Coherent Backscattering, Photon Localization and Random Laser with Cold Atoms

Transcription

1 Coherent Backscattering, Photon Localization and Random Laser with Cold Atoms Robin Kaiser CLXXIII International School of Physics "Enrico Fermi" "Nano optics and atomics: transport of light and matter waves«varenna, Como Lake, Italy June 23rd to July 3rd

2 Overview of this lecture : 1. Coherent Light Transport in Cold Atoms 1.1 Coherent Backscattering 1.2 Quantum Multiple Scattering 2. Random Laser with Cold Atoms 2.1 Lasing with Cold Atoms 2.2 Random Lasing with Cold Atoms 2

3 Overview of this lecture : 1. Coherent Light Transport in Cold Atoms 1.1 Coherent Backscattering 1.2 Quantum Multiple Scattering 2. Random Laser with Cold Atoms 2.1 Lasing with Cold Atoms 2.2 Random Lasing with Cold Atoms 3

4 Scattering in disordered systems Single scattering scat 1 nσ Beer-Lambert law : T coh =exp(-l/ scat ) L Multiple scattering Ohm s law : T diff = scat / L 1.1 Coherent Backscattering 4

5 Interferences and speckle θ fixed scatterers : speckle pattern scattered intensity N E=Σ E i i=1 configuration average? 1.1 Coherent Backscattering θ 5

6 Configuration Averaged Intensity uncorrelated paths add incoherently I 0 k in θ (1) r in r out correlated (i.e. reciprocal) paths add coherently k out θ (2) ϕ=(k in +k out ).(r in -r out ) θ=0 ϕ = 0 for any path 1.1 Coherent Backscattering Coherent Backscattering <I(0)> <I(θ)> = 2 6

7 Experimentel Setup cooled CCD beamsplitter scattering medium lens ( f =500mm ) laser beam 1.1 Coherent Backscattering 7

8 Configuration Average Single realization Configuration average 1.1 Coherent Backscattering θ (mrad) 8

9 scattered intensity Diluted Milk Teflon Paper Polystyrene θ (mrad) 1.1 Coherent Backscattering 9

10 cone with : θ=2π Coherent backscattering λ 0 scat I N max Σ N=2 I I { θ scat θ cone height : reciprocal amplitudes (phase, intensity) Young double slits / self-aligned multiple Sagnac interferometer θ 1.1 Coherent Backscattering 10

11 Lens beam splitter CCD MOT Probe laser atoms excited on resonance 1.1 Coherent Backscattering 11

12 PROBING and MANIPULATING the COHERENCE of photons in disordered systems scattering effect (cross section) vs propagation effect (index of refraction) interference contrast : differential amplitude and/or phase effects (geometrical phase compensated) E I e iφ I + E II e iφ II 1.1 Coherent Backscattering 12

13 Influence of internal structure 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'=4 h // h 1.1 Coherent Backscattering angle (mrad) 13

14 Influence of internal structure degenerated ground state : quantum magnets broken reciprocity reduced contrast! Amplitude effect :an example : Rayleigh scattering on J=1/2 J =1/2 J=1/2 z J=1/2 - - h + = σ h + = σ - direct path : amplitude E I 0 reverse path : amplitude E I = Coherent Backscattering

15 Other results on coherent backscattering with cold atoms : CBS + internal structure Experiment : PRL (1999); PRL (2002); Theory : PRL (2000); PRA (2001); CBS + Hanle / Faraday effect Experiment : PRL (2002), PRL (2004) CBS + inelastic scattering Experiment : PRE (2004); Theory : PRA (2004), PRE (2005) CBS + dynamical breakdown Experiment : PRL (2006) 1.1 Coherent Backscattering more on also : M. Havey (Norfolk, USA) 15

16 Perspectives :Towards strong localization of light Ioffe-Regel : k 1 Dynamical Breakdown Dynamical Breakdown k 1000 N= T [K] Weak Localization of Light Rb Strong Localization of Light BEC N= 10 8 k BEC Strong Localization + BEC Coherent Backscattering n [cm -3 ] 16

