Short-range tests of gravity and the Casimir effect Astrid - - PowerPoint PPT Presentation

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Short-range tests of gravity and the Casimir effect Astrid - - PowerPoint PPT Presentation

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Short-range tests of gravity and the Casimir effect Astrid Lambrecht Laboratoire Kastler Brossel, Paris (ENS, CNRS, U. Pierre et Marie Curie) http://www.lkb.ens.fr/Vacuum EU Framework 6 project Workshop on Advances in Precision Tests and

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Workshop on Advances in Precision Tests and Experimental Gravitation in Space, Florence 2006

Short-range tests of gravity and the Casimir effect

Astrid Lambrecht Laboratoire Kastler Brossel, Paris (ENS, CNRS, U. Pierre et Marie Curie)

http://www.lkb.ens.fr/Vacuum

EU Framework 6 project NEST (New Emerging Science & Technology)

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Workshop on Advances in Precision Tests and Experimental Gravitation in Space, Florence 2006

Motivation : Tests of the Newtonian law

New hypothetical forces (cf. G.Veneziano’s and G. Tino’s talk)

Generic representation : Yukawa + Newtonian potential Modification of Newtonian law between pointlike masses

( ) ( ) ( )

r V r V r V

Y N

+ =

( ) ( )

) / exp( λ α r r V r V

N Y

− =

( )

r M M G r V

N N 2 1

− =

( ) ( )

) / exp( 1 λ λ α r r r F r F

N Y

− ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + =

The Search for Non-Newtonian Gravity, E. Fischbach & C. Talmadge (1998)

( )

2 2 1

r M M G r F

N N

− =

( ) ( ) ( )

r F r F r F

Y N

+ =

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Workshop on Advances in Precision Tests and Experimental Gravitation in Space, Florence 2006

Courtesy : J. Coy, E. Fischbach, R. Hellings,

  • C. Talmadge, and E. M. Standish (2003)

Measurement give constraints in the the plane(

)

α λ, Open window at short distances…

Satellites Laboratory Geophysical LLR Planetary

How to test the Newtonian law ?

The Search for Non-Newtonian Gravity, E. Fischbach & C. Talmadge (1998)

m 10 3

−

< λ and at long distances

(cf. Marc Jaekel’s talk)

m 1016 > λ

Log10λ (m) Log10α

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Workshop on Advances in Precision Tests and Experimental Gravitation in Space, Florence 2006

Test at short distances

( )

) / ( 1

2 1

λ α r e r M GM − +

Gravity measurements at millimetric distances

λ ≤30µm : comparison

between experimental results and theoretical predictions of the Casimir force

  • E. Adelberger et al Ann. Rev. Nucl. Part. Sci. (2003) hep-ph/0307284

Log10λ (μm) Log10α

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Workshop on Advances in Precision Tests and Experimental Gravitation in Space, Florence 2006

Casimir 1948

Order of magnitude

  • f the Casimir pressure

A L c F

4 2 Cas

240 π h =

Pa 10 m 1

3 −

≈ → = A F L

Cas

μ

Assumptions

plane parallel mirrors perfect reflection zero temperature perfectly flat surfaces

A L c E

3 2 Cas

720 π h − =

2

L A >> L

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Workshop on Advances in Precision Tests and Experimental Gravitation in Space, Florence 2006

Plane-sphere geometry

BUT

Casimir forces are not

additive

Approximation is valid for

PP PS

RE F π 2 =

Proximity force

approximation (PFA)

contributions of surface elements are added up independently

A x F x d F

PP PS

) (

2

∫

=

L R >> L R >> L

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Workshop on Advances in Precision Tests and Experimental Gravitation in Space, Florence 2006

Mohideen et al. (Riverside)

Atomic force microscope (AFM)

Plane-sphere geometry Sphere and plane covered

with Au

Distances 60-900nm Optical readout Experimental accuracy

~ 1% @ short distances

PRL 81, 4549 (1998) PRA 62 052109 (2000) Courtesy U. Mohideen

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Workshop on Advances in Precision Tests and Experimental Gravitation in Space, Florence 2006

5 10 15 20 25 30 35

  • 0.5
  • 0.4
  • 0.3
  • 0.2
  • 0.1

0.0

Experiment Theory

Casimir force (10 -9N) Plate-sphere surface separation (nm)

Agreement at ~ % level after having accounted for

Plane-sphere geometry Imperfect reflection Room temperature

(correction < 1%)

Surface roughness

Courtesy U. Mohideen

Theory - experiment comparison

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Workshop on Advances in Precision Tests and Experimental Gravitation in Space, Florence 2006

  • R. Decca et al Phys. Rev. D68, 116003 (2003)

Fischbach et al. (Purdue University)

Au-coated sphere (R= 100-600µm) Cu-coated plate mounted on a torsional MEMS Capacitive readout

Static or dynamic measurements Courtesy E. Fischbach L=260-1200nm

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Workshop on Advances in Precision Tests and Experimental Gravitation in Space, Florence 2006

Origin of the Casimir Force

Vacuum radiation pressure

  • utside the cavity :

inside the cavity :

Spectral mode density :

θ ω

2

cos 2 h

) ( cos 2

2

ω θ ω g × h

longitudinal wave vector

2 2 2 1 2 2 2 1

) ( ) ( 1 ) ( ) ( 1 ) (

L ik p p L ik p p p k

z z

e r r e r r g ω ω ω ω ω − − =

θ ω cos c kz =

θ

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Workshop on Advances in Precision Tests and Experimental Gravitation in Space, Florence 2006

