EXPERIMENTS ON THE OPTICAL MODULATION OF THE CASIMIR FORCE UMAR MOHIDEEN Dept. of Physics &...

EXPERIMENTS ON THE OPTICAL MODULATION OF THE CASIMIR

FORCE

UMAR MOHIDEENUMAR MOHIDEEN

Dept. of Physics & Astronomy, Dept. of Physics & Astronomy,

University of CaliforniaUniversity of California

Riverside, CARiverside, CA

Motivation

• Demonstrate optical modulation of the Casimir force

• Probe puzzling applications of the Lifshitz theory for dielectric materials by taking a material from dielectric

phase to a metallic phase

1. H.B.G. Casimir , Proc. Kon. Nederl. Akad. Wet. 51 (1948) p. 793. Ideal Metal plates

2. E.M. Lifshitz, Sov. Phys., JETP (USA)2 (1956)p. 73. Real Materials

3. I.E. Dzyaloshinskii, E.M. Lifshitz, L.P. Pitaevskii, Sov. Phys. --USP (USA)4 (1961)p. 153…..….…

Theory of the Casimir Force

Lifshitz approach is general to non-ideal boundaries through use of and includes role of thermal photons

Lifshitz Formula

-Based on Maxwells Equation with a fluctuating E & H field from the zero point photons and thermal photons leads to surface currents-And the Fluctuation-Dissipation theorem

lk

l

lk

li

kk

llk

l

kll

kl

ik

qK

qKKr

Kq

KqKr

)(

)()(

)()(

)()()(

// ),(,),(

]})()(1ln[])()(1{ln[)1()( 2,

)2(

,

)1(

0 0

2,

)2(

//,

)1(

//021 zq

lll

zqlllBc

ll eKrKreKrKrdKKTRKzF

2/12)()(2/12 ])([,)( 2

2

2

2

KiKKqcl

kklcl

ll

R

z

R>>zR>>z

2

1

TlkB

l

2 At l=0, Matsubara Freqs.

Reflection Coeffs:

Puzzles in Application of Lifshitz Formula

For two metals and for large z (or high T), =0 term dominates

For ideal metals put ∞ first and l,0 next

1),0(),0( )()(// KrKr kk

lk

l

lk

li

kk

llk

l

kll

kl

ik

qK

qKKr

Kq

KqKr

)(

)()(

)()(

)()()(

// ),(,),(

Milton, DeRaad and Schwinger, Ann. Phys. (1978)

Recover ideal metal Casimir Result

For Real Metals if use Drude

and is the relaxation parameter

For =0, , only half the contribution even at z≈100 mm, where it should approach ideal behavior

Get large thermal correction for short separation distances z~100 nm

Entropy S≠0 as T0 (Third Law violation) for perfect lattice where (T=0)=0 If there are impurities (T=0) ≠0 , Entropy S=0 as T0

Bostrom & Serenelius, PRL (2000); Physica (2004)Genet, Lambrecht & Reynaud, PRA (2000). Geyer, Klimchitskaya & Mostepanenko, PR A (2003)Hoye, Brevik, Aarseth & Milton PRE (2003); (2005)Svetovoy & Lokhanin , IJMP (2003)

][1)(

)(

2

e

pi

2/1

*

2

)(m

nep

0),0(,1),0( )()(// KrKr kk

Puzzles in Applying Lifshitz Formula

][)()(

2

0

pii

Two Dielectric Surfaces

If the dielectric losses due to DC conductivity is included in the permittivity even a negligible amount)

p represents the carrier concentration and is the relaxation parameter

Same Puzzling questions as with metals

Geyer,Klimchitskaya&Mostepanenko, PRD (2005)

True for negligible conductivity!!!

One metal and one dielectric surface (Present Experiment):

If the dielectric losses due to DC conductivity in the permittivity then

0),0(,1),0( )()(// KrKr kk

Again same puzzles as with metals

Geyer, Klimchitskaya, Mostepanenko, IJMP A (2006)

True for negligible conductivity of dielectric !!!

