Bart van Tiggelen Laboratoire de Physique et Modélisation des Milieux Condensés CNRS/University of Grenoble, France

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1 Analogies between Quantum Waves and Classical Waves : deceiving, surprising, and complementary Bart van Tiggelen Laboratoire de Physique et Modélisation des Milieux Condensés CNRS/University of Grenoble, France Michel Campillo (LGIT-Grenoble) Grenoble) Ludovic Margerin (LGIT-Grenoble) Roger Maynard (LPMMC( LPMMC-Grenoble) Geert Rikken (LCMP Toulouse) Patrick Sebbah (LPMC-Nice) Sergey Skipetrov (LPMMC Grenoble) Mathias Fink (LOA-Paris) Arnaud Tourin (LOA( LOA-Paris) Julien De Rosny (LOA( LOA-Paris) Ad Lagendijk (Amsterdam Netherlands) John Page (Winnipeg, Canada) Michael Cowan (Toronto, Canada) Azriel Genack (Queens College,, NY) Andrey Chabanov (San Antonio, Texas) Richard Weaver (Urbana( Urbana-Champaign) John Scales (Golden-Colorado) PhD: Eric Larose,, Domitille Anache,, Nicolas Trégourès,, Felipe Pinheiro,, David Lacoste, Anja Sparenberg Support: GDR PRIMA & IMCODE (CNRS), Ministère de la Recherche (ACI jeune chercheur), NSF (USA)

2 abstract Mesoscopic physics Some mesoscopic concepts with light Phase of ultrasound Optical vortices Mesoscopic seismology

3 CLASSICAL QUANTUM ( r ) Ψ Ψ S( r t) c t, Ψ Energy Potential Energy Ψ Ψ V( r) Ψ 0 measurable ω Noise absorption Product space [ ε( r) ] ω ( ) ( ) t Ψ ε Ψ Η Source S, no mass, no charge i t Ψ Energy Potential Probability decoherence Sum Space measurable E V(r) Ψ Η H H No source, mass,, charge

4 Mesoscopic criterion τ < T( L) T ( L) D vl d l τ v Dτ max L : d D L max < τ max τ τ φ Diffusion time abs Diffusion constant Mean free path Absorption length /decoherence time log source noise h E Thouless All waves behave in a similar way l < L < L max L. Brillouin, 960

5 Coherent Backscattering in Optics Maret, Maynard, Akkermans & Wolf, Grenoble, PRL, 985 Van Albada & Lagendijk,, Amsterdam, PRL, 985 λ l IN OUT CBS in,out ( OUT) exp[ ik ( r r )] G IN in out

6 Transport Velocity in Random Media D 3 v E l Electron conduction Standard literature v E hk m F A G L 4e 3m k F l Fermi velocity Electrical conductance

7 Transport Velocity in Random Media D 3 v E l Classical waves Van Albada,, Van Tiggelen, Lagendijk, Tip,, 990 v E ω k φ ' ( ω ) τ Not group velocity not phase velocity 4 T 3 Ak l L Diffuse transmission

8 Transport Velocity in Random Media D 3 v E l Classical waves Van Albada,, Van Tiggelen, Lagendijk, Tip,, 990 v E ω k φ ' ( ω ) τ Not group velocity not phase velocity Random Mie spheres: : f 5 %

9 Magneto-Optics in Diffuse Media E± ( r, t) exp( iωt ik r) exp( ± ivb r) Faraday effect Radiatif transfer is well described by a diffusion equation J D B ( ) ρ Do photons exhibit a Hall effect? Gradient imposed by parity! J D B H ρ Yes! Rikken & Van Tiggelen, Nature (996) Can photons diffuse without a gradient in density? J D Bρ MC No! Pinheiro & Van Tiggelen, JOSA A (00)

10 Photonic Hall Effect Rikken & Van Tiggelen, Nature 38, 54 (996) J D B H ρ PHE of CeF3 at 77K I I B ( 0 ) 5 T > < packing l*(mm) fraction f

11 Photonic Photonic Spintronics Spintronics 3 bb' aa' bb' aa' * b' a' b a b' a' b a C C t t T T > < > < δ δ g g ( ) ' ' ' ' ' ' ' ' ' ' * ' ' b a bb aa bb aa b a bb aa bb aa b a bb aa b b a a T C T C T C t t δ δ δ δ Conductance de Conductance de Thouless L Ak L N g l l 4π Thouless ab b T a G : Landauer de e Conductanc ( ) 5 5 h e g T N h e G g h e T N h e G b a b a

12 Photonic Spintronics E( S ) E( D ) S D sample HP analyzer (Malus law) δ δ aa' bb'' cos cos θ θ S D λ a 5 mm, l 5 cm, L m, L 50 cm Ak N l l g.3 ± 0.05 L π L δt (0,0) δt ( θ, θ ) a b cos cos g 3 [ cos cos ] θ θ θa θb a b g 5 Genack, Chabanov, Trégourès,, Van Tiggelen, 003

13 Photonic Spintronics Genack, Chabanov, Trégourès,, Van Tiggelen, 003 CC3 a x x b a b x x CCos θ D C 3 /5 exp CC3 /8 C3 Brouwer, PRB 998 θ D absorption L / L a

