Multiple scattering of light by cold atoms

Transcription

1 Multiple scattering of light by cold atoms Robin KAISER INLN, Nice, France Waves and disorder, Cargèse, France, July 1 11, 2014

2 Lecture 1: 1.1 Two level atoms 1.2 Diffusion Lecture 2: 2.1 The case for Anderson 2.2 The case for Dicke 2.3 Anderson and Dicke

3 INLN: G. Labeyrie, D. Wilkowski, C. Miniatura, W. Guerin N. Mercadier, Q. Baudouin, L. Bellando, T. Bienaimé, J. Chabé, T. Rouabah, G.L. Gattobigio, F. Michaud, T. Chanelière, V. Guerrara, C. Müller, Y. Bidel + S. Tanzilli, J. Barré, B.Marcos, M. Faurobert, M. Lintz, F. Impens, F. Bouchet, D. Delande, R. Carminati, S. Skipetrov, L. Froufe-Pérez, R. Pierrat, A. Picozzi + E. Akkermans, N. Piovella, L. Celardo, R. Bacherlard, P. Courteille, E. Perreira, M. Havey, T. Ackemann,, J. Tabosa, M. Chevrollier, T.Pohl, J. Ott, T. Menconça, H. Tercas, G. Alvarez, G. Robb, A. Arnold, W. Firth, G.L. Oppo

4 Coherent Multiple Scattering Anderson Localisation Dicke Superradiance Multiple scattering Local Global Interferences mesoscopic transport (superconductors, insulators) Cooperative emission (superradiant lasers, antennas, quantum memories)

5 How to trap a photon with N atoms? disorder Anderson Localization Radiation Trapping Dicke Subradiance order Photonic Crystal slow/stopped light, quantum holography decoherence coherence

6 The case for Anderson

7 Weak Localization => Coherent Backscattering uncorrelated paths add incoherently correlated (i.e. reciprocal) paths add coherently k in I 0 k out θ θ (1) r in r out (2) ϕ=(k in +k out ).(r in -r out ) Coherent Backscattering θ=0 ϕ = 0 for any path <I(0)> <I(θ)>> θ CBS )> = 2 multiple self-aligned Sagnac interferometer

8 Configuration Average Single realization θ (mrad)

9 Configuration Average Single realization Configuration average θ (mrad)

10 Weak Localisation with resonant scattering by atoms Lens beam splitter CCD MOT Probe laser N T 100µK kl 1000 Coherence after resonant scattering with atoms! also : M. Havey et al. Phys. Rev. Lett., 83, 5266 (1999)

11 Theory : no exact solution diagrammatic approach Excellent agreement (no free parameter) ^=4 =1 q CBS enhancement h Rb 85 : F=3 - F'=4 h // experiment MC simulation CBS enhancement 2 Sr 88 : J=0 - J'=1 h // lin lin // (mrad) (mrad) Phys. Rev. Lett., 85, 4269 (2000)

12 COHERENT BACKSCATTERING = coherent probe Internal structure : Rb = quantum magnets Sr = classical dipole Quantum fluctuations : inelastic scattering non linear response Restoring two level atoms: (negative magneto-resistance) enhancement factor 2,0 1,9 1,8 1,7 1,6 1,5 1,4 1,3 1,2 1,1 1,0 Sr Rb Sr 88 : J=0 - J'=1 Rb 85 : F=3 - F'= angle (mrad) PRL, 85, 4269 (2000) PRL, 88, (2002) PRL, 89, (2002) PRL, 93, (2004) CBS enhancement Sr saturation parameter PRE, 70, (2004) Temperature : fast atomic dynamics slow transport of light CBS enhancement CBS enhancement 1,35 h // 1,30 1,25 1,20 1,15 1,10 1,05 MC B = 43G exp. B = angle (mrad) 1, B (G) PRL, 93, (2004) 1,15 1,10 T = 80µK Rb 85 T = 50mK PRL, 97, (2006) 1,05 0,01 0,1 1 k v rms / Γ

13 Towards strong localization of light : dense atomic clouds Ioffe-Regel : k l 1 k l 1000 N= N= 10 7 k l 3 Dipole Trap (M. Havey) T [K] Dynamical Breakdown Weak Localization of Light BEC Dynamical Breakdown Strong Localization of Light Strong Localization + BEC BEC

14 The case for Dicke

15 Single photon superradiance Dicke : N 2-level atoms Superradiant pair eg>+ ge> ee> eg>- ge> 1 excitation shared by many atoms gg> Subradiant pair R. Dicke (1954) Reviews by : R,Friedberg, S.R.Hartmann, J.T;Manassah (1973) M.Gross, S.Haroche (1982) Regained interest Theory : M. Scully, R,Friedberg, J.T.Manassah S.Prassad, R.Glauber Experiments: R. Roehlsberger C. Adams

16 Effective Hamiltonian Diagonal : On site energy Off diagonal : transport Open System Reminiscent of Anderson Hamiltonian Heisenberg model with global coupling

