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

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 NEST (New Emerging Science & Technology) 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 : V r V r V r N Y Yukawa + Newtonian ( ) M M potential = − 1 2 V r G N N r ( ) ( ) ( ) = + ( ) ( ) F r F r F r = α − λ V r V r exp( r / ) N Y Y N ( ) M M = − 1 2 F r G Modification of N N 2 r Newtonian law between ⎛ + ⎞ ( ) ( ) r = α − λ ⎜ ⎟ pointlike masses F r F r 1 exp( r / ) λ Y N ⎝ ⎠ Workshop on Advances in Precision Tests and The Search for Non-Newtonian Gravity, E. Fischbach & C. Talmadge (1998) Experimental Gravitation in Space, Florence 2006

How to test the Newtonian law ? Measurement give constraints in the the plane ( ) λ , α Geophysical Laboratory Open window Log 10 α at short distances… Satellites − λ < 10 3 m LLR Planetary and at long distances Log 10 λ (m) λ > 10 16 m Courtesy : J. Coy, E. Fischbach, R. Hellings, C. Talmadge, and E. M. Standish (2003) (cf. Marc Jaekel’s talk) Workshop on Advances in Precision Tests and Experimental Gravitation in Space, Florence 2006 The Search for Non-Newtonian Gravity, E. Fischbach & C. Talmadge (1998)

Test at short distances � Gravity measurements at millimetric distances GM M ( ) + α − λ 1 2 1 e ( r / ) r Log 10 α � λ ≤ 30µm : comparison between experimental results and theoretical predictions of the Log 10 λ ( μ m) Casimir force Workshop on Advances in Precision Tests and E. Adelberger et al Ann. Rev. Nucl. Part. Sci. (2003) hep-ph/0307284 Experimental Gravitation in Space, Florence 2006

Casimir 1948 π 2 h c = F A A >> 2 Cas L 4 240 L π 2 h c = − E A Cas 3 720 L L � Assumptions � Order of magnitude � plane parallel mirrors of the Casimir pressure � perfect reflection F − = μ → Cas ≈ 3 L 1 m 10 Pa � zero temperature A � perfectly flat surfaces Workshop on Advances in Precision Tests and Experimental Gravitation in Space, Florence 2006

Plane-sphere geometry � Proximity force approximation (PFA) R >> L contributions of surface elements are added up L independently � BUT F ( x ) ∫ = 2 PP F d x � Casimir forces are not PS A additive = π F 2 RE � Approximation is valid for PS PP R >> L Workshop on Advances in Precision Tests and Experimental Gravitation in Space, Florence 2006

Mohideen et al. (Riverside) Atomic force microscope (AFM) Courtesy U. Mohideen � Plane-sphere geometry � Sphere and plane covered with Au � Distances 60-900nm � Optical readout � Experimental accuracy ~ 1% @ short distances PRL 81, 4549 (1998) Workshop on Advances in Precision Tests and Experimental Gravitation in Space, Florence 2006 PRA 62 052109 (2000)

Theory - experiment comparison Agreement at ~ % level after having accounted for 0.0 � Plane-sphere geometry Experiment -0.1 � Imperfect reflection Casimir force (10 -9 N) Theory � Room temperature -0.2 (correction < 1%) -0.3 � Surface roughness -0.4 -0.5 5 0 10 0 15 0 20 0 25 0 30 0 35 0 Plate-sphere surface separation (nm) Workshop on Advances in Precision Tests and Courtesy U. Mohideen Experimental Gravitation in Space, Florence 2006

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 L=260-1200nm Courtesy E. Fischbach Workshop on Advances in Precision Tests and R. Decca et al Phys. Rev. D68, 116003 (2003) Experimental Gravitation in Space, Florence 2006

Origin of the Casimir Force Vacuum radiation pressure θ ω h � outside the cavity : θ 2 cos 2 ω h � inside the cavity : θ × ω 2 cos g ( ) 2 Spectral mode density : 2 − ω ω ω cos p p 2 ik L z 1 r ( ) r ( ) e k z = θ 1 2 ω = p ( ) g c k 2 − ω ω p p 2 ik L z 1 r ( ) r ( ) e longitudinal wave vector 1 2 Workshop on Advances in Precision Tests and Experimental Gravitation in Space, Florence 2006

