Tests of Gravity and Gravitational PhysicsCase Western Reserve University, May 19 th, 2009....

Tests of Gravity and Gravitational Physics Case Western Reserve University, May 19th, 2009.

Micromechanical oscillators in the Casimir regime:A tool to investigate the existence of hypothetical forces

Ricardo S. DeccaDepartment of Physics, IUPUI


Daniel López Argonne National Labs

Ephraim Fischbasch Purdue University

Dennis E. Krausse Wabash College and Purdue University

Valdimir M. Mostepanenko Noncommercial Partnership “Scientific Instruments”, Russia

Galina L. Klimchitskaya North-West Technical University, Russia

Ho Bun Chan University of Florida

Jing Ding IUPUI

Hua Xing IUPUI

NSF, DOE, LANL

Collaborators

Funding


Jonathan L. Feng, Science 301, 795

(’03)

The strength of gravity for various numbers of large extra dimensions n, compared to the strength of electromagnetism (dotted)

Without extra dimensions, gravity is weak relative to the electromagnetic force for all separation distances.

With extra dimensions, the gravitational force rises steeply for small separations and may become comparable to electromagnetism at short distances.

What is the background?


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

• Non-retarded: van der Waals

• Retarded: Casimir

Attractive force!

4480a

hcPC

2a

k

EBE

BE

,

222

2

1 0||0 0|(|0 ½

0 0||0 0||0

k

No mode restriction on the outside


Importance of the Casimir effect

• Consequences in nanotechnology (MEMS and NEMS)“Long-range” interaction between moving partsPossibility of controlling the interaction by engineering materials

• Consequences in quantum field theoryThermal dependence

• Consequences in gravitation and cosmologyBackground to measure deviations from Newtonian potential at smallseparationsSource of “missing mass”


Yukawa-like potential

/21 1)( rer

mmGrV

Arises from very different pictures:

• Compact extra-dimensions

• Exchange of single light (but massive, =1/) bosonModuli; Graviphotons; Dilatons;Hyperphotons; Axions

PRL 98, 021101 (2007)

ff1 ff2

11 22

massboson =

range =

c

h


1 0

- 7

1 0

- 6

1 0

- 5

1 0

- 4

1 0

2 0

1 0

1 6

1 0

1 2

1 0

8

1 0

4

1 0

0

5

3

4

m e t e r s

1

Gauged Baryons

Exclu dedby

exper iments2

Gluon m odulus

Strange m od ulus

Yukawa-like potential

/21 1)( rer

mmGrV

Arises from very different pictures:

• Compact extra-dimensions

• Exchange of light (but massive, =1/) boson-Moduli-Graviphotons-Dilatons-Hyperphotons-Axions

How do we establish limits?

Measure background and subtract it

Get rid of the background altogether


Experimental setup

bzzzz goimetal


Dynamic measurements

z

F

I

b C

oor 2

222 1

CC

CC PRz

FERF

22

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)


Separation measurement

bzzzz goimetal

zg = (2389.6 ± 0.1) nm, interferometer

zi = ~(10000.0 ± 0.2) absolute interferometer

zo = (6960.1 ± 0.5) nm, electrostatic calibration

b = (210 ± 3) m, optical microscope

= ~(1.000 ± 0.001) rad

zg

zmeas 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

)

VAu

(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

)()( 2

zz

RVVF

metal

Auoe

Determine:• R • VAu

• o

• metalzOriginally using the whole expression,

lately using the 8 term fit found on Mohideen’s papers


Pressure determination

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

400 600 800 10000

50

100

150

200

250

PC (

mP

a)

z (nm)

R = 300 m R = 150 m


2

1

2

2221

12112

21

21

0

22

1

)(

1ln1ln2

)(

ps

zFvF

dpepsps

pspse

psps

pspspdR

czF

ii

CSi

iC

czp

czp

CS

Comparison with theory

vi: Fraction of the sample at separation zi

)(zFvF CSi

iC

AFM image of the Au plane


“Casimir-less” experiments

)()(

)(

32

1

4

GePtpAu

CrsAu

sAu

ddd

GeAup

dd

sCr

d

CrAuAus

ps

z

hyp

eeK

eeK

KRKeGF

Au Ge

Au

Si MTO

Al2O3 Al2O3Al2O3


Signal optimization:Work at o!!!

