precise measurements of the casimir force: experimental...
Post on 24-Feb-2019
214 Views
Preview:
TRANSCRIPT
New Frontiers in Casimir Force Control Santa Fe, New Mexico, September 28, 2009
Precise Measurements of the Casimir Force:Experimental Details
Ricardo S. DeccaDepartment of Physics, IUPUI
New Frontiers in Casimir Force Control Santa Fe, New Mexico, September 28, 2009
Daniel López Argonne National LabsEphraim 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 Lab.Peter Milonni Los Alamos National Lab.
NSF, DOE, LANL, DARPA
Funding
Collaborators
New Frontiers in Casimir Force Control Santa Fe, New Mexico, September 28, 2009
Motivation• Precise measurements of the Casimir force
-Background for hypothetical forces-Allows for comparison with theory-Temperature dependence and effects on nanosystems
400 600 800 10000
50
100
150
200
250
PC (m
Pa)
z (nm)
R = 300 μm R = 150 μm
New Frontiers in Casimir Force Control Santa Fe, New Mexico, September 28, 2009
Outline
• Experimental setup, sample preparation, and characterization
• Measurement of the interaction
• Measurement of the separation dependence
• Comparison with theory
• Proposed measurements to see the effects of geometry
• Summary
New Frontiers in Casimir Force Control Santa Fe, New Mexico, September 28, 2009
Experimental setup
Θbzzzz goimetal −−−=In our last measurements we have changed the setup, the sphere is on the oscillator, the plate is on top
-Larger sample, requires different deposition.
-Measurements done in vacuum at room temperature, in an oil-free chamber.
MEMS plate: 500µm x 500µmPlate thickness: 3.5 µmSpring lengths: 500 µmKtorsion ~ 10-10 Nm/radSphere radii: 10 µm – 150 µmResonance frequency ~ 1000 HzQuality factor ~ 10000 (@ 10-6 Torr)
New Frontiers in Casimir Force Control Santa Fe, New Mexico, September 28, 2009
Sample preparation and characterization
-Au on the sapphire sphere is deposited by thermal evaporation.
-Au on the oscillator is also deposited by thermal evaporation
-In new, larger 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 is mounted into the system, baked to ~ 60 oC for ½ hour.
(10x10 μm2)~ 20 nmpp
New Frontiers in Casimir Force Control Santa Fe, New Mexico, September 28, 2009
2/32 )(4)(
pp
TT
Tωτω
πρ ∝⋅
=
eV)1.09.8( ±=pω
Resistivity and spectroscopic ellipsometry
-R vs T and spectroscopic ellipsometry (190 nm to 830 nm) used to determine ωp.
-Both methods indicate a rather good Au sample
New Frontiers in Casimir Force Control Santa Fe, New Mexico, September 28, 2009
100 1000-60
-50
-40
-30
-20
-10
0
10
ε RE
λ (nm)10 100 1000
-2
0
2
4
6
8
10
Resistivity and spectroscopic ellipsometry
ε IM
λ (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, giving similar results. Palik values are used on the rest of this presentation.