OPTICAL MODULATION OF THE CASIMIR FORCE

Experimental History on Optical Modulation

W. Arnold, S. Hunklinger, and K. Dransfeld, Phys. Rev. B, 19, p. 6049 (1979)

1. Uncontrolled electrostatic systematic errors due to glass surface used.

2. Anamalous force decrease at short distances.

INSTRUMENT USED: ATOMIC FORCE MICROSCOPEINSTRUMENT USED: ATOMIC FORCE MICROSCOPE

Room Temperature10-7-10-8 Torr vacuum

Force Sensitivity 10-17 N possible

We achieve 10-13N

200 micron Polystyrene Sphere on AFM Cantilever

Gold coating = 82±2nmDiameter = 197.8±0.3 m

Optical Modulation of the Casimir ForceIn Semiconductors

Silicon

Plate LA

SE

R

e-h e-h e-h e-h e-h e-h e-h e-h e-h

Modulate Dielectric Constant of Boundary with Light

Gold Sphere

FCasimir

SAMPLE REQUIREMENTS

1. Need to increase Carrier Density from 1014 (impure dielectric) to 1019 /cc (metal)

----- Long Lifetimes + Thin Membranes

2. Flat bands at surface and no surface charge charge traps

control electrostatic forces

3. Need 2-3 micron thick samples to reduce transmitted photon force (Optical absorption depth of Silicon= 1 micron)

4. Allow excitation from bottom to reduce photon pressure systematics

LASER

Silicon Membrane

Membrane Fabrication

SiSiO2

Hydrogen Passivation

5 m Si <100> top layer400nm SiO2

600 m Si substraten~5x 1014 cm-3 p-type

Membrane Thickness=4±0.3m

ELECTROSTATIC CALIBRATION OF CANTILEVER

1

2

0 cothcothcsch2)(n

o nnnVVzF

V= voltage on plate V0= Residual voltage difference between uncharged sphere and plate

where cosh-1(1+z/R)

V

,300357,383084,5.90200,45.9592

,366.571,2375.22,18260.1,5.0

))(()()(2)(

6543

2101

1

20

200

CCCC

CCCC

VVzXcVVzFi

iRz

i

Apply to horizontal axis:z= zpiezo +z0- Deflection signal * m

1. zpiezo= Distance moved by piezo

2. z0 = Surface separation on contact = 97 nm

3. m= rate of change in distance due to cantilever tilt=137.2±0.6 nm per unit Def.

From fitting electrostatic curve

Larger applied V lead to earliercontact

0 1000 2000 3000 4000 5000 6000-0.15

-0.10

-0.05

0.00

0.05

0.10

Def

lect

ion

sign

al (

arb

itrar

y un

its)

Z (nm)

Calibrated interferometrically

Electrostatic Calibration, Measurement of Contact Separation and Deflection Coefficient

DC Voltages between 0.65 to -0.91 V + square pulses between 1.2to -0.6V applied to plate

A

OM

Functiongenerator 100Hz

Lock-in amplifier

Force difference

Vacuumchamber

Cantilever

Au Sphere

z

514nmAr laser

Optical filter Photo-

diodes

640 nm laser beam

Experimental Setup

Silicon membrane

)(])())[(()( 20

20 zFVVVVzXzF Cll

tot

Experimental Measurement of Modulation of Casimir Force due to Light

00 ,VV l= Residual voltage for light on and light off respectively

VV l , = Applied synchronous voltage pulse for light on and light off respectively

)()()( zFzFzF Cl

CC = Change in Casimir Force for light on and light off

Electric Force

5 ms wide Light Pulse on Membrane

Voltage Pulse Vl with V~V0 on Membrane

V

Vl VlVl

V V

Generate Parabolas in Vl at every z . Maxima of Parabola lead tolV0 =-.303±.002V

Repeat with different V and fixed Vl every z . 0V =-.225±.002V

)(])())[(()( 20

20 zFVVVVzXzF Cll

tot

Measurement of Potential Differences between surfaces

00 ,VV l= Residual voltage for light on and light off respectively

VV l , = Applied synchronous voltage pulse for light on and light off respectively

