corsini casimir

7/23/2019 Corsini Casimir

1/19

The Casimir effectThe Casimir effectPhysics 250 Spring 2006Physics 250 Spring 2006

Dr BudkerDr BudkerEric CorsiniEric Corsini

CasimirCasimir

Patron Saint of PolandPatron Saint of Poland

and Lithuaniaand Lithuania (March 4(March 4thth))

Hendrik Casimir (1909-2000)Hendrik Casimir (1909-2000)

utch theoretical !h"sicistutch theoretical !h"sicist

Predicted the #force fromPredicted the #force fromno$here% in 194&no$here% in 194&


2/19

AstractAstract

The Casimir !orceThe Casimir !orce

The Casimir Force was first predicted byThe Casimir Force was first predicted by Dutch theoretical physicist HendrikDutch theoretical physicist HendrikCasimir and was first effectively measured by Steve Lamoreaux in 1!"Casimir and was first effectively measured by Steve Lamoreaux in 1!"

The boundary conditions imposed on the electroma#netic fields by metallicThe boundary conditions imposed on the electroma#netic fields by metallicsurfaces lead to a spatial redistribution of the $ero%point ener#y mode densitysurfaces lead to a spatial redistribution of the $ero%point ener#y mode densitywith respect to free space& creatin# a spatial #radient of the $ero%point ener#ywith respect to free space& creatin# a spatial #radient of the $ero%point ener#y

density and hence a net force between the metals" That force is the mostdensity and hence a net force between the metals" That force is the mostsi#nificant force between neutral ob'ects for distances (1))nmsi#nificant force between neutral ob'ects for distances (1))nm

*ecause of that dependence on boundary conditions& the Casimir Force*ecause of that dependence on boundary conditions& the Casimir Forcespatial dependence and si#n can be controlled by tailorin# the shape of thespatial dependence and si#n can be controlled by tailorin# the shape of theinteractin# surfaces"interactin# surfaces"

+n this presentation + briefly review the formalism pertainin# to the $ero point+n this presentation + briefly review the formalism pertainin# to the $ero point

ener#y and summari$e the recent experiment *y *ell and Lucent labs&ener#y and summari$e the recent experiment *y *ell and Lucent labs&investi#atin# the effect of the Casimir Force on a dynamic system"investi#atin# the effect of the Casimir Force on a dynamic system"


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"rigin of the Casimir force"rigin of the Casimir forceThe short ans#erThe short ans#er

The vacuum cannot have absolute $ero ener#yThe vacuum cannot have absolute $ero ener#y

that would violatethat would violateHeisenber# uncertainty principle"Heisenber# uncertainty principle"


4/19

The $ong ans#erThe $ong ans#er %green& ook approach%green& ook approach

,e show a 1%1 relationship- SH. /,e show a 1%1 relationship- SH. /E&ME&MFieldField

0axwell Coulomb #au#e0axwell Coulomb #au#e 22"34)5"34)5

2no local current6char#e52no local current6char#e5

7eneral sol to wave e8uation7eneral sol to wave e8uation

ThenThen

)9

99

=

t

5:52:5221

5&2

5::21

5&2

;5"2;5"2

;5"2;5"2

rkirki

trkitrki

etCetCV

tr

eCeCV

tr

+=

+=

2+m?==5>2@e?A=9

152

B

1 999

999 tCtC

cdVBE SubstituteV += +=


5/19

Consider the S'"Consider the S'"

ote-ote-

Then there is a 1%1 relationThen there is a 1%1 relation

+f we set+f we set ooto be such thatto be such that

Then& per modeThen& per mode EEwe have-we have-

52999

99

1&-@e999

PQqm

m

pSHO

Qm

qPmpscale

SHO += +===

5sin2525&cos252 ttPttQthen

dt

dQP

dt

dqmp oo ====

525>2+m?

525>2@e?

tPtC

tQtC

=

=

5252

9

iPQctC +=

529

99

PQME +=


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(e can then app$y the S'" mechanics(e can then app$y the S'" mechanics

to the E)* fie$dto the E)* fie$d

Gi#enstates =nGi#enstates =n

Gi#envalues GGi#envalues Gnn4 I4 IEE2n2n11669955

+n particular G+n particular Goo4 I4 IEE69 J ) for mode69 J ) for mode EE

HoweverHowever

=

=196


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But #e are on$y concerned in theBut #e are on$y concerned in the

difference in energy densitydifference in energy density *etween two conductin# parallel*etween two conductin# parallel

plates only virtual photons whoseplates only virtual photons whosewavelen#ths fit a whole numberwavelen#ths fit a whole numberof times between the platesof times between the plates

contribute to the vacuum ener#ycontribute to the vacuum ener#ythere is a force drawin# thethere is a force drawin# the

plates to#ether"plates to#ether"

1)nm52dob'ectsneutralobetween twforceStron#est

1atmKacal1)Kressure1)nmd

Kascal1)KressureorC1)m1d&1cm3

d

3

LB)

c

!

