from Dicke Sub- and Superradiance to Anderson localisation Robin - - PowerPoint PPT Presentation

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from dicke sub and superradiance to anderson localisation
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from Dicke Sub- and Superradiance to Anderson localisation Robin - - PowerPoint PPT Presentation

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Universit de Nice Sophia Antipolis - CNRS Universit de Nice Sophia Antipolis - CNRS I N L N Institut Non Linaire de Nice Collective effects in light scattering: from Dicke Sub- and Superradiance to Anderson localisation Robin KAISER

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Université de Nice Sophia Antipolis - CNRS I N L N Université de Nice Sophia Antipolis - CNRS

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 25th – 29th 2016

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M O T f l u

  • r

e s c e n c e Nth

Université de Nice Sophia Antipolis - CNRS I N L N

Dicke vs Anderson astrophysics (self-oscillations, random lasing, Lévy flight of photons) plasma physics / pattern formation

Nature Photonics 8, 321 (2014) Nature Physics 9, 357 (2013)

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N  1010 T100µK

Long range light-matter interactions : Effects on atomic motion

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Université de Nice Sophia Antipolis - CNRS I N L N

Mechanical Effects of Multiple Scattering of light Coulomb type force

2 2

4 r q F

eff ij

 

Fij Iij  Pdiff / rij

2

long range component (C3/r3, 1/r2, 1/r)

  • f resonant dipole-dipole interaction
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Université de Nice Sophia Antipolis - CNRS I N L N

from Phys.Rev. Lett. 64, 408 (1990)

MOT size : ‘One Component Plasma’

bad for BEC  Multiple scattering to be avoided…

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MOT fluorescence Nth ce N

  • G. Labeyrie, F. Michaud, R. K.
  • Phys. Rev. Lett. 96, 023003 (2006)

Self Sustained Oscillation of MOT

« Cepheid » type instability : Unstable Competition between compression and radiation pressure induced repulsion

complex spatio-temporel evolution !

  • T. Pohl, G.Labeyrie, R.K.
  • Phys. Rev. A 74, 023409 (2006)
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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)

g2(t) g2(r)

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Université de Nice Sophia Antipolis - CNRS I N L N

Looking at the internal degrees of freedom

  • f the atoms
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Université de Nice Sophia Antipolis - CNRS I N L N

Dicke States Multiple Scattering of Light in Atomic samples : Disorder vs cooperative effects Multiple Scattering Interferences Anderson Localization

“Local” “Global”

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Université de Nice Sophia Antipolis - CNRS I N L N

The case for Anderson : ‘Random walk of photons’

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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 Accoustics : Aluminium Beads Matter Waves : BEC in Disordered Potential, Kicked Rotator Light Scattering : Semiconductor powder, White Paint, Atoms NMR : Nuclear Spins

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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 :

In 3D : threshold for disorder

Ioffe-Regel criterion : kl=1

g L g e g

L

ln ln ln    

metal (g>>1)

ln g

 ln g  ln L b(g)=

1D 2D 3D g : dimensionless conductance

1  g

insulating metallic

1  g

Abrahams et al., PRL 42, 673 (1979) No microscopic theory self consistent theory of localization, numerical simulations of toy systems

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Université de Nice Sophia Antipolis - CNRS I N L N

D.Wiersma et al., Nature 1997

Semi-conductor powder

C.Aegerter et al., EPL 2006

White Paint

Anderson Localization of Light in 3D :

phase transition  strong scattering required

  • F. Scheffold et al., Nat. Photon. 7, 934 (2013)

T Sperling et al., New J. Phys. 18, 013039 (2016)

  • F. Scheffold et al., Nature 398, 206(1999)
  • T. v. der Beek et al., PRB 85 115401 (2012)

=> Not observed so far

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Université de Nice Sophia Antipolis - CNRS I N L N

CCD Lens MOT beam splitter Probe laser

N  1010 T100µK kl  1000

Coherence after resonant scattering with atoms ! See also :

  • M. Havey’s group
  • G. Labeyrie et al., Phys. Rev. Lett., 83, 5266 (1999)

Weak Localisation = precursor of strong Localisation?

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  • T. Jonckheere et al., Phys. Rev. Lett., 85, 4269 (2000)

Theory :

  • no “exact” solution
  • diagrammatic approach

Excellent agreement (no free parameter)

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Université de Nice Sophia Antipolis - CNRS I N L N

Towards strong localization of light : dense atomic clouds

Strong Localization + BEC BEC

1014 1012 1016 1018 1020 1010 10-10 10-8 10-6 10-4 10-2 10-0

Dynamical Breakdown Dynamical Breakdown

T [K]

Weak Localization

  • f Light

BEC Ioffe-Regel : Strong Localization

  • f Light

k l  1000 k l  1 k l  3 Dipole Trap (Havey, Browaeys) k l < 1

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Ligth scattering from point dipoles : 1/r outgoing wave

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Building up a refractive index « ab inito » (from individual atoms)

bm bj

E0

18

Esc

bi :amplitude of dipole i

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Université de Nice Sophia Antipolis - CNRS I N L N

Spherical gaussian cloud : emission diagram

refractive index (mean field)

Far field emission diagram Cloud of atoms

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Incoherent model (particles trajectories, scattering in ‘empty modes’) Mesoscopic physics: Weak localization (waves beyond mean field)