Electric Force

Generate Parabolas in Vl at every z . Maxima of Parabola lead tolV0 =-.303±.002V

Repeat with different V and fixed Vl every z . 0V =-.225±.002V

Fto

t

Vl

lV0

Blokland & Overbeek

TFCS,78

)(])())[(()( 20

20 zFVVVVzXzF Cll

tot Electric Force

lV0 =-.303±.002V

0V =-.225±.002V

Use

in

Apply small synchronous voltages Vl~ lV0 , V~V0

Measure Ftot and subtract out the Electric force to get FC , the change in the Casimir Force due to absorption of light

Fto

t

Vl

FC

100 200 300 400 500-4.0

-3.5

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0.5

9.3 mW Power

Dif

fere

nce

Cas

imir

Fo

rce

(pN

)

Separation Distance (nm)

Experimental Results

Average of 31 Repititions

0 1 2 3 4 5

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

Ch

ang

e o

f re

flec

tivi

ty (

arb

itra

ry u

nit

s)

Time (ms)

Excited Carrier Lifetime Measurement

Argon Laser

AOM

AOM Driver

Probe Laser

=1.3m Photo Diode

Function Generator

OscilloscopeSi Membrane

9.3mW =8.5 mW =0.38±0.03 ms

4.7mW =0.47±0.01 ms

Excited Carrier Density

Gaussian Beam Width =0.23±0.01mm

Recombination Rate measured earlier

2

4

d

Pn

eff

Excited Carrier Density

effP=Power in is uniformly distributed= 0.393 Ptotal

9.3 mW n=(2.1±0.4) 1019 /cc8.5 mW n=(2.0±0.4) 1019 /cc4.7 mW n=(1.4±0.3) 1019 /cc

,][][

)()()(

)(

)(

)( 22

p

pp

e

ep

Si ii

,)( 2/1*,

2),(

pe

pep

m

ne

,/10)4.01.4(,/10)4.07.3(

,/10)5.06.5(,/10)5.00.5(

,/10)6.07.5(,/10)5.01.5(

14)(,

14)(,

14)(,

14)(,

14)(,

14)(,

sradsrad

sradsrad

sradsrad

pcP

ecP

pbP

ebP

paP

eaP

Dielectric Permittivity of Silicon Membrane

11 12 13 14 15 16 170

5

10

15

20

25

9.3mW 8.5mW 4.7mW 0mW 0mW

Si(i

)

log[(rad/s)]

100 200 300 400 500-4.0

-3.5

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0.5

9.3 mW Power

Dif

fere

nce

Cas

imir

Fo

rce

(pN

)


Experimental Results

Average of 31 Repititions

100 200 300 400 500-4.0

-3.5

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0.5

9.3 mW Power DC conductivity Zero Temperature No DC conductivity

Dif

fere

nce C

asim

ir F

orc

e (

pN

)


Comparison of Experiment with Theory

100 200 300 400 500-4.0

-3.5

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0.5


Dif

fere

nce C

asim

ir F

orc

e (

pN

)



Inclusion of DC conductivity for high resistivity Si (dark phase) does not agree with results

100 200 300 400 500

-3.5

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0.5


Dif

fere

nce C

asim

ir F

orc

e (

pN

)



Experiment: Average of 41 Repititions


100 200 300 400 500

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0.5


Dif

fere

nce C

asim

ir F

orc

e (

pN

)



Experiment: Average of 33 Repititions


Experimental Errors

Systematic Errors

Force Calibration 0.6%

Instrument Noise 0.08 pN

Instrument Resolution 0.02 pN

Total Systematic Error @ 95% confidence

0.092 pN to 0.095 pN

Experimental Random Error @ 95% confidence(8.5 mW)

0.32 pN @ 100nm

0.23 pN @ 250nm

Roughness Effects

.....61

2

z

AFF cc

Roughness Correction

Roughness Amplitude A (measured with AFM)

~<1% effectMaradudin & Mazur, PR B (1981)Chen,Klimchitskaya,U.M, & Mostepanenko, PR A (2003)Genet, Lambrecht Neto & Reynaud, Euro P.L (2003)Emig, et al PRA (2003)