M%N%9


8/19

+otes+otes

*osons*osons attractive Casimir forceattractive Casimir force

FermionsFermions repulsive Casimir forcerepulsive Casimir force

,ith supersymmetry there is a fermion for,ith supersymmetry there is a fermion foreach *osoneach *oson no Casimir effect"no Casimir effect"

Hence if supersymmetry exists it must be aHence if supersymmetry exists it must be a

broken symmetrybroken symmetry


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Casimir !orceCasimir !orce

!rom theory to e,periment!rom theory to e,periment

Kredicted by Dutch physicist Hendrick Casimir in 1B"Kredicted by Dutch physicist Hendrick Casimir in 1B" First attempt to measure the Casimir Force- 1!B by 0"O"SparnaayFirst attempt to measure the Casimir Force- 1!B by 0"O"Sparnaay

% Psed the attraction between a pair of parallel plates"% Psed the attraction between a pair of parallel plates"

% *ut irreducible systematic errors% *ut irreducible systematic errors measurements had a 1))Qmeasurements had a 1))Quncertainty& 2but it fit the expectations5uncertainty& 2but it fit the expectations5

Sparnaay #ave three #uidelinesRSparnaay #ave three #uidelinesR% The plates should be free of any dust or debris& with as little surface rou#hness as possible% The plates should be free of any dust or debris& with as little surface rou#hness as possible

% Static electrical char#es should be removed 2electrostatic force can easily swamp the weak Casimir% Static electrical char#es should be removed 2electrostatic force can easily swamp the weak Casimirattraction5"attraction5"

% The plates should not have different surface potentials% The plates should not have different surface potentials

% @ef- 0easurements of 3ttractive Forces *etween Flat Klates% @ef- 0easurements of 3ttractive Forces *etween Flat Klates

2Sparnaay& 1!B5 Khysica&2Sparnaay& 1!B5 Khysica& 2424!"#$%!"#$%

9nd attempt and first successful results- 1U by Steven Lamoreaux- % +n9nd attempt and first successful results- 1U by Steven Lamoreaux- % +na#reement with theory to within uncertainty of !Q"a#reement with theory to within uncertainty of !Q" Several other successful experiments since"Several other successful experiments since"


10/19

Steve LamoreauxSteve Lamoreaux

2Pniversity of2Pniversity of,ashin#ton V,ashin#ton VSeattle5Seattle5

0easured the0easured theCasimir forceCasimir force

between a cmbetween a cmdiameter sphericaldiameter sphericallens and an opticallens and an optical8uart$ plate about8uart$ plate about9"! cm across& both9"! cm across& bothcoated with coppercoated with copper

and #old" The lensand #old" The lensand plate wereand plate wereconnected to aconnected to atorsion pendulum"torsion pendulum"

Steven LamoreauxW experimental set upSteven LamoreauxW experimental set up


11/19

There are only a few do$en published experimentalmeasurements of the Casimir force

*ut there are more than 1))) theoretical papers 3nd citations of CasimirWs 1B paper are #rowin#

exponentially"


12/19

Effects of edgesEffects of edgesshape of decay function is strong$y dependent on si-e and separation of surfacesshape of decay function is strong$y dependent on si-e and separation of surfaces

ref.http.//imagesgoog$ecom/imgres1ref.http.//imagesgoog$ecom/imgres1

imgur$http.//###srhamacuk/yr3pasr/pro4ect/casimir/currentthum4pg)imgrefur$http.//###srhamacuk/yr3pasr/pro4ect/casimir/)h25)#25)s-3)tnidBuy27D8+9E:i6*.)tnh0;)tn#0;)h$en)start20)pre:/imaimgur$http.//###srhamacuk/yr3pasr/pro4ect/casimir/currentthum4pg)imgrefur$http.//###srhamacuk/yr3pasr/pro4ect/casimir/)h25)#25)s-3)tnidBuy27D8+9E:i6*.)tnh0;)tn#0;)h$en)start20)pre:/ima

ges


13/19

Krior experiments have focused on static FKrior experiments have focused on static FCC

and adhesion Fand adhesion FCC This experiment investi#ates the dynamicThis experiment investi#ates the dynamic

effect of Feffect of FC-C- 3 HookeWs law sprin# provides the restorin#3 HookeWs law sprin# provides the restorin#

forceforce FFCCbetween a movable plate and a fixedbetween a movable plate and a fixed

sphere provides the anharmonic forcesphere provides the anharmonic force

For $dFor $dC@TCAC@TCAsystem is bistablesystem is bistable KG has a local #lobal minimaKG has a local #lobal minima FFCCmakes the shape of local min anharmonicmakes the shape of local min anharmonic

ote-ote- chosin# a sphere as one of thechosin# a sphere as one of thesurfaces avoids ali#nment problemssurfaces avoids ali#nment problems