Mode density and Casimir force g � Cavity resonances 1 � Casimir force = k z π / c L integral over all field modes ∞ = ∑∫ 2 d k d k ∫ z ω Θ ω = 2 p h F A cos ( 1 -g ( )); p TE, TM π π k 2 4 2 p 0 C. Genet, A. Lambrecht & S. Reynaud, Phys. Rev. A67 043811 (2003) Workshop on Advances in Precision Tests and Experimental Gravitation in Space, Florence 2006

The force between metallic mirrors Au: λ p ~ 137nm � Plasma model π ω 2 2 c ω = ε ω = − P 1.0 ( ) 1 λ P ω 2 P F << λ η F = L P F Cas � Reduction of the force 0.1 ≤ λ L plasma model P α 1 L = ∝ F F λ λ Cas 0.0 3 L −2 −1 0 1 2 10 10 10 10 10 P P / λ L P Workshop on Advances in Precision Tests and A. Lambrecht & S. Reynaud, Eur. Phys. J. D8 309 (2000) Experimental Gravitation in Space, Florence 2006

Temperature correction � Vacuum and thermal fluctuations in TD equilibrium ω ω h h 3.0 + e ω − h / k T 2 1 B = 2.0 perfect mirrors, T 300 K � T= 300K F = h c imperfect refl., T 300 K λ = kT ≈ μ F 7 m Cas T 1.0 0.9 0.8 0.7 � Important at = 0.6 imperfect reflection , T 0 K long distances 0.5 L μ [ m ] 0.1 1.0 10.0 Workshop on Advances in Precision Tests and C. Genet, A. Lambrecht & S. Reynaud, Phys. Rev. A 62, 012110 (2000) Experimental Gravitation in Space, Florence 2006

Surface state � Surface roughness: PFA and specular reflection λ >> L X � Characteristic lengthscale C Courtesy U. Mohideen Workshop on Advances in Precision Tests and P. Maia Neto, A. Lambrecht & S. Reynaud, EPL (2003) & (2005) Experimental Gravitation in Space, Florence 2006

Surface state � Non specular reflection: mixes wavevectors and h ( x , y ) 1 polarizations k � Surface roughness correction: important at short distances k ' and intertwined with finite Z z 0 reflectivity correction � Violation of PFA measurable in lateral Casimir force P. Maia Neto, A. Lambrecht & S. Reynaud, PRA 72, 012115 (2005) Workshop on Advances in Precision Tests and R. Rodrigues, P. Maia Neto, A.Lambrecht & S. Reynaud, PRL. 96, 100402 (2006) 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 < L < distance range 100 nm 500 nm � Going beyond the % level � Discussions are still going on for non zero T � No experiments at distances > μ m � New trends : NEMS, repulsive Casimir forces beyond PFA : lateral Casimir force Casimir-Polder forces (BEC), non-thermal-equilibrium effects (cf. Mauro Antezza’s talk),… 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 10 μ m where a variety of models can be ruled out or confirmed Workshop on Advances in Precision Tests and Experimental Gravitation in Space, Florence 2006 A. Lambrecht, V. Nesvizhevsky, R. Onofrio, and S. Reynaud, Class. Quant. Grav. (2005)

New Casimir force measurement � Experiment with Valery Nesvizhevsky (ILL, Grenoble) High precision torsion balance � Very high quality mirrors � Very good control of parallelism � � Expected new constraints for 0.1 μ m � 1 μ m � 3 μ m � 10 μ m thickness of Au layer � Workshop on Advances in Precision Tests and Experimental Gravitation in Space, Florence 2006 A. Lambrecht, V. Nesvizhevsky, R. Onofrio, and S. Reynaud, Class. Quant. Grav. (2005)

Casimir Polder Force Using Cold Atoms in an Optical Lattice mirror � Atomic interferometer: coherent 203 nm 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 of magintude P. Wolf, P. Lemonde, A. Lambrecht, S. Bize, A. Landragin, A. Clairon, Workshop on Advances in Precision Tests and Experimental Gravitation in Space, Florence 2006 Proc. IEEE Freq. Controle Symposium (2006); ArXiv:physics/0608021

Casimir Team Astrid Lambrecht François-Xavier Dezael with Serge Reynaud Cyriaque Genet (now Strasbourg) & Brahim Lamine Francesco Intravaia (now Potsdam) Guillaume Jourdan Irina Pirozhenko 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) Workshop on Advances in Precision Tests and Experimental Gravitation in Space, Florence 2006 Paulo Maia-Neto (Univ. Rio de Janeiro – CAPES COFECUB contract)