33

1

17

1

)2(0

)1(0 ,0)()(

k llikk vhHvhH

33

1

17

1

)2(0

)1(0 ),()(

k llkiClki

theorC hhHHzFvvzF

AFM Image of surface

Roughness Contribution to Force1.2% @ 100nm0.5% @ 150nm

Theoretical Errors

Uncertainty in Excited Charge

Carrier Concentration ±20% (lead to 12% error in Force)

±1 nm Uncertainty in Separation Distance

< 3% error in Force @100 nm

Light Pressure Force < 0.05-0.02 pN

100 200 300 400 5000.20

0.25

0.30

0.35

0.40

0.45

0.50

0.55

0.60

0.65

0.70

Exp

erim

enta

l Ran

do

m E

rro

r (p

N)


9.3 mW 8.5 mW 4.7 mW

100 200 300 400 5000.0

0.1

0.2

0.3

0.4

0.5

9.3 mW 8.5 mW 4.7 mW

Th

eore

tica

l Err

or

(pN

)


Experimental and Theoretical Errors as a Function of Distance

})]([)]([),()(min{ 22exp)2(exp theorC

tottC

tottheorC

tC

tot FFkFtotF

100 105 110 115 120 125 130 135 140 145 150-3.5

-3.0

-2.5

-2.0

-1.5

-1.0

D

iffe

ren

ce C

asim

ir F

orc

e (

pN

)


8.5 mW Power No DC conductivity DC conductivity

Comparison between Experiment and Theories Error bars represent 95% confidence level

Chen, Klimchitskaya, Mostepanenko, Mohideen PRB (2007)

100 105 110 115 120 125 130 135 140 145 150-3.5

-3.0

-2.5

-2.0

-1.5

-1.0

D

iffe

ren

ce C

asim

ir F

orc

e (

pN

)


8.5 mW Power No DC conductivity DC conductivity

Comparison between Experiment and Theories Error bars represent 95% confidence level



100 120 140 160 180 200 220 240-1.0

-0.5

0.0

0.5

1.0

1.5

Error Bar Data-Theory without DC Conductivity Data-Theory with DC Conductivity

Exp

eri

men

tal F

orc

e -

Th

eo

reti

cal F

orc

e (

pN

)


Power = 9.3 mW

100 120 140 160 180 200 220 240-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

Power = 4.7 mW

Exp

erim

enta

l Fo

rce

- T

heo

reti

cal F

orc

e (p

N)


100 120 140 160 180 200 220 240-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

Power = 8.5 mW

Exp

erim

enta

l Fo

rce

- T

heo

reti

cal F

orc

e (p

N)


Comparison of Difference Force (Theories -Expt.) with Total Errors at 95% Confidence Level


100 120 140 160 180 200 220 240-1.0

-0.5

0.0

0.5

1.0

1.5

Error Bar Data-Theory without DC Conductivity Data-Theory with DC Conductivity

Exp

eri

men

tal F

orc

e -

Th

eo

reti

cal F

orc

e (

pN

)


Power = 9.3 mW

100 120 140 160 180 200 220 240-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

Power = 4.7 mW

Exp

erim

enta

l Fo

rce

- T

heo

reti

cal F

orc

e (p

N)


100 120 140 160 180 200 220 240-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

Power = 8.5 mW

Exp

erim

enta

l Fo

rce

- T

heo

reti

cal F

orc

e (p

N)


Comparison of Difference Force (Theories -Expt.) with Total Errors at 95% Confidence Level



Conclusions

1. Optical Modulation of the Casimir Force was demonstrated.

2. The results have the correct distance dependence

3. Inclusion of DC conductivity in the Lifshitz formula for the high resistivity Si leads to disagreement with the experimental results

Acknowledgements

Experiment

F. Chen

Theoretical Analysis

V.M. Mostepanenko

G.L. Klimchitskaya

Research Funded by: National Science Foundation & US Department of Energy

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EXPERIMENTS ON THE OPTICAL MODULATION OF THE CASIMIR FORCE UMAR MOHIDEEN Dept. of Physics &...

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