Université de Nice Sophia Antipolis - CNRS Université de Nice Sophia Antipolis - CNRS I N L N Institut Non Linéaire de Nice Collective effects in light scattering: from Dicke Sub- and Superradiance to Anderson localisation Robin KAISER INLN, Nice, France Conference on Long-Range-Interacting Many Body Systems: from Atomic to Astrophysical Scales Trieste, Italy July 25 th – 29 th 2016
Université de Nice Sophia Antipolis - CNRS I N L N plasma physics / pattern formation Dicke vs Anderson Nature Photonics 8, 321 (2014) astrophysics (self-oscillations, random lasing, Lévy flight of photons) e N th c n e c s e r o u l f T O M 0 Nature Physics 9, 357 (2013) 0 1 2 3 4 5 6 7 8 9 loading time (s)
N 10 10 T 100µK Long range light-matter interactions : Effects on atomic motion
Université de Nice Sophia Antipolis - CNRS I N L N Mechanical Effects of Multiple Scattering of light Coulomb type force 2 q eff F ij 2 I ij P diff / r ij 4 r 2 0 F ij long range component (C 3 /r 3 , 1/r 2 , 1/r) of resonant dipole-dipole interaction
Université de Nice Sophia Antipolis - CNRS I N L N MOT size : ‘One Component Plasma’ from Phys.Rev. Lett. 64 , 408 (1990) bad for BEC Multiple scattering to be avoided…
Université de Nice Sophia Antipolis - CNRS I N L N Self Sustained Oscillation of MOT « Cepheid » type instability : Unstable Competition between compression and radiation pressure induced repulsion ce MOT fluorescence N N th complex spatio-temporel evolution ! 0 0 1 2 3 4 5 6 7 8 9 loading time (s) G. Labeyrie, F. Michaud, R. K. T. Pohl, G.Labeyrie, R.K. Phys. Rev. Lett. 96, 023003 (2006) Phys. Rev. A 74, 023409 (2006)
Université de Nice Sophia Antipolis - CNRS I N L N Photon bubbles T. Mendonca, R. K., Phys. Rev. Lett,108,033001 (2012) Photon bubble experiments (in Lisbon and Nice) g 2 (t) g 2 (r)
Université de Nice Sophia Antipolis - CNRS I N L N Looking at the internal degrees of freedom of the atoms
Université de Nice Sophia Antipolis - CNRS I N L N Multiple Scattering of Light in Atomic samples : Disorder vs cooperative effects Dicke Anderson States Localization Multiple Scattering “Local” “Global” Interferences
Université de Nice Sophia Antipolis - CNRS I N L N The case for Anderson : ‘Random walk of photons’
Université de Nice Sophia Antipolis - CNRS I N L N Wave propagation in disordered media : < 1958 : on average : interferences washed out : random walk / diffusion Light : radiation trapping in stars Electrons : metal (Drude model) 1958 : P.W. Anderson : vanishing diffusion for strong disorder ! Solid State Physics : Metal-Insulator Transitions for electrons Light Scattering : Semiconductor powder, White Paint, Atoms Matter Waves : BEC in Disordered Potential, Kicked Rotator Accoustics : Aluminium Beads NMR : Nuclear Spins
Université de Nice Sophia Antipolis - CNRS I N L N Anderson Localization of non interacting waves in 1,2 and 3D Scaling theory of localization : Abrahams et al., PRL 42 , 673 (1979) g : dimensionless conductance ln g metallic b (g)= 3D ln L 1 g In 3D : threshold for disorder 2D Ioffe-Regel criterion : k l =1 ln g insulating 1D 1 g metal (g>>1) L g e ln g ln g ln L No microscopic theory self consistent theory of localization, numerical simulations of toy systems
Université de Nice Sophia Antipolis - CNRS I N L N Anderson Localization of Light in 3D : phase transition strong scattering required Semi-conductor powder White Paint D.Wiersma et al., Nature 1997 C.Aegerter et al., EPL 2006 F. Scheffold et al., Nat. Photon. 7, 934 (2013) F. Scheffold et al., Nature 398, 206(1999) T Sperling et al., New J. Phys. 18, 013039 (2016) T. v. der Beek et al., PRB 85 115401 (2012) => Not observed so far
Université de Nice Sophia Antipolis - CNRS I N L N Weak Localisation = precursor of strong Localisation? beam Lens splitter CCD MOT N 10 10 Probe laser T 100µK k l 1000 Coherence after resonant scattering with atoms ! See also : M. Havey’s group G. Labeyrie et al., Phys. Rev. Lett., 83 , 5266 (1999)
Université de Nice Sophia Antipolis - CNRS I N L N Theory : • no “exact” solution • diagrammatic approach Excellent agreement (no free parameter) T. Jonckheere et al., Phys. Rev. Lett., 85 , 4269 (2000)
Université de Nice Sophia Antipolis - CNRS I N L N Towards strong localization of light : dense atomic clouds k l 1 Ioffe-Regel : Dynamical Breakdown Dynamical Breakdown k l 1000 10 -0 Strong BEC Localization Weak 10 -2 of Light T [K] Localization k l 3 of Light 10 -4 Dipole Trap 10 -6 (Havey, Browaeys) Strong Localization 10 -8 + BEC BEC 10 -10 k l < 1 10 10 10 12 10 14 10 16 10 18 10 20