Mode density and Casimir force

Cavity resonances Casimir force =

integral over all field modes

TM TE, )); 1 cos 2 d 4 d

2 2 2

= Θ = ∑∫

∫

∞

p (

  • g

( k k A F

p k p z

ω ω π π h

kz π / c L

g 1

  • C. Genet, A. Lambrecht & S. Reynaud, Phys. Rev. A67 043811 (2003)
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Workshop on Advances in Precision Tests and Experimental Gravitation in Space, Florence 2006

10

−2

10

−1

10 10

1

10

2

0.0 0.1 1.0

The force between metallic mirrors

Plasma model

Au: λp~ 137nm

Reduction of the force

2 2 P

1 ) ( ω ω ω ε − =

Cas

F F

F =

η

P

λ ≤ L

P P

2 λ π ω c =

3 P Cas P

1 L F L F λ λ α ∝ =

P

/ λ L

P

λ << L

model plasma

  • A. Lambrecht & S. Reynaud, Eur. Phys. J. D8 309 (2000)
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Workshop on Advances in Precision Tests and Experimental Gravitation in Space, Florence 2006

Vacuum and thermal fluctuations in TD equilibrium T= 300K Important at

long distances

0.1 1.0 10.0 0.5 0.6 0.7 0.8 0.9 1.0 2.0 3.0

Temperature correction

1 2

B

/

− +

T k

e ω ω ω

h

h h

] [ m L μ

K T , reflection imperfect = K T 300 mirrors, perfect = K T 300 refl., imperfect =

  • C. Genet, A. Lambrecht & S. Reynaud, Phys. Rev. A 62, 012110 (2000)

Cas

F F

m 7

T

μ λ ≈ = kT c h

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Workshop on Advances in Precision Tests and Experimental Gravitation in Space, Florence 2006

Surface roughness:

PFA and specular reflection

Characteristic lengthscale

X

Courtesy U. Mohideen

L

C

>> λ

Surface state

  • P. Maia Neto, A. Lambrecht & S. Reynaud, EPL (2003) & (2005)
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Workshop on Advances in Precision Tests and Experimental Gravitation in Space, Florence 2006

Non specular reflection:

mixes wavevectors and polarizations

Surface roughness correction:

important at short distances and intertwined with finite reflectivity correction

Surface state

z Z

) , (

1

y x h

' k k

  • P. Maia Neto, A. Lambrecht & S. Reynaud, PRA 72, 012115 (2005)
  • R. Rodrigues, P. Maia Neto, A.Lambrecht & S. Reynaud, PRL. 96, 100402 (2006)

Violation of PFA measurable in lateral Casimir

force

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Workshop on Advances in Precision Tests and Experimental Gravitation in Space, Florence 2006

State of the art

The Casimir force is now measured with an experimental

accuracy ~ %

Theory and experiment agree at the same level in the

distance range

Going beyond the % level Discussions are still going on for non zero T No experiments at distances > μm New trends :

NEMS, repulsive Casimir forces beyond PFA : lateral Casimir force Casimir-Polder forces (BEC), non-thermal-equilibrium effects (cf. Mauro Antezza’s talk),… nm 500 nm 100 < < L

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Workshop on Advances in Precision Tests and Experimental Gravitation in Space, Florence 2006

New Casimir force measurement

Experiment with Valery

Nesvizhevsky (ILL, Grenoble)

  • High precision torsion balance
  • Very high quality mirrors
  • Very good control of parallelism

Advantage in window around

10μm where a variety of models can be ruled out or confirmed

  • A. Lambrecht, V. Nesvizhevsky, R. Onofrio, and S. Reynaud, Class. Quant. Grav. (2005)
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Workshop on Advances in Precision Tests and Experimental Gravitation in Space, Florence 2006

Expected new constraints for

  • 0.1 μm
  • 1 μm
  • 3 μm
  • 10 μm thickness of Au layer

New Casimir force measurement

Experiment with Valery

Nesvizhevsky (ILL, Grenoble)

  • High precision torsion balance
  • Very high quality mirrors
  • Very good control of parallelism
  • A. Lambrecht, V. Nesvizhevsky, R. Onofrio, and S. Reynaud, Class. Quant. Grav. (2005)
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Workshop on Advances in Precision Tests and Experimental Gravitation in Space, Florence 2006

mirror 203 nm

Atomic interferometer: coherent

superposition between atomic states at different lattice sites

Measuring the atom-surface

interaction potential :

Casimir Polder interaction Search for new interactions :

improvement by 2 to 4 orders

  • f magintude

Casimir Polder Force Using Cold Atoms in an Optical Lattice

  • P. Wolf, P. Lemonde, A. Lambrecht, S. Bize, A. Landragin, A. Clairon,
  • Proc. IEEE Freq. Controle Symposium (2006); ArXiv:physics/0608021
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Workshop on Advances in Precision Tests and Experimental Gravitation in Space, Florence 2006

Experimental collaborations: Philippe Andreucci (CEA Grenoble – Carnot Institute & ANR MONACO) Joël Chevrier (LEPES, Grenoble) Valery Nezvishevsky (ILL, Grenoble) NANOCASE (FP6-NEST contract) Theory collaborations: Gert Ingold (Univ. Augsburg - BFHZ contract) Marc-Thierry Jaekel (LPT-ENS Paris) Paulo Maia-Neto (Univ. Rio de Janeiro – CAPES COFECUB contract)

Casimir Team

Astrid Lambrecht François-Xavier Dezael Cyriaque Genet (now Strasbourg) Francesco Intravaia (now Potsdam) Guillaume Jourdan Irina Pirozhenko with Serge Reynaud & Brahim Lamine