17 Overview of this lecture : 1. Coherent Light Transport in Cold Atoms 1.1 Coherent Backscattering 1.2 Quantum Multiple Scattering 2. Random Laser with Cold Atoms 2.1 Lasing with Cold Atoms 2.2 Random Lasing with Cold Atoms 17

18 How to trap a photon with N atoms? disorder Anderson Localization Radiation Trapping Dicke Subradiance order Photonic Crystal slow/stopped light, quantum holography decoherence / classical world 1.2 Quantum Multiple Scattering quantum coherence / entanglement 18

19 dilute 1/ n λ 3 kl dense Quantum Multiple Scattering E-3 1E-4 1E-5 1E-6 1E-7 1E-8 small few atoms Single Atom Dicke Radiation Trapping Anderson many atoms! L/λ large 19

20 1954 : Dicke super- and subradiant states Superradiance = symetric state (easy to observe) Subradiance = antisymetric states ( fragile : difficult to observed) = = Correlated dipoles R. Dicke 1954 Feld et al Quantum Multiple Scattering 20

21 Photon Escape Rates from effective Hamiltonian H e = ~ω 0 i ~Γ 0 2 Sz + ~Γ 0 2 P i6=j V ijs + i S j 1.2 Quantum Multiple Scattering size : a = L/λ disorder parameter W=1/kl 21

22 Photon Escape Rates from effective Hamiltonian scaling parameter C C(a,W)= 1-2 R 1 dγp (Γ) b= cooperative effects dominate no phase transition observed with P(Γ) 1.2 Quantum Multiple Scattering 22

23 Cloud of Atoms = Large Molecule (with atoms) molecular spectrum? dilute molecule dense molecule 1.2 Quantum Multiple Scattering 23

24 What s next? Cloud Compression! Detection techniques : 1.2 Quantum Multiple Scattering 24

25 Overview of this lecture : 1. Coherent Light Transport in Cold Atoms 1.1 Coherent Backscattering 1.2 Quantum Multiple Scattering 2. Random Laser with Cold Atoms 2.1 Lasing with Cold Atoms 2.2 Random Lasing with Cold Atoms 25

26 Gain Mechanisms with Cold Atoms Mollow gain (used in lasing without inversion ) internal degree of freedom of 2 level system excited/ground state population inversion : π e > π g requires high pump intensities Recoil induced resonances / Rayleigh gain (used in Collective Atomic Recoil Laser ) external degree of freedom (motion) population inversion : π(v+dv)>π(v) (free moving atoms) vibrational levels of ground population inversion : π n > π n (atoms bound in lattice) Raman gain internal degree of freedom of multilevel system population inversion : π g1 > π g2 large in cold atoms Four Wave Mixing phase conjugation self-alignement / multimode 2.1 Lasing with Cold Atoms e> g> P e (v) P g (v) 1,n> 2,n> gain 1,n-1> 2,n-1> m 2 > g> m 1 > e> g> 26 e>

27 Gain Mechanisms with Cold Atoms b : optical thickness 2.1 Lasing with Cold Atoms 27

28 Experimental setup for laser cavity R=95% R=99.5% low finesse cavity : = 16 N at Pump power : 10-50mW, waist 3mm : s 0 >>1 2.1 Lasing with Cold Atoms 28

29 Cavity + Cold Atoms with Gain : cold atoms inside Laser Radiation 300µW 2.1 Lasing with Cold Atoms 29

30 With One Pump Beam MULTIPLE COLD ATOM LASERS Pump Detuning Raman Laser Mollow Laser Raman Laser 2 µw 30 µw 2 µw Polar Narrow spectrum (<1MHz) Polar // «large» spectrum (>6MHz) Polar Narrow spectrum (<1MHz) 2.1 Lasing with Cold Atoms 30

31 With Two Pump Beam MULTIPLE COLD ATOM LASERS Pump Detuning FWM Laser Mollow Laser FWM Laser 300 µw 30 µw 300 µw Polar Very narrow spectrum emission on very many transverse modes 2.1 Lasing with Cold Atoms Polar // «large» spectrum (>6MHz) Polar // Very narrow spectrum emission on very many transverse modes 31