Université de Nice Sophia Antipolis - CNRS I N L N Ligth scattering from point dipoles : 1/r outgoing wave
Université de Nice Sophia Antipolis - CNRS I N L N Building up a refractive index « ab inito » (from individual atoms) E sc b j E 0 b m b i :amplitude of dipole i 18
Université de Nice Sophia Antipolis - CNRS I N L N Spherical gaussian cloud : emission diagram Cloud of atoms Far field emission diagram Incoherent model refractive index (particles trajectories, (mean field) scattering in ‘ empty modes’) Mesoscopic physics: Weak localization (waves beyond mean field) 19 S. Bromley et al., Nat. Comm. 7, 11039 (2016)
Université de Nice Sophia Antipolis - CNRS I N L N Theory : Effective Hamiltonian Diagonal : Off diagonal : On site energy transport • Open System • Reminiscent of Anderson Hamiltonian • Heisenberg model with global coupling • Long range hopping • No decoherence (coupling to phonons, …)
Université de Nice Sophia Antipolis - CNRS I N L N Eigenvalues for N coupled dipoles Important near field terms for high densities e ikr ( 1/kr + 1/kr 2 + 1/kr 3 ) e ikr /kr
Université de Nice Sophia Antipolis - CNRS I N L N Resonance Overlap (« Thouless ») Scaling function b (g) NO ANDERSON LOCALISATION FOR S. Skipetrov, I. Sokolov, PRL 112, 023905 (2014) VECTORIAL LIGHT Bellando et al,. Phys. Rev. A 90, 063822 (2014) IN 3D ?
Université de Nice Sophia Antipolis - CNRS I N L N TIME vs SPACE LOCALISATION (2D) Spatially extended mode (vectorial case) Mode width NOT correlated to localisation length : temporal vs spatial localisation Spatially localized mode (scalar case) C. E. Maximo, N. Piovella, Ph. W. Courteille, R. K., R. Bachelard, PRA 92, 062702 (2015)
Université de Nice Sophia Antipolis - CNRS I N L N The quest for Dicke subradiance
Université de Nice Sophia Antipolis - CNRS I N L N 1954 : Dicke super- and subradiant states R. Dicke 1954 First experimental observation of superradiance Feld et al. 1973
Université de Nice Sophia Antipolis - CNRS I N L N Single photon excitation / low intensity limit Superradiant pair Subradiant Subradiant pair N-1 metastable states |ee> G max ~ N G 0 |eg>+ |ge> |eg>- |ge> Extended Volume : b 0 =N at /N modes |gg> Cooperativity without cavity (also Random lasing)
Université de Nice Sophia Antipolis - CNRS I N L N Subradiant pairs : N=2 R. G. DeVoe, R. G. Brewer, PRL 76, 2049 (1996). Forward ‘ subradiance echo ’ from inverted system t nat =7ns l 3 5ns laser pulse ~ 0.5 mm l 4 ~ 20 mm Pencil shape excitation D. Pavolini et al. , Phys. Rev. Lett. 54, 1917 (1985)
Université de Nice Sophia Antipolis - CNRS I N L N Fragile subradiance Single Photon Dicke subradiance for N two level systems (in free space, N>>2) has not been observed • Does not require large spatial densities (near field effect maybe even bad : Gross&Haroche 1982) • Requires large optical densities in all directions (b 0 >>1) • Exploits the 1/r long range dipole-dipole interaction
Université de Nice Sophia Antipolis - CNRS I N L N Time dependent experiments : coherent scattering Superradiance = bright state Subradiance = metastable ‘ dark ’ states W | E > | D > G D G N L | G > Numerical Simulation of N driven coupled dipoles
Université de Nice Sophia Antipolis - CNRS I N L N Subradiance vs incoherent scattering t sub b 0 t Rad.Trap. b( d ) 2 • Random walk of photons • Does not require large spatial densities (without interference) • Requires large optical densities • Diffusion equation t Anderson exp{b( d )} • Density Threshold ?
Université de Nice Sophia Antipolis - CNRS I N L N Experiment N=10 9 87 Rb T=50 µK R=1 mm r =10 11 /cc b 0 = 20…100 detector
Université de Nice Sophia Antipolis - CNRS I N L N Experimental results Long decay at b( d )<1 Scaling with SYSTEM SIZE ! t (b 0 ) b 0 d Increases as b 0 = r s L
Université de Nice Sophia Antipolis - CNRS I N L N Single Photon Super- vs Subradiance The ‘super’ of ‘single photon Dicke states’ Subradiant Superradiant
Université de Nice Sophia Antipolis - CNRS I N L N Superradiance in dilute and large cloud of cold atoms Coupled Dipoles (Numerics) Off-axis Superradiance ≠ forward superradiance Experiments M. O. Araujo, I. Kresic, R. K., W. Guerin, to appear in PRL (2016)
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