  • S. Bromley et al.,
  • Nat. Comm. 7, 11039 (2016)
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Theory : Effective Hamiltonian

Off diagonal : transport Diagonal : On site energy

  • Open System
  • Reminiscent of Anderson Hamiltonian
  • Heisenberg model with global coupling
  • Long range hopping
  • No decoherence (coupling to phonons, …)
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eikr ( 1/kr + 1/kr2 + 1/kr3) eikr/kr

Eigenvalues for N coupled dipoles

Important near field terms for high densities

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Resonance Overlap (« Thouless »)

Scaling function b(g)

  • S. Skipetrov, I. Sokolov, PRL 112, 023905 (2014)

Bellando et al,. Phys. Rev. A 90, 063822 (2014)

NO ANDERSON LOCALISATION FOR VECTORIAL LIGHT IN 3D ?

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Spatially localized mode (scalar case) Spatially extended mode (vectorial case)

TIME vs SPACE LOCALISATION (2D)

Mode width NOT correlated to localisation length : temporal vs spatial localisation

  • C. E. Maximo, N. Piovella, Ph. W. Courteille, R. K., R. Bachelard, PRA 92, 062702 (2015)
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The quest for Dicke subradiance

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1954 : Dicke super- and subradiant states

  • R. Dicke 1954

Feld et al. 1973 First experimental observation

  • f superradiance
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Superradiant pair Subradiant pair

|ee> |eg>+ |ge> |gg> |eg>- |ge>

Gmax ~ N G0

b0=Nat/Nmodes

Subradiant N-1 metastable states

Cooperativity without cavity (also Random lasing) Extended Volume :

Single photon excitation / low intensity limit

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  • D. Pavolini et al. , Phys. Rev. Lett. 54, 1917 (1985)

tnat=7ns Pencil shape excitation

~ 20 mm ~ 0.5 mm

Forward ‘subradiance echo’ from inverted system l3 l4

5ns laser pulse

  • R. G. DeVoe, R. G. Brewer, PRL 76, 2049 (1996).

Subradiant pairs : N=2

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Université de Nice Sophia Antipolis - CNRS I N L N

Fragile subradiance

  • Does not require large spatial densities

(near field effect maybe even bad : Gross&Haroche 1982)

  • Requires large optical densities in all directions (b0>>1)
  • Exploits the 1/r long range dipole-dipole interaction

Single Photon Dicke subradiance for N two level systems (in free space, N>>2) has not been observed

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W | G > | E > | D > GN GD

Superradiance = bright state Subradiance = metastable ‘dark’ states

Time dependent experiments : coherent scattering

L

Numerical Simulation

  • f N driven coupled dipoles
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Subradiance vs incoherent scattering

tsub  b0 tRad.Trap.  b(d)2 tAnderson  exp{b(d)}

  • Does not require large spatial densities
  • Requires large optical densities
  • Random walk of photons

(without interference)

  • Diffusion equation
  • Density Threshold ?
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detector

N=109 87Rb T=50 µK R=1 mm r=1011/cc b0 = 20…100

Experiment

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Université de Nice Sophia Antipolis - CNRS I N L N

Experimental results

Long decay at b(d)<1  Increases as b0 = r s L  b0 d

Scaling with SYSTEM SIZE !

t(b0)

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Subradiant

Single Photon Super- vs Subradiance The ‘super’ of ‘single photon Dicke states’

Superradiant

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Off-axis Superradiance ≠ forward superradiance

  • M. O. Araujo, I. Kresic, R. K., W. Guerin, to appear in PRL (2016)

Coupled Dipoles (Numerics) Experiments

Superradiance in dilute and large cloud of cold atoms

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Combining Anderson and Dicke Toy Model : Open Disordered System:

  • A. Biella, F. Borgonovi, R. K., G.L. Celardo, EPL, 103, 57009 (2013)

3D Anderson model on 10x10x10 lattice hoping (W) + disorder (W) + opening (g) All sites coupled to one single decay channel : Qij=1

W

g

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Hybrid Subradiant States « decoupled » from outside world

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Outlook :

  • Subradiance vs Radiation trapping

Radiation trapping for small beam and intermediate regimes: subradiance dominant at long times

  • Towards Anderson of subradiant Dicke states
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Perspectives :

  • Anderson Localisation of Light in Cold Atoms

With diagonal disorder / magnetic field ? Identify experimental signatures Technical issuses : Rb  …Yb 

  • Long range interactions and mechanical effects

Photon bubbles Debye Screening Long range attractive forces in 3D (mimic ‘gravity’ in the lab?)

  • Super- and subradiant states :

fast and slow relaxation : connection to quasi-stationnary states ?

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Université de Nice Sophia Antipolis - CNRS I N L N

Precious Collaborators INLN:

  • G. Labeyrie, W. Guerin, M. Fouché, M. Araujo, I. Kresic

Collaborations :

  • E. Akkermans, A. Gero
  • L. Celardo, F. Borgonovi, A. Biella, M. Angeli
  • R. Bachelard, P. Courteille, N. Piovella, C. Maximo
  • J. Ye, A. M. Rey, M. Lukin, J. Schachenmayer, et al.
  • J. Barré, B. Marcos, A.Olivettti, D.Metivier
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Thank you for your attention