
1.0
1.2
77 K 4.2 K 1.5 K 300 KP
(P
a)
z (nm)
Low temperature measurement
Results
Measurements at 1.5 K seem to have the lowest noise
All data seem to coincide with the room temperature measurements
The error on the low T measurement, el (400 nm) = 5 mPa is larger than the difference between the Drude and plasma models of 2.4 mPa
This statement holds true at all temperaturesand separations investigated
PASI- Frontiers on Casimir Physics Ushuaia, Argentina, 10/7/2012
Summary
• Measurement of the Casimir force, done with different mechanical transducers
• Our MTO used as example for minimum detectable force, SNR, etc
• Description on system characterization
• Possibilities for the future?