New Frontiers in Casimir Force Control Santa Fe, New Mexico, September 28, 2009
Pressure measurements
⎟⎟⎠
⎞⎜⎜⎝
⎛∂
∂−=
zF
Ib C
oor 2
222 1
ωωω
CC
CC PRz
FERF ×=∂
∂⇒×= ππ 22
400 600 800 10000
50
100
150
200
250
PC (m
Pa)
z (nm)
R = 300 μm R = 150 μm
100 200 300 400 500 600 700 800
-2
0
2
4
6
8
10
ΔP
(mPa
)
z (nm)
New Frontiers in Casimir Force Control Santa Fe, New Mexico, September 28, 2009
Pressure determination⎟⎟⎠
⎞⎜⎜⎝
⎛∂
∂−=
zF
Ib C
oor 2
222 1
ωωω
CC
CC PRz
FERF ×=∂
∂⇒×= ππ 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 (Hz)
t (s)
z= 550 nmfo=713.250 Hz
Determined by:-Looking into the response of the oscillator in the thermal bath -Inducing a time dependent separation between the plate and the sphere
New Frontiers in Casimir Force Control Santa Fe, New Mexico, September 28, 2009
Pressure measurements
⎟⎟⎠
⎞⎜⎜⎝
⎛∂
∂−=
zF
Ib C
oor 2
222 1
ωωω
CC
CC PRz
FERF ×=∂
∂⇒×= ππ 22
Errors Minimum values
Frequency: 6mHz ~28 mHz (at 750 nm)R: 0.2 μm 150 μmb2/I: 0.0005 μg-1 1.2432 μg-1
Errors:Random: 0.46 mPa (162 nm) Systematic: 2.12 mPa (162 nm)
0.11 mPa (300 nm) 0.44 mPa (300 nm)
New Frontiers in Casimir Force Control Santa Fe, New Mexico, September 28, 2009
Separation measurement
Θ−−−= bzzzz goimetal
zg = (2172.8 ± 0.1) nm, interferometer
zi = ~(12000.0 ± 0.2) absolute interferometer
zo = (8162.3 ± 0.5) nm, electrostatic calibration
b = (207 ± 2) μm, optical microscope
Θ = ~(1.000 ± 0.001) μrad
zg
zo is determined using a known interaction
zi, Θ are measured for each position
New Frontiers in Casimir Force Control Santa Fe, New Mexico, September 28, 2009
Separation measurementElectrostatic force calibration
-15 -10 -5 0 5 10 15 20 250.0
0.2
0.4
0.6
0.8
1.0
Θ (μ
rad)
VAu (mV)
z = 3 μmz = 5 μm
3.00 3.25 3.50 3.75 4.00 4.25 4.50 4.75 5.00100125150175200225250275300325350
F e (pN
)
zmetal (μm)
ΔV = 0.35 V
ΔV = 0.27 V
Rzzu
zzRAVV
nununuVVF
metal
i
metaliAuo
nAuoe
)(1
)()(2
~sinh
cothcoth)(2
17
0
2
2
++=
⎟⎟⎠
⎞⎜⎜⎝
⎛
+−−
−−−=
−
∑
∑
πε
πε
metalz
New Frontiers in Casimir Force Control Santa Fe, New Mexico, September 28, 2009
Separation measurement
Electrostatic force calibration
-15 -10 -5 0 5 10 15 20 250.0
0.2
0.4
0.6
0.8
1.0
Θ (μ
rad)
VAu (mV)
z = 3 μmz = 5 μm
z = 3.5 μm
New Frontiers in Casimir Force Control Santa Fe, New Mexico, September 28, 2009
Separation measurement
Electrostatic force calibration
0 1000 2000 3000 400010
12
14
16
18
20
V o (mV)
z (nm)
0 10000 20000 300001011121314151617181920
Vo (m
V)
t (s)
… and time
Vo must be constant as a function of separation…
Otherwise, Vo needs to be determined at each point 10 x 10 grid, 5 μm pitch
14.5 15.0 15.5 16.00
20
40
60
80
100
120
140
Num
ber
Vo (mV)
New Frontiers in Casimir Force Control Santa Fe, New Mexico, September 28, 2009
Separation measurement
Electrostatic force calibration
Rzzu
zzRAVV
nununuVVF
metal
i
metaliiAuo
nAuoe
)(1
)()(2
~sinh
cothcoth)(2
1
0
2
2
++=
⎟⎟⎠
⎞⎜⎜⎝
⎛
+−−
−−−=
−
=∑
∑
πε
πε
z
-After measuring the deflection (expressed as force here), we adjust for the unknown separation.-The figure shows the ΔFe for the optimal and oneoff by 1.5 nm-The error in the force associated with the error in Vo is < 1 fN.
