Robin KAISER INLN, Nice, Francemesoimage.grenoble.cnrs.fr/IMG/pdf/cargese2014/kaiser2.pdf · beam splitter Probe laser N ≈ 10 10 T≈100µK kl ≈ 1000 Coherence after resonant

Université de Nice Sophia Antipolis - CNRS I N L N

Multiple scattering of light by cold atoms

Robin KAISER

INLN, Nice, France

Waves and disorder, Cargèse, France, July 1 – 11, 2014


Lecture 1: 1.1 Two level atoms1.2 Diffusion

Lecture 2: 2.1 The case for Anderson2.2 The case for Dicke2.3 Anderson and Dicke


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


DickeSuperradiance

Coherent Multiple Scattering

Multiplescattering

Interferences

Anderson Localisation

“Local” “Global”

mesoscopic transport(superconductors, insulators)

Cooperative emission (superradiant lasers, antennas,

quantum memories)


AndersonLocalization

RadiationTrapping

DickeSubradiance

PhotonicCrystal

disorder

order

coherencedecoherence

slow/stopped light, quantum holography

How to trap a ‘photon’ with N atoms?


The case for Anderson …


θθθθ

((((1111))))kin

((((2222))))

I0

rin

routkout

θθθθ

Weak Localization => Coherent Backscattering

· uncorrelated paths add incoherently

∆ϕ=(kin+kout).(rin-rout) θ=0 ⇒ ∆ϕ = 0 for any path

<I(0)>

<I(θ)>>∆θCBS)>= 2

Coherent

Backscattering

· correlated (i.e. reciprocal) paths

add coherently

multiple self-aligned Sagnac interferometer


Single

realization

Configuration Average

θ (mrad)


Single

realization

Configuration Average

θ (mrad)

Configuration

average


CCD

Lens

MOT

beam

splitter

Probe laserN ≈ 1010

T≈100µKkl ≈ 1000

Coherence afterresonant scattering

with atoms !

also : M. Havey et al.

Phys. Rev. Lett., 83, 5266 (1999)

Weak Localisation with resonant scattering by atoms


Phys. Rev. Lett., 85, 4269 (2000)

Theory : • no “exact” solution• diagrammatic approach

Excellent agreement (no free parameter)

0 2 4 6-2-4-6

q

(mrad)

experimentMC simulation

h

^

CB

Sen

han

cem

ent

1.00

1.05

1.10

1.15

1.20

h //

lin //lin

^

Rb85 : F=3 - F'=4=4

Sr88 : J=0 - J'=1

=1

CB

Sen

han

cem

ent

1

2

0 2 4 6-2-4-6

q

(mrad)

h //

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

-3 -2 -1 0 1 2 3

1,0

1,1

1,2

1,3

1,4

1,5

1,6

1,7

1,8

1,9

2,0

Rb

Sr

Sr88 : J=0 - J'=1

Rb85 : F=3 - F'=4

angle (mrad)

enhan

cem

ent

fact

or

Quantum fluctuations :inelastic scattering non linear response

Internal structure : Rb = quantum magnets Sr = classical dipole

Restoring two level atoms:(negative magneto-resistance)

0.0 0.2 0.4 0.6 0.81.5

1.6

1.7

1.8

1.9

2.0

CB

S e

nh

ance

men

t

saturation parameter

Sr88

COHERENT BACKSCATTERING = coherent probe

PRL, 85, 4269 (2000) PRE, 70, 036602 (2004)

PRL, 88, 203902 (2002)

PRL, 89, 163901 (2002)

PRL, 93, 143906 (2004)

-10 0 10 20 30 40 501,00

1,05

1,10

1,15

1,20

1,25

1,30

1,35

-60 -40 -20 0 20 40 60

CB

Sen

han

cem

ent

B (G)

angle (mrad)

B = 0

B = 43G

h //

MC

exp.

PRL, 93, 143906 (2004)

Temperature :‘fast’ atomic dynamics ‘slow’ transport of light

0,01 0,1 11,05

1,10

1,15

CB

S e

nhan

cem

ent

k vrms

/ Γ

T = 80µK T = 50mK

Rb85

PRL, 97, 013004 (2006)


Towards strong localization of light : dense atomic clouds

Strong Localization

+BECBEC

10141012 1016 1018 10201010

10-10

10-8

10-6

10-4

10-2

10-0

Dynamical BreakdownDynamical BreakdownT

[K

]

Weak Localization

of Light

BEC

Ioffe-Regel :

Strong Localization

of Light

k l ≈ 1000N= 1010

k l ≈ 1

N= 107

k l ≈ 3

Dipole Trap(M. Havey)


The case for Dicke …


Single photon superradianceDicke : N ’’2-level’’ atoms

R. Dicke (1954)Reviews by : R,Friedberg, S.R.Hartmann, J.T;Manassah (1973)M.Gross, S.Haroche (1982)

1 excitation shared by many atoms

Regained interestTheory : M. Scully,

R,Friedberg, J.T.ManassahS.Prassad, R.Glauber

Experiments: R. RoehlsbergerC. Adams

Superradiant pair

Subradiant pair

|ee>

|eg>+ |ge>

|gg>

|eg>- |ge>


Effective Hamiltonian

• Open System • Reminiscent of Anderson Hamiltonian• Heisenberg model with global coupling

Off diagonal :transport

Diagonal :On site energy


Photon Escape Rate Distribution

∝ Im(Heff)


Photon Escape Rate Distribution


Photon Escape Rates : single parameter scaling

E. Akkermans, A. Gero, RK, PRL, 101, 103602 (2008)

cooperative effects dominate over disorder !no phase transition observed with P(Γ)

Single parameter scalingb0 = N/N⊥

Dicke > Anderson

Measure of long lived photons


Two level + polarisation

no phase transition observed with P(Γhν)


Cloud of Atoms = Large Molecule (with 1010 atoms)

‘dilute’ molecule‘dense’ molecule

molecular spectrum ?