14 ImΨ Ψ Ψ Ψ Ψ Ψ3... ReΨ probability distribution P exp π detc ( ) ( * Ψ Ψ Ψ ) *,... Ψ C Ψ C <Ψ Ψ >, N N ij i j diffusion equation

15 Gaussian Speckles P Ψ I e iφ intensity phase. Stationary: : Distribution of speckle intensity ( ) P I, φ exp( I/ < > ) < I> I. Dynamics :Distribution of «Wigner delay» time Ω Ω ( * Ψ C Ω Ψ) Ψ Ψ ω, ω exp ( ) π det C dφ Q P φ ' dω Q dφ dω ( ˆ' φ ) 3/

16 Diffuse Acoustic Wave Spectroscopy ψ t, τ) ( τ ψ t, τ) ( ψ ( t, τ ), ψ( t, τ ) ψ( t) g( τ) exp ( ( ) ) k n r τ 6 ct n l* g( τ ) exp τ 6 t D AWS

17 Diffuse Acoustic wave Spectroscopy John Page, Dave Weitz, Michael Cowan amplitude Wrapped phase unwrapped phase l*.5mm; τ* µs NORMALIZED FIELD AMP -0,0 PHASE (rad) 0,0 0, INPUT (a) TRANSIT TIME (µs) FIELD 7,5 8,0 8,5 (c) t s AMPLITUDE 7,5 8,0 8,5 (d) TRANSIT TIME (µs) TRANSMITTED (b) PHASE 7,5 8,0 8,5 0, (f) 0,0 0 - (g) 0 (h) t (s) 3 4 Time (seconds!) 0,0 0,00-0,0 (e) π 0 π

18 Probability distribution P( Φ) for phase shift Φ() τ after time τ 0, (a) τ 0 ms (c) τ 300 ms 0, P dφ dτ Q Q 6t DAWS Q dφ dτ 3/ P( Φ) 0,0 E-3 0, (b) τ 00 ms (d) τ s 0,0 0,5 0,0 t DAWS 00ms 0,0 0,05 P π ( φ ) ( π φ ) ,00 Φ (rad)

19 Probability Probability distribution of distribution of SECOND SECOND derivative derivative [ ] ( ) ( ) 3/ 0 4 " ) (4 " R x x R x dx P φ π φ [ ] ( ) 3/ " 4 " " " T T P φ φ φ φ ( ) ( ) (4) (4) "(0) (0) 3 4 "(0) (0) g g T g g R

20 Probability distribution of SECOND derivative P(Φ'') (Normalized) 0, 0,0 E-3 ms data ms data (/ power) ms data (σ ) Bart's Theory (R ) Bart's Theory (R 3) Slope - E-4 0,0 0, 0 φ " t DAWS Φ''*τ DAWS

21 Optical Vortices L 6D Patrick Sebbah Azriel Genack

22 theorem dl φ( r) πq Q q i zero i - - θ Q 0 - R Q dφ θ dφ π 0 dθ dθ ( ) π circle d θ θ

23 dimensions 3 dimensions Q Count the mean free path? dφ θ dφ π 0 dθ dθ ( ) π circle d θ θ [ ( r ), ψ( r ), ψ( r3 ), ψ( r4 )] Pψ ψ ( rψ ) *( r') J0( k r)exp( r/l)

24 Q R implies screening of topological charge ρ (Halperin,, 98, Berry 000, Wilkinson, 004) ( r) q δ i i () ( r r i ) Topological charge density Q d r ρ( r) Topological A C( x) ρ ( r x) ρ( r) Topological charge Topological pair correlation Q ( R) πr R R n d x C( x) Ο( R) d x C( x) 0 Q ( R) constant??? Berry & Dennis, 000

25 receiver source Free surface. Distance source receiver < wavelength. Symmetry source symmetry receiver & magnitude measure y CBS( r) u Earth quake x x u y J 0 π r λ x measure div u Explosion e t/τ magnitude measure u z Sledge hammer

26 Seismic waves in the French Auvergne Eric Larose,, Ludovic Margerin,, Michel Campillo et Bart van Tiggelen, PRL, July 004 Operator noise Mesoscopic signal Background noise

27 Coherent Backscattering in the French Auvergne 5 Hz λ Mean free time0.7 seconds Wavelength 0 meter c Rayleigh 300 m/s Mean free path 0 m

28 Coherent Backscattering in Concrete Structure Larose, De Rosny, Goudeard, Anache, Margerin, Campillo, Van Tiggelen, 005

29 Coherent Backscattering in Concrete Structure Larose, De Rosny, Goudeard, Anache, Margerin, Campillo, Van Tiggelen, 005 Energy enhancement - 0 r(meters) CBS( r) J 0 π r λ x e t/τ

30 Equipartition Correlation Green function Helio-seismology Duval, Nature 993 Thermal phonons Weaver & Lobkis,, PRL 00 Seismic coda/noise Campillo etal Science 003, 005 u r A, t τ u r B, t τ G( AB, τ) G( AB, τ)

31 Relation with Time-Reversal and Coherent backscattering receiver Time reversal machine source [ S TRM R]( τ ) dt [ TRM S] ( t τ) [ TRM R]( t τ ) Time-reversal correlation method l a R( z, τ) S( τ) CBS θ θ λ λ a speckle Stable time-reversal at source.. with CBS cusp!! D Wa <<