precise measurements of the casimir force: experimental...

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


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


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


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


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)


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


AFM measurements


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


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.


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)


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


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)


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


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



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




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)




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


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)


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


Finite conductivity and finite temperature


2222 4

⎟⎟⎠

⎞⎜⎜⎝

⎛+= ⊥ c

Tlkkq Bl h

π

10 100 1000-2

0

2

4

6

8

10

ε IM

λ (nm)



Bentsen et al., J. Phys. A (2005)

2

2

2

1)(

)(1)(

ωω

ωε

γωωω

ωε

p

p

i

−=

+−=


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)


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)


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


• “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


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.

precise measurements of the casimir force: experimental...

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