Beyond Photon escape times :

proximity resonances

(Heller et al)

Mie-Debye model

(Sokolov et al)


Eigenvalues

eikr/kr

Full vector model

Scalar model

eikr ( 1/kr + 1/kr2 + 1/kr3)

Two level

+ polarisation


Eigenvalues


What about Random Matrix Theory ?

No energy level repulsion … but in the complex plane

Dilute gas Dense gas


Partition Ratio

N-1/3 N-2/3


Level repulsion vs Level WidthResonance overlap in superradiant transition (doorway states) and Anderson transition (Thouless criterion)

metal (g>>1)

ln g

∂ ln g

∂ ln L

β(g)=

1D

2D

3D

g : dimensionless conductance

1<<g

insulating

metallic

1>>g


Resonance overlap


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

Resonance overlap

metal (g>>1)

ln g

∂ ln g

∂ ln Lβ(g)=

1D

2D

3D

g : dimensionless conductance

1<<ginsulati

ng

metallic1>>g

g = 10-L/ξ

• M. Antezza, Y. Castin, D. Hutchinson

Phys. Rev. A 82, 043602 (2010).


So far :

Effective Hamiltonian :

Escape rate : no phase transition

Eigenvalue analysis : phase transition in the scalar case

Observable?


Hamiltonian(RWA)

Markov approx.

Low saturation

Heffcoherent

drive

Trace over environment

N coupled equations to be solved

Driven System of N Dipoles

γij ∝ exp(ikrij)/krji


N coupled equations :A many body problem with 1 photon and N atoms

• Mean Field Ansatz (Timed Dicke Ansatz)

• Continuous field β(r)

• Numerical solution of the many body problem (‘exact’)• Experiments

index of refraction


Experimental observable : Average force on center of mass (easier to measure):

“Mean Field” result (driven Timed Dicke Ansatz)

DisorderEmissionDiagram

(Mie)

Superradiance

Nat/Nmodes ∝∝∝∝ Nat / (L/λλλλ)2 ∝∝∝∝ b0Σ ≠ ∫


PRL, 104, 183602 (2010)

A new experiment

Reduced radiation pressure force

explained by

cooperative scattering


also works with ultra-cold atoms

in dipole trap

will work in all large ultra(cold) atom clouds !

Experiments in Tübingen (Ph. Courteille et al.)PRA 82, 011404 (2010)


Beyond Mean Field :

• What to expect at resoance, when b(δ)>>1? • Multiple scattering … opaque sample …

more reflected light … larger momentum transfer Fc>Find ?

• No analytical result available • Numerical solution of the many body problem (‘exact’)• Experiments


2

4

6

30

210

60

240

90

270

120

300

150

330

180 0

Many body

Timed Dicke

Incoherent

Spherical gaussian cloud : emission diagram


How to probe coherent multiple scattering


Cloud of Atoms = Large Molecule (with 1010 atoms)

‘dilute’ molecule‘dense’ molecule

molecular spectrum : narrow and broad lines

(see nuclear physics)

Broadband excitation vs coherent excitation

Time dependent experiments : coherent scattering


Temnov, Woggon,PRL 95, 243602 (2005)

ΩΩΩΩ⊥⊥⊥⊥

| G >

| E >| D >

ΓΓΓΓN

ΓΓΓΓD

Inhomogeneous broadening in |ei> => coupling in |TD>

Superradiance = bright stateSubradiance = metastable state

Time dependent experiments : coherent scatteringInverted system

T. Bienaimé, N. Piovella, R.K. PRL (2012)


Fano Coupling and controlled subradiance

Fano

DopplerRandom Light shift

T. Bienaimé, N. Piovella, R.K. PRL (2012)


0 50 100 150

tran

smit

ted

dif

fuse

inte

nsi

ty

t (Γ−1

)

10−1

1

b = 19

b = 2.4

b = 34

probe

beamcold

atoms

0 t

PM

0

∝ e- t/τ0

t

IscI

in

L

Time dependent experiments : incoherent scattering


probe

beamcold

atoms

0 t

PM

0

∝ e- t/τ0

t

IscI

in

L

Time dependent experiments : incoherent scattering

Experimental work in progress

Inelastic Raman scattering to avoid: Zeeman pumping in streched state


Time dependant scattering : beyond diffusion

C. Aegerter et al., EPL, 2006

Anderson localisationt0∝∝∝∝ exp(-L)

?

…Dicke

subradiancet0∝∝∝∝1/L ?


Transmission in dense media?

Milk

Coupled Dipoles(dense clouds)


Combining Anderson and Dicke …


Toy Model : Open Disordered System:A. Biella et al., EPL, 103, 57009 (2013)

3D Anderson model on 10x10x10 latticehoping (Ω) + disorder (W) + opening (γ)

All sites coupled to one single decay channel : Qij=1

Ω

γ


Hybrid Subradiant States « decoupled » from outside world


What’s next :

• Hybrid state with Heff

novel road vs localisation of light

• Subradiance experiments

• Atomic clocks (best clock)

• Dipole blockade• Quantum Optics• NMR: dipole-dipole coupling

probe

beamcold

atoms

0 t

PM

0

∝ e- t/τ0

t

IscI

in

L


Robin KAISER INLN, Nice, Francemesoimage.grenoble.cnrs.fr/IMG/pdf/cargese2014/kaiser2.pdf · beam splitter Probe laser N ≈ 10 10 T≈100µK kl ≈ 1000 Coherence after resonant

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