Rzzu
zzRAVV
nununuVVF
metal
i
metaliAuo
nAuoe
)(1
)()(2
~sinh
cothcoth)(2
17
0
2
2
++=
⎟⎟⎠
⎞⎜⎜⎝
⎛
+−−
−−−=
−
∑
∑
πε
πε
New Frontiers in Casimir Force Control Santa Fe, New Mexico, September 28, 2009
100 200 300 400 500 600 700 800
-2
0
2
4
6
8
10
ΔP
(mPa
)
z (nm)100 200 300 400 500 600 700 800
-2
0
2
4
6
8
10
Equivalent PC measurement
ΔP
(mPa
)
z (nm)
New sample (September 2009) Old data (2005)
New Frontiers in Casimir Force Control Santa Fe, New Mexico, September 28, 2009
vi: Fraction of the sample at separation zi
)(zFvF CSi
iC ∑=
Roughness corrections
Roughness corrections are ~0.5% to the Casimir force at 160 nm
Comparison with theory
New Frontiers in Casimir Force Control Santa Fe, New Mexico, September 28, 2009
Finite conductivity and finite temperature
Comparison with theory
2222 4
⎟⎟⎠
⎞⎜⎜⎝
⎛+= ⊥ c
Tlkkq Bl h
π
10 100 1000-2
0
2
4
6
8
10
ε IM
λ (nm)
New Frontiers in Casimir Force Control Santa Fe, New Mexico, September 28, 2009
Comparison with theory
Bentsen et al., J. Phys. A (2005)
2
2
2
1)(
)(1)(
ωω
ωε
γωωω
ωε
p
p
i
−=
+−=
New Frontiers in Casimir Force Control Santa Fe, New Mexico, September 28, 2009
Pressure determination
-Dark grey, Drude model approach-Light grey, impedance approach
PRD 75, 077101
There is a significant issue: Drude does not agree with the data-Experimental problem?-Theoretical problem?-Theory not applied to the right experiment?
Theoretical errors:-Sample dependence: 0.5%-Separation dependence: 1.5% (162 nm)
0.32%(750 nm)
~19 mPa @162 nm (Exp: ~2.5 mPa @162 nm)
New Frontiers in Casimir Force Control Santa Fe, New Mexico, September 28, 2009
Geometrical effects
Real-time manipulation
• Integration of nanostructure with MEMS• Displacement ~ 500nm• Precise control of motion (± 1nm)• Shielded surfaces (fringe fields)
Dynamically deformable nanostructure
“Role of surface plasmons in the Casimir effect”, F. Intravaia et al., PRA 76 (2007)
New Frontiers in Casimir Force Control Santa Fe, New Mexico, September 28, 2009
Metallic nanostructures
• Electroplating process• HSQ molds (highest resolution resist)• 100keV electron beam lithography tool
• pattern thick resist (1 µm)• large depth of focus• small electron scattering
Geometrical effects
New Frontiers in Casimir Force Control Santa Fe, New Mexico, September 28, 2009
• “Role of surface plasmons in the Casimir effect”, F. Intravaia et al., PRA 76 (2007)• Metallic nanowire (w < λp) close to a flat metallic surface
attractive repulsive repulsive
negligible negligible
Net contribution from the first 5 plasmonic modes is repulsive for d ≥200nmNet contribution from the first 5 plasmonic modes is repulsive for d ≥200nm
Dimension < 100nmAspect ratio > 5:1
Geometrical effects
New Frontiers in Casimir Force Control Santa Fe, New Mexico, September 28, 2009
Summary
• Precise experiments of the Casimir force between Au-Au surfaces
• Good agreement with plasma modelDifferences with Drude model cannot be explained as a problem in the separation measurement, or the Au layer properties. It appears that any model with a finite relaxation time will give discrepancies when comparing with the Casimir force. Why do Casimir modes decouple from the dissipative part?
• Geometrical effectsAn innovative MEMS that allows to modify the geometry in situ is being designed and tested. This system will be used to investigate the plasmonic contributions to the Casimir effect.
top related