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Controlling spontaneous Controlling spontaneous emissionemission

J-J GreffetLaboratoire Charles Fabry

Institut d’Optique, CNRS, Université Paris Sud Palaiseau (France)

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Lecture 1

Controlling spontaneous emission: nanoantennas and super radiance

Lecture 2

Harnessing blackbody radiation

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Goal of an antenna Goal of an antenna for single photon for single photon emissionemission

Electrical Engineering point of view:

The source drives the antenna currentsThe currents radiate

Quantum optics point of view:

The atom excites the antenna modeThe antenna mode has radiative losses

How can we get more energy out of one atom ?

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Example of Example of antennaantenna

Chevalet

5Mühlschlegel et al. Science 308 p 1607 (2005)

Optical NanoantennasOptical Nanoantennas

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Kühn et al. PRL 97, 017402 (2006)Anger et al., PRL 96, 113002 (2006)

Nanoantenna for Nanoantenna for fluorescencefluorescence

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Drexhage

Tailoring decay rate

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Controlling the directionControlling the direction

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Controlling the Controlling the lifetimelifetime

Fermi golden rule :

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Increasing the decay Increasing the decay raterate

Akselrod et al., Nature Photonics 8, p 835 (2014)

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Controlling Controlling spontaneous spontaneous

emission with a emission with a plasmonic resonatorplasmonic resonator

Nanoantennas Nanoantennas for light for light

emission by emission by inelastic inelastic tunnelingtunneling

Scattering by a dense cloud of cold atoms

Outline

F. Bigourdan B. Habert N. Schilder

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Nanoantennas for light emission Nanoantennas for light emission by inelastic tunnelingby inelastic tunneling

Can we overcome quenching ?

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What is the gap plasmon mode ?

500 nm 800 nm

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Emission with a nanocylinder antenna

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Where is the improvement coming from ?

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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

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Suppressing blinking of quantum dots

Collaboration: B. Dubertret, ESPCI

B. Habert

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Plasmonic nanoresonator

B. Ji et al., Nature Nanotechnology 10, p 170 (2015)

The gold nanoshell serves as a nanoantenna

Collaboration: B Dubertret (LPEM)

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+ - + -

B. Ji et al., Nature Nanotechnology 10, p 170 (2015)

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Colloidal Quantum Dots

Blinking

Collaboration: B Dubertret (LPEM)

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Neutral excitonCharged exciton (trion)

160 ns

80 ns

20 ns

Decay acceleration

B. Ji et al., Nature Nanotechnology 10, p 170 (2015)

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Is it a Purcell effect ?

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The gold nanoshell supresses the blinking

Neutral excitonCharged exciton (trion)

160 ns

80 ns

20 ns

Blinking suppression

B. Ji et al., Nature Nanotechnology 10, p 170 (2015)

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Plasmonic resonator

The gold nanoshell increases the stability of the QD:

B. Ji et al., Nature Nanotechnology 10, p 170 (2015)

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Collective effects in light Collective effects in light scatteringscattering

N.J. Schilder, C. Sauvan, J.P. Hugonin, A. Browaeys,

Y. Sortais, F. Marquier

Laboratoire Charles Fabry, Institut d’Optique, Palaiseau (France)

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System of System of interestinterest

Dense cloud of ~ 1 - 500 atomsRandom atom distribution

1 μm ~

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1. Dense sample: or

1. Dipole energy dominates temperature:

T < 100 μK ( ~ 1 MHz)

Laser cooled atomic gases

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)

Experiments with large (106 - 109) and optically thick cold samples

λ ~1 μm

Conditions to observe optical resonant dipole-dipole interactions

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•Spontaneous emission (low excitation regime)

•Scattering of light (low excitation regime)

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Spontaneous Spontaneous emissionemission

What is the influence of collective effects on the spontaneous emission rate in the presence of strong interactions?

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Wigner-Weisskopf Wigner-Weisskopf theorytheory

Hamiltonian of the system:

Atom-photon coupling constant

No rotating Wave Approximation is made in order to keep all interactions mediated by virtual photons ! (by evanescent waves for nanophotonics people).

Fixed polarization + along the cloud axis.

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Wigner-Weisskopf Wigner-Weisskopf theorytheory

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Choice of the general form of the wavefunction (low excitation)

Linear system for the eigenstates

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Wigner-Weisskopf Wigner-Weisskopf theorytheory

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Choice of the general form of the wavefunction (low excitation)

Linear system for the eigenstates

Discussion: i) The system is identical to the classical pictureii) The near-field vectorial interactions are essential(and therefore no RWA can be performed).

Li et al., PRA 87, 053837 (2013)

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EigenstatesEigenstates

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Type 1 and 2Type 1 and 2

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Structure of super radiant Structure of super radiant statesstates

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Type 3Type 3

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Superradiant polaritonic Superradiant polaritonic modesmodes

Properties

1. Large decay rate (> 15 0)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 ?

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Superradiant polaritonic Superradiant polaritonic modesmodes

Properties

1. Large decay rate (> 15 0)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 ?

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Experimental investigations: weak excitation limit

F = 1

F = 2

F’ = 3 Δ

Laser - cooled 87Rb atoms T ~ 100 K

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Scattering in the low excitation Scattering in the low excitation regimeregime

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.

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Role of super radiant Role of super radiant modesmodes

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Coherent and incoherent Coherent and incoherent scatteringscattering

Light scattering by a suspension of latex beads in water.

<E> = mean field (ensemble average)= coherent field= collimated fieldE = fluctuating field= incoherent field= diffuse field

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Coherent and incoherent Coherent and incoherent scatteringscattering

It can be shown that:

In a diagrammatic approach, the effective permittivity is essentially given by the so-calledmass-operator. For dense media, the inclusion of recurrent scattering terms is required.

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Far-field scattering patternFar-field scattering pattern

Coherent scattering Incoherent scattering

Most of the light is scattered coherently !

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Is Clausius Mossotti formula Is Clausius Mossotti formula valid ? valid ?

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Order of magnitude Order of magnitude analysisanalysis

Estimate of the permittivity:

At resonance:

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Effective permittivityEffective permittivity

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Structure of super radiant Structure of super radiant statesstates

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Controlling Controlling spontaneous spontaneous

emission with a emission with a plasmonic resonatorplasmonic resonator

Nanoantennas Nanoantennas for light for light

emission by emission by inelastic inelastic tunnelingtunneling

Scattering by a dense cloud of cold atoms