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Controlling spontaneous emission
J-J Greffet
Laboratoire Charles Fabry
Institut d’Optique, CNRS, Université Paris Sud
Palaiseau (France)
1
Lecture 1
Controlling spontaneous emission:
nanoantennas and super radiance
Lecture 2
Harnessing blackbody radiation
2
Goal of an antenna for
single photon emission
Electrical Engineering point of view:
The source drives the antenna currents
The currents radiate
Quantum optics point of view:
The atom excites the antenna mode
The antenna mode has radiative losses
How can we get more energy out of one atom ?
3
Example of antenna
Chevalet
4
Optical Nanoantennas
Mühlschlegel et al. Science 308 p 1607 (2005)
5
Nanoantenna for fluorescence
Anger et al., PRL 96, 113002 (2006)
Kühn et al. PRL 97, 017402 (2006)
6
Tailoring decay rate
Drexhage
7
Controlling the direction
8
Controlling the lifetime
Fermi golden rule
:
G=
1
t
is proportional to LDOS
t vacuum
LDOS
FP =
=
t mc
LDOSvacuum
w2
LDOSvacuum (w ) = 2 3 ; LDOSmc (w ) =
3p c
( Dw / 2p )
(w - w0 )
2
1
2
æ Dw ö Vmod e
+ç
÷
è 2 ø
; LDOSmc (w 0 ) =
2Q
pw 0Vmod e
LDOSmc (w )
3Ql3
Fp =
=
LDOSvacuum (w ) 4 p 2Vmod e
9
Increasing the decay rate
Akselrod et al., Nature Photonics 8, p 835 (2014)
10
Outline
Nanoantennas for
light emission by
inelastic tunneling
F. Bigourdan
Controlling spontaneous Scattering by a dense
emission with a
cloud of cold atoms
plasmonic resonator
B. Habert
N. Schilder
11
Nanoantennas for light emission by
inelastic tunneling
Can we overcome quenching ?
12
13
What is the gap plasmon mode ?
500 nm
800 nm
14
Emission with a nanocylinder antenna
15
Where is the improvement coming from ?
16
Nanoantenna design rules
Chen et al., Phys. Rev. Lett. 108, 233001 (2012)
Akselrod et al., Nature Nanophotonics 8, p 835 (2014)
Bigourdan et al., Opt. Exp. 22, 2337 (2014)
Kern et al., arxiv 1502.04935
17
Suppressing blinking of quantum dots
B. Habert
Collaboration: B. Dubertret, ESPCI
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Plasmonic nanoresonator
The gold nanoshell serves as a nanoantenna
Collaboration: B Dubertret (LPEM)
B. Ji et al., Nature Nanotechnology 10, p 170 (2015)
19
+ -
+
B. Ji et al., Nature Nanotechnology 10, p 170 (2015)
-
20
Colloidal Quantum Dots
Blinking
Collaboration: B Dubertret (LPEM)
21
Decay acceleration
Charged exciton
(trion)
Neutral exciton
160 ns
80 ns
20 ns
B. Ji et al., Nature Nanotechnology 10, p 170 (2015)
22
Is it a Purcell effect ?
23
Blinking suppression
Charged exciton
(trion)
Neutral exciton
160 ns
80 ns
20 ns
The gold nanoshell supresses the blinking
B. Ji et al., Nature Nanotechnology 10, p 170 (2015)
24
Plasmonic resonator
The gold nanoshell increases the stability of the QD:
B. Ji et al., Nature Nanotechnology 10, p 170 (2015)
25
Collective effects in light scattering
N.J. Schilder,
C. Sauvan,
J.P. Hugonin,
A. Browaeys,
Y. Sortais, F. Marquier
Laboratoire Charles Fabry, Institut d’Optique, Palaiseau (France)
26
System of interest
1 μm ~ l
Dense cloud of ~ 1 - 500 atoms
Random atom distribution
n
3
»1
27
Conditions to observe optical resonant
dipole-dipole interactions
1. Dense sample:
or
λ ~1 μm 
1. Dipole energy dominates temperature:
 T < 100 μK (G ~ 1 MHz)
Laser cooled atomic gases
Experiments with large (106 - 109) and optically thick cold samples
T. Bienaimé et al., PRL 104, 183602 (2010)
H. Bender et al., PRA 82 011404 (2010)
Chalony et al., PRA 84 011401 (2011)
Balik et al., PRA 87, 053817 (2013)
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• Spontaneous emission (low excitation
regime)
• Scattering of light (low excitation
regime)
29
Spontaneous emission
What is the influence of collective effects on the spontaneous emission rate in the
presence of strong interactions?
30
Wigner-Weisskopf theory
Hamiltonian of the system:
Atom-photon coupling constant
Fixed polarization s+ along the cloud axis.
No rotating Wave Approximation is made in order to keep all interactions mediated by
virtual photons ! (by evanescent waves for nanophotonics people).
31
Wigner-Weisskopf theory
Choice of the general form of the wavefunction (low excitation)
+
Linear system for the eigenstates
32
Wigner-Weisskopf theory
Choice of the general form of the wavefunction (low excitation)
+
Linear system for the eigenstates
Discussion:
i) The system is identical to the classical picture
ii) The near-field vectorial interactions are essential
(and therefore no RWA can be performed).
Li et al., PRA 87, 053837 (2013)
33
Eigenstates
34
Type 1 and 2
35
Structure of super radiant states
36
Type 3
37
Superradiant polaritonic modes
Properties
1. Large decay rate (> 15 G0)
2. All atoms are excited.
3. Spatial structure accounting for the
retardation.
4. There are typically 5 superradiant
states among 450 states.
Why 5 states ?
38
Superradiant polaritonic modes
Properties
1. Large decay rate (> 15 G0)
2. All atoms are excited.
3. Spatial structure accounting for the
retardation.
4. There are typically 5 superradiant
states among 450 states.
Why 5 states ?
39
Experimental investigations: weak excitation limit
F’ = 3
Δ
F=2
F=1
Laser - cooled 87Rb atoms
T ~ 100 mK
40
Scattering in the low excitation regime
Eill (rn ) = Einc ( rn ) + å G ( rn , rm ) pm
m¹n
pm = a Eill (rm )
The positions are generated randomly.
The calculation is repeated over an ensemble of random realizations.
Both the field and the square of the field are averaged.
41
Role of super radiant modes
42
Coherent and incoherent scattering
Light scattering by a suspension of latex beads in water.
E = E + d E
E
2
= E
2
+ d E
2
<E> = mean field (ensemble average)= coherent field= collimated field
dE = fluctuating field= incoherent field= diffuse field
43
Coherent and incoherent scattering
It can be shown that:
w2
k ´ k ´ E + eeff ( k, w ) 2 E = 0
c
In a diagrammatic approach, the effective permittivity is essentially given by the so-called
mass-operator. For dense media, the inclusion of recurrent scattering terms is required.
44
Far-field scattering pattern
Coherent scattering
Incoherent scattering
Most of the light is scattered coherently !
45
Is Clausius Mossotti formula valid ?
e -1 na
= e+2
3
46
Order of magnitude analysis
Estimate of the permittivity:
c " = n s (w )
At resonance:
3l 2
s (w 0 ) = = 6p 2p
2
c "(w0 ) = 6p n
3
47
Effective permittivity
48
Structure of super radiant states
49
Nanoantennas for
light emission by
inelastic tunneling
Controlling spontaneous Scattering by a dense
emission with a
cloud of cold atoms
plasmonic resonator
50