HeterodyneOscillate plate at f1, sphere at f2

such that f1 + f2 = fo

tfF

tftfe

ohyp

GeAu

z

2cos

2cos;2cos 21

)()(

)(

32

1

4

GePtpAu

CrsAu

sAu

ddd

GeAup

dd

sCr

d

CrAuAus

ps

z

hyp

eeK

eeK

KRKeGF



-40 -20 0 20 40

-40

-20

0

20

40

Q

ua

dra

ture

(fN

)

In Phase (fN)-40 -20 0 20 40

-40

-20

0

20

40

-40 -20 0 20 40

-40

-20

0

20

40

-40 -20 0 20 40

-40

-20

0

20

40

1 sec

1000 sec100 sec

10 sec

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

0.0 0.2 0.4 0.6 0.8 1.0-40

-20

0

20

40

t/Tr

0.1 s, 2000 s,

F (

fN)

z = 500 nm


Signal optimization:Work at o!!!

Oscillate plate at f1, sphere at f2

such that f1 + f2 = fo

0.1 1 10 100 10000.1

1

10

F

(fN

)

(s)

z = 150 nm z = 300 nm z = 500 nm Thermodynamic limit

F

tfF

tftfe

ohyp

GeAu

z

2cos

2cos;2cos 21

95% confidence level

Net force!



-4 -2 0 2 4

-4

-2

0

2

4

Sanity check: more samples!



1

2

3

4

567

1

2

3

4

567

200 300 400 500

F

pp(f

N)

z (nm)

F

1 0

- 7

1 0

- 6

1 0

- 5

1 0

- 4

1 0

2 0

1 0

1 6

1 0

1 2

1 0

8

1 0

4

1 0

0

5

3

4

m e t e r s

1

Gauged Baryons

Exclu dedby

exper iments2

Gluon m odulus

Strange m od ulus


Au

Background

Au Ge

Si MTO

Al2O3

Au

Motion not parallel to the axis(too small)

Step(0.1 nm needed)

Difference in electrostatic force(0.1 mV needed)

Difference in Au coating(unlikely)

Au coating not thick enough(unlikely)


-Reduce background

What next?

Si

Ti

Si

Si

Ti

Si

Si

Ti

Si Au

Si

Ti

Si Au

Glass

Au

Ti

Si Au

Glass

r/n

-Improve signal


1 0

- 7

1 0

- 6

1 0

- 5

1 0

- 4

1 0

2 0

1 0

1 6

1 0

1 2

1 0

8

1 0

4

1 0

0

5

3

4

m e t e r s

1

Gau ged Baryon s

Excludedby

exper im ents

Glu

on

mod

ulus

2

Str

ang

e m

od

ulu

s

Two orders of magnitude improvement

About five orders ofmagnitude improvement


Conclusions

• Most sensitive measurements of the Casimir Force and Casimir Pressure

• Unprecedented agreement with theory

First realization of a “Casimir-less” experiment

• Improvement of about three orders of magnitude in Yukawa-like hypothetical forces



Electrostatic force calibration

0 1000 2000 3000 400010

12

14

16

18

20

Vo (

mV

)

z (nm)

Vo must be constant as a function of separation…

… and time

0 10000 20000 3000010

11

12

13

14

15

16

17

18

19

20

Vo

(m

V)

t (s)


-Dark grey, Drude model approach-Light grey, Leontovich impedance approach

PRD 75, 077101



-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

Distance measurement

2arctan)(

fkNA

fG

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

CW 1550 nm (high coherence) in

x

Mirror (v ~ 10 m/s)

x = zi

Readout


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

CW 1550 nm (high coherence) in

x

Mirror (v ~ 10 m/s)

x = zi

Readout

-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’/(CW)2 Instead of 2x’/CW

(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

Distance measurement


bQf

TkF

r

B 12

serp

Sis L

Ewt

6

3

t

w

L

tEw Sir 3

2 3

w, t = 2m

40r

s

Experimental setup


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

400 600 800 10001E-15

1E-14

1E-13

1E-12

1E-11

F N

/Hz1/

2

Freq (Hz)

22

2

1

41

elth

el

o

B

FFb

AQ

Tk

bF

elF

thF

Experimental setup

Tests of Gravity and Gravitational PhysicsCase Western Reserve University, May 19 th, 2009....

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Transcript of Tests of Gravity and Gravitational PhysicsCase Western Reserve University, May 19 th, 2009....