32 Cold Atoms Laser as a Class C laser : Chaotic Laser atomic populations optical coherences (atoms) optical field 2.1 Lasing with Cold Atoms time frequency 32

33 Overview of this lecture : 1. Coherent Light Transport in Cold Atoms 1.1 Coherent Backscattering 1.2 Quantum Multiple Scattering 2. Random Laser with Cold Atoms 2.1 Lasing with Cold Atoms 2.2 Random Lasing with Cold Atoms 33

34 What is a random standard laser? Two ingredients for a random standard laser : 1) An amplifying material 2) Feedback : by an multiple optical cavity scattering + mode selection (spatial and longitudinal coherence) - Feedback provides Chain reaction: intensity grows until gain saturation occurs The «Photonic Bomb» (Lethokov, 1967) 34

35 Incoherent Random Laser Photonic Bomb unfolded path length > gain length ( L l sc ) 2 l sc >l g Volume Gain vs Surface Loss critical mass/volume L>2π 2.2 Random Lasing with Cold Atoms l g l sc 3 35

36 Some Random Lasers : semi-conductors, dye, astrophysical laser cold atoms? ZnO powder Recent reviews: H. Cao, Waves Random Media 13, 1 (2003). H. Cao, J. Phys. A 38, (2005). D. Wiersma, Nature Physics 4, 359 (2008). 2.2 Random Lasing with Cold Atoms S. Johansson, V. Letokhov, PRL, 90, (2003) Y. P. Varshni, C. S. Lam, Astrophysics and Space Science 45, 87 (1976) 36

37 Random Laser requires : radiation trapping + gain 2.2 Random Lasing with Cold Atoms 37

38 COMBINE radiation trapping and gain Problem : the scatterers and amplifiers are the same atoms! Scattering Gain Is it possible to get bot simultaneously? Pumping, necessary to get gain, reduces drastically the scattering cross-section 2.2 Random Lasing with Cold Atoms 38

39 Letokhov diffusive model = linear gain length (sphere geometry) = mean free path Transmission experiments: with the extinction length 2.2 Random Lasing with Cold Atoms 39

40 The atomic polarizability = on-resonance atomic cross-section = polarizability (with ~ : dimensionless) On-resonance optical depth : α depends on : Rabi frequency Ω of the pump atom-pump detuning 2.2 Random Lasing with Cold Atoms detuning δ from the pump 40

41 Example : Mollow gain with Ω,, δ in unit of Γ. The best : b 0cr 200. Hard, but it s reached in some cold-atoms experiments. 1) A threshold exists! 2) ± within reach 2.2 Random Lasing with Cold Atoms 3) signature? 41

42 Random Laser with Cold Atoms Lasing at and close to resonance : Threshold prediction increase optical thickness to 300 : but Signature of random laser with cold atoms??? Cold atoms required??? 2.2 Random Lasing with Cold Atoms Laser Action in Wolf-Rayet WC stars 42

43 Conclusion : 1. Coherent Light Transport in Cold Atoms Interference in Multipe Scattering Quantum Multiple Scattering. 2. Random Laser with Cold Atoms Lasing with Cold Atoms Random Lasing with Cold Atoms. 43

44 Cold Atoms in Nice : www. kaiserlux.eu/coldatoms Rubidium 1 W. Guerin (Post-doc) N. Mercadier (Ph. D.) BEC G. Labeyrie X.-L. Song (Post-doc) Rubidium 2 T. Bienaimé (Ph. D.) H. Terças (visiting Ph. D.) Strontium D. Wilkowski * M. Chalony (Ph. D.) J.-F. Schaff (Ph. D.) Theory G. Batrouni C. Miniatura * P. Vignolo F. Hébert M. Gattobigio * on leave to Singapour Collaborations R. Carminati, S. Skipetrov D. Delande E. Akkermans Ph. Courteille, N. Piovella, G.Robb : CNRS, UNSA, PACA, CG06, 44 BNM, ESF, ANR, INTERCAN

45 45