17 Photon Escape Rate Distribution Im(H eff )

18 Photon Escape Rate Distribution

19 Photon Escape Rates : single parameter scaling Measure of long lived photons Single parameter scaling b 0 = N/N cooperative effects dominate over disorder! no phase transition observed with P(Γ) Dicke > Anderson E. Akkermans, A. Gero, RK, PRL, 101, (2008)

20 Two level + polarisation no phase transition observed with P(Γ hν )

21 Beyond Photon escape times : Cloud of Atoms = Large Molecule (with atoms) dilute molecule dense molecule molecular spectrum? proximity resonances (Heller et al) Mie-Debye model (Sokolov et al)

22 Eigenvalues + polarisation Full vector model Scalar model e ikr /kr e ikr ( 1/kr + 1/kr 2 + 1/kr 3 ) Two level

23 Eigenvalues

24 What about Random Matrix Theory? Dilute gas Dense gas No energy level repulsion but in the complex plane

25 Partition Ratio N -1/3 N -2/3

26 Level repulsion vs Level Width Resonance overlap in superradiant transition (doorway states) and Anderson transition (Thouless criterion) g : dimensionless conductance β(g)= ln g ln L 3D metallic g >>1 2D insulating g <<1 1D ln g metal (g>>1)

27 Resonance overlap

28 Resonance overlap g : dimensionless conductance ln g β(g)= ln L 3D metallic g >>1 insulati g <<1 ng 1D 2D ln g metal (g>>1) g = 10 -L/ξ S. Skipetrov, I. Sokolov PRL 112, (2014) M. Antezza, Y. Castin, D. Hutchinson Phys. Rev. A 82, (2010).

29 So far : Effective Hamiltonian : Escape rate : no phase transition Eigenvalue analysis : phase transition in the scalar case Observable?

30 Driven System of N Dipoles Hamiltonian (RWA) Markov approx. Low saturation Trace over environment coherent drive H eff γ ij exp(ikr ij )/kr ji N coupled equations to be solved

31 N coupled equations : A many body problem with 1 photon and N atoms Mean Field Ansatz (Timed Dicke Ansatz) Continuous field β(r) index of refraction Numerical solution of the many body problem ( exact ) Experiments

32 Experimental observable : Average force on center of mass (easier to measure): Mean Field result (driven Timed Dicke Ansatz) Superradiance N at /N modes N at / (L/λ) 2 b 0 Disorder Σ Emission Diagram (Mie)

33 A new experiment Reduced radiation pressure force explained by cooperative scattering PRL, 104, (2010)

34 also works with ultra-cold atoms Experiments in Tübingen (Ph. Courteille et al.) PRA 82, (2010) in dipole trap will work in all large ultra(cold) atom clouds!

35 Beyond Mean Field : What to expect at resoance, when b(δ)>>1? Multiple scattering opaque sample more reflected light larger momentum transfer F c >F ind? No analytical result available Numerical solution of the many body problem ( exact ) Experiments

36 Spherical gaussian cloud : emission diagram Many body Timed Dicke Incoherent

37 How to probe coherent multiple scattering

38 Time dependent experiments : coherent scattering Cloud of Atoms = Large Molecule (with atoms) dilute molecule dense molecule molecular spectrum : narrow and broad lines (see nuclear physics) Broadband excitation vs coherent excitation

39 Time dependent experiments : coherent scattering E > Ω D > Γ D Superradiance = bright state Subradiance = metastable state Inverted system Γ N G > Inhomogeneous broadening in e i > => coupling in TD> Temnov, Woggon,PRL 95, (2005) T. Bienaimé, N. Piovella, R.K. PRL (2012)

40 Fano Coupling and controlled subradiance Fano Doppler Random Light shift T. Bienaimé, N. Piovella, R.K. PRL (2012)

41 Time dependent experiments : incoherent scattering I in 0 t probe beam L PM cold atoms I sc 0 e - t/τ 0 t transmitted diffuse intensity b = 2.4 b = 34 b = t (Γ 1 )

42 Time dependent experiments : incoherent scattering I in PM I sc e - t/τ 0 0 t 0 t probe beam L cold atoms Experimental work in progress Inelastic Raman scattering to avoid: Zeeman pumping in streched state

43 Time dependant scattering : beyond diffusion C. Aegerter et al., EPL, 2006 Anderson localisation t 0 exp(-l)? Dicke subradiance t 0 1/L?

44 Transmission in dense media? Milk Coupled Dipoles (dense clouds)

45 Combining Anderson and Dicke

46 Toy Model : Open Disordered System: A. Biella et al., EPL, 103, (2013) 3D Anderson model on 10x10x10 lattice hoping (Ω) + disorder (W) + opening (γ) Ω All sites coupled to one single decay channel : Q ij =1 γ

47 Hybrid Subradiant States «decoupled» from outside world

48 What s next : Hybrid state with H eff novel road vs localisation of light Subradiance experiments I in 0 t PM I sc 0 e - t/τ 0 t Atomic clocks (best clock) probe beam L cold atoms Dipole blockade Quantum Optics NMR: dipole-dipole coupling

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