Casimir force measurements using mechanical transducers: sensitivity, noise and background

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


• Dominant electronic force at small (~ 1 nm) separations

• Non-retarded: van der Waals• Retarded: Casimir

Attractive interaction

4480zhcPC

z

k

EBE

BE

,

222

21 0||0 0|(|0 ½

0 0||0 0||0

k

No mode restriction on the outside


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 theory400 600 800 1000

0

50

100

150

200

250

P C (m

Pa)

z (nm)

R = 300 m R = 150 m


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


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 (m

Pa)

z (nm)

R = 300 m R = 150 m


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)


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)



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 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


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



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



Effect of hydrogen-switchable mirrors on the Casimir forceIannuzzi, Lisanti, and CapassoProc. Nat. Acad. of Sci. 101, 4019



More yet!

Lateral Casimir effect

Measurements on corrugated samples Phase-change materials

Indium-Tin Oxide (ITO)



- 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



df

Qffiff

fS

oo

o

rms

0

2

22

2

2

ff

f oo

o

r

curr

Qffff

Qff

dfZ

kTQfRkT

ZQ

SNR

2222

2

44

NlEwt

s 48

3



Not considering intrinsic losses Newell(1986)

Optimal strategy: Decrease , increase Q, work at fo, and low T



What is ? 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)


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.



703.4 703.6 703.8 704.0 704.20.0

0.2

0.4

0.6

0.8

1.0

Nor

mal

ized

am

plitu

de

Freq (Hz)

Hzrad10 9

HzfNFF

b

AQTk

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



Measurement of the interaction

zF

Ib C

oor 2

222 1

CC

CC PRzFERF

22


zF

Ib C

oor 2

222 1

CC

CC PRzFERF

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).




zF

Ib C

oor 2

222 1

C

CCC PR

zFERF

22

Errors Minimum values

Frequency: 6 mHz ~28 mHz (at 750 nm)b2/I: 0.0005 g-1 1.2432 g-1

R: 0.2 m 150 m

400 600 800 10000

50

100

150

200

250

P C (m

Pa)

z (nm)

R = 300 m R = 150 m

100 200 300 400 500 600 700 800

-2

0

2

4

6

8

10

P (m

Pa)

z (nm)


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) m, optical microscope

= ~(1.000 ± 0.001) rad

zg

zo is determined using a known interaction

zi, are measured for each position


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 5.00100125150175200225250275300325350

F e (pN

)

zmetal (m)

V = 0.35 V

V = 0.27 V

Rzzu

zzRAVV

nununuVVF

metal

i

metaliiAuo

nAuoe

)(1

)()(2

~sinh

cothcoth)(2

1

0

2

2

metalz




-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




0 1000 2000 3000 400010

12

14

16

18

20

V o (mV)

z (nm)Vo is constant as a function of separation…

… and time

0 10000 20000 300001011121314151617181920

V o (mV)

t (s)

Otherwise, Vo needs to be determined at each point

10 x 10 grid, 5 m pitch




Rzzu

zzRAVV

nununuVVF

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 Fe for the optimal and oneoff by 1.5 nm

z



-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

fNAf

G arctan)(

lLC =(1240 +/- ) nm (low coherence),

lCW 1550 nm (high coherence) in

x

Mirror (v ~ 10 m/s)

x = zi

Readout



lLC =(1240 +/- ) nm (low coherence),

lCW 1550 nm (high coherence) input

x

Mirror (v ~ 10 m/s)

x = zi

Readout(independent at each wavelength)

-Phases obtained doing a Hilbert transform of the amplitude-Changes in about 2 nm) give different curves. Intersections provide x-Quite insensitive to jitter. Only 2x’/(lCW)2 Instead of 2x’/lCW

(Yang et al., Opt. Lett. 27, 77 (2005)

)2(mod)()(

int4

21

54

l

xxS

SSz

DDphase

phasefringeCW

i

CWLCD

0.30.40.50.60.70.80.91.01.11.21.31.41.5

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 sig

nal

t (s)



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 m2)~ 20 nmpp


Sample characterization


2/32 )(4)(

pp

TT

T

eV)1.09.8( p

- vs T and spectroscopic ellipsometry (190 nm to 830 nm) used to determine optical properties.

-Both methods indicate a rather good Au sample



100 1000-60

-50

-40

-30

-20

-10

0

10

RE

l (nm)10 100 1000

-2

0

2

4

6

8

10

IM

l (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.



022

)(''21)( dxx

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)



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 (P

a)

zmetal (nm)

Both samples on the left panel. Difference between them on the right one



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


Finite conductivity and finite temperature


2222 4

c

Tlkkq Bl



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

2

2

2

1)(

)(1)(

p

p

i


- Dark grey, Drude model approach-Light grey, plasma model approach

PRD 75, 077101



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

P C (m

Pa)

zmetal (nm)

(V - Vo) = 5 mV

Rzzu

zzRAVV

nununuVVF

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

V o (m

V)

zmetal (nm)

(a)


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.


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



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 (Hz)

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 +/- ) nm

lCW 1550 nm

xx = zi

Readout

Measured error is ~ 5 nm.

Mechanical vibrations

And problems with the interferometer


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!



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

(Pa)

z (nm)


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


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?

Casimir force measurements using mechanical transducers: sensitivity, noise and background

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