The Casimir force. !The Casimir force. !CC

on *icroe$ectromechanica$ systems *E*Son *icroe$ectromechanica$ systems *E*SP@. ' B Chan et a$ Be$$ a ) ucent Tech Pu$ished "ct 200P@. ' B Chan et a$ Be$$ a ) ucent Tech Pu$ished "ct 200

0ock set up0ock set up

Y4 )")1 m%1Y4 )")1 m%1Sphere radius 4 1))Sphere radius 4 1))ZZmm

ddE78B@8*E78B@8* 4 )nm4 )nm

M

M

d

@

MU)

c

d

3

B)

c

== FF to


14/19

The actua$ set upThe actua$ set up .scillator- M"!%mm%thick& !))%mm.scillator- M"!%mm%thick& !))%mm9&9& #old plated 2on top5& polysilicon plate#old plated 2on top5& polysilicon plate

@oom temp V 1 milli Torr@oom temp V 1 milli Torr

3 drivin# volta#e3 drivin# volta#e VV3C3Cexcites the torsional mode of oscillationexcites the torsional mode of oscillation

22VVDC1DC1- bias5- bias5

[[dc-dc-bias to one of the two electrodes under the plate to lineari$e the volta#ebias to one of the two electrodes under the plate to lineari$e the volta#e

dependence of the drivin# tor8uedependence of the drivin# tor8ue [[DC9-DC9- detection electrodedetection electrode

ote- amplitude increases with [ote- amplitude increases with [3C3C4 M!"4 M!"ZZ[ to N9"![ to N9"! ZZ[[

Torsional Sprin# constant- k49"1 1)%B rad%1Torsional Sprin# constant- k49"1 1)%B rad%1Fund res" Fre8" 4 9N!M"N H$Fund res" Fre8" 4 9N!M"N H$

+ 4 N"1 1)%1N k#m+ 4 N"1 1)%1N k#m99

System behaves linearly w6o sphereSystem behaves linearly w6o sphere


15/19

Add a go$d p$ated po$ystyrene sphere radius 200Add a go$d p$ated po$ystyrene sphere radius 200FFmm

G8uation of motionG8uation of motion

Fb

Fb

torquedri'in(o)amplitude

coe)dampin(

k

approachclosesto)ancedist***

*F

t*F

btoup*aboutpande+,a-lorb*F

CC

o

o

U&

9

&

5219)

@c52

cos5>2?9

52

M

1

1

M

M99

9

M

=

=

=

==

=+

=

=++

>91? 9)

9

)1

M9

F

b

andintermsthe(norin(

C

=

Fre8 shiftFre8 shift ~ F~ FCCgradient (Fgradient (FCC))

- e>ui$ dist sphGp$ate #/o !C

Due to !C

Due to E$ectrostatic force


16/19

!!CC anharmonic eha:ioranharmonic eha:ior

+- Sphere far away+- Sphere far away normal resonnancenormal resonnance Sphere is moved closer to plate +Sphere is moved closer to plate + +[+[

@es" fre8 shifts as per model@es" fre8 shifts as per model 3t close distance3t close distance hysteresis occurshysteresis occurs

ie- amplitude 3 has up to M roots-ie- amplitude 3 has up to M roots-

linearit-non*escharacteri

..

=

=+

9

M

11

9

1

9

999

1

9

19

!

B

M

>?2

>

9

1?9

)

9

)1

Fb C

=


17/19

.r we can keep a constant excitation fre8.r we can keep a constant excitation fre8

29NBH$5& vary sphere%plate distance& and29NBH$5& vary sphere%plate distance& and

measure amplitude"measure amplitude"

Fre8 ( resonant fre8 Fre8 resonant fre8

Depends on history


18/19

s repu$si:e Casimir force physica$ 1s repu$si:e Casimir force physica$ 1

Klate%plate- attractiveKlate%plate- attractive

Sphere%plate- attractiveSphere%plate- attractive

Concave surface V concave surface- can beConcave surface V concave surface- can berepulsive or attractive dependin# on separationrepulsive or attractive dependin# on separation

pendulumpendulum

Klate%plate with specific dielectric propertiesKlate%plate with specific dielectric propertiescan be repulsivecan be repulsive nanotech applicationsnanotech applications


19/19

@eferences@eferences

+on$inear *icromechanica$ Casimir "[email protected] M1 .ctober 9))1

H" *" Chan&; [" 3" 3ksyuk& @" " Yleiman& D" O"

*ishop& and Federico Capasso\Bell /aboratories0/ucent ,echnolo(ies0 Murra- Hill0 1e2 3erse- 45% Ph-sics 6orld article 7Sept 84489 : .uthor;.strid

/ambrecht

@GK.@TS . [email protected]@GSS + KH]S+CS@ep" Kro#" Khys" 6I 29))!5 9)1V9MU

Ste'en /amoreau+

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