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Quantum Optics with Single CdSe/ZnS Colloidal Nanocrystals 739

a cavity. The ﬁ rst experiments were carried out in the microwave domain for which the size of

the needed cavities is relatively large. Remarkable technological improvements obtained during

the last 20 years offered the possibilty of realizing CQED experiments with semiconductor devices

and optical frequencies. Using epitaxially grown quantum dots and three-dimensional cavities

exhibiting large quality factors and small volume modes, the modiﬁ cation of spontaneous emis-

sion rate and the strong coupling regime between one electromagnetic mode and an individual

emitter have been observed. In this section, we detail the experiments involving optical cavities

and colloidal quantum dots already realized. We ﬁ rst summarize the crucial characteristics of

the various optical cavities distinguishing dieletric structures and metallic structures.

24.8.2 Weak coupling regime

In 1946, E.M. Purcell published the paper which is the pioneer work in the ﬁ eld of CQED [151] .

In this very short paper, he suggests that the radiative rate of an emitter can be modiﬁ ed using a

cavity, the modiﬁ cation depending on the quality factor Q and the effective volume of the cavity

mode V . Since then various theoretical works have dealt with the interaction between an emitter

and an optical mode of a cavity. Two regimes can be destinguished. The ﬁ rst one is the weak cou-

pling regime for which the spectral linewidth of the electromagnetic mode is much larger than

the one of the emitter. In this case, the energy excited emitter is irreversibly transferred from the

emitter to the continuum formed by the electromagnetic states. The modiﬁ cation of the radiative

rate can be found using Fermi’s golden rule. Hence, it depends also on the efﬁ ciency of the cou-

pling between the emitter and the ﬁ eld. For example, to increase the radiative rate, the emitter

must be located at a maximum of the electric ﬁ eld. The radiative rate is then multiplied by a fac-

tor usually called the Purcell factor and noted F

which is given by:

eff



(24.23)

where λ is the wavelength emission, Q , is the quality factor of the cavity and V

eff

the effective vol-

ume of the electromagnetic mode. Equation 24.23 shows that high Purcell factors are achieved

with cavities showing high quality factors and low mode-volumes.

The second regime, called strong coupling regime, corresponds to the case of a two-level sys-

tem coupled to the mode of a cavity characterized by a high quality factor Q . The Rabi oscillation

period which characterizes the energy exchange between the ﬁ eld and the emitter is much lower

than the lifetime of the photon in the cavity. This regime is at the heart of fundamental physics

experiments demonstrating the quantum non-locality or enabling the study of decoherence.

The conditions required by the strong coupling regime are the most difﬁ cult to obtain experi-

mentally and has not been observed yet for colloidal quantum dots. We now examine the differ-

ent optical cavities which can be used to get an F

factor as large as possible.

24.8.3 Dielectric cavities

The choice of the optical resonator is determined by various factors. The ideal cavity exhibits a

strong quality factor and a low mode volume, enables an easy collection of the emitted photons

and is easy to fabricate.

Three types of dielectric cavities are mainly used in solid-state CQED experiments. Microdisks

(or microtores) are produced by electron beam lithography and several wet etching steps. They

conﬁ ne light at their edges in whispering gallery modes exhibiting high quality factors. Their

main drawback lies in the difﬁ culty of collecting the light which corresponds to evanescent

waves located in the plane of the disk.

Micropillars are obtained by etching planar microcavities made of two Bragg mirrors. Light

conﬁ nement is due to two different effects. Vertically, it comes from the Bragg mirrors. Laterally, it

is due to total internal reﬂ ection at the air/semiconductor interface. Quantum dots can be grown

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740 Handbook of Self Assembled Semiconductor Nanostructures for Novel Devices in Photonics and Electronics

by epitaxy between the mirrors during the fabrication of the microcavity. Inserting colloidal

quantum dots is more difﬁ cult since the temperature of epitaxy is often too high to preserve the

high photoluminescence of nanocrystals.

Photonic crystals are periodic dielectric structures with a periodicity of the order of the emis-

sion wavelength. This gives rise to a particular dispersion of photons. The photon density of states

can be tailored, the light localized, the propagation strongly directed and the radiative emission

rate strongly modiﬁ ed. From a general point of view, photonic crystals are usually produced by

electron beam lithography and dry etching. For technical reasons, high quality factors have not

yet been achieved in three-dimensional structures. The best structures are the two-dimensional

photonic crystals etched in a membrane, which ensures the conﬁ nement in the direction perpen-

dicular to the plane corresponding to the structure. The size of the pattern depends strongly on

the wavelength. Since very low-dimensional structures are more difﬁ cult to produce, devices for

infrared wavelength about 1.5 μ m exhibit higher quality factors than the ones for visible light.

Quality factors as high as 10

have been obtained [152] . Very promising for telecommunication

applications, such structures cannot be used to control the emission of colloidal quantum dots

which emit visible light.

Until now, various alternative solutions have been found to fabricate photonic crystals suited

to modify colloidal quantum dots emission. Barth et al. prepared three-dimensional photonic

crystals by sedimentation of polystyrene beads [153] . After inserting colloidal quantum dots,

they performed defocused imaging to investigate the angular dependance of nanocrystal emis-

sion at the single molecule level. They demonstrated the anisotropy of photonic stop bands.

This experiment is a proof of principle of a new application of colloidal nanocrystals as nano-

metric probes of conﬁ ned electromagnetic ﬁ elds in nanophotonic structures. As the quantum

dot emission wavelength can be tuned over a wide range, this method could be applied to many

nanostructures.

In order to control the radiative lifetime of nanocrystals, Lohdahl et al . performed an experi-

ment with titania inverse opals which consists in face-centred cubic structures of air spheres

in a titania material [154] . The photonic crystal was made by inverting template-assisted self-

assembled structures. A modiﬁ ed lifetime was observed on quantum dots ensemble over a large

frequency bandwidth. Angle-resolved spectral measurements also proved the effect on the direc-

tionality of the emission. By changing the lattice parameter, they succeeded in inhibiting (by a

factor of 1.6) as well as accelerating (by a factor of 1.3) the radiative rate of CdSe nanocrystals.

The last structure was obtained by nanoimprint lithography in a composite polymer incorpo-

rating the colloidal quantum dots. Reboud et al . observed an enhancement of the light collection

efﬁ ciency by a factor of 2 compared to an unpatterned sample [155] .

24.8.4 Metallic photonic cavities

The conﬁ nement of light in dielectric structures is limited to dimensions of the order of the wave-

length. The corresponding micrometre-scale of photonic components such as optical ﬁ bres has

strongly limited the integration of photonic devices in electronic chips, which have reached nan-

ometre size. Recently, devices exhibiting surface plasmons have been proposed to realize circuits

with nanoscale features enabled to carry optical signals. Such plasmonic chips may solve the size

compatibity problem between electronics and photonics.

Surface plasmons are an extension of the plasmon physics (for a more precise description of

surface plasmons, one can read the review by H. Raether [156] ). The resolution of Maxwell equa-

tions at a metal/dielectric interface shows that optical waves can propagate along the surface of the

metal. The electromagnetic ﬁ eld decays exponentially in the direction perpendicular to the interface

and the dispersion curve of surface plasmons lies at the right of the light cone. Hence, they do not

propagate in this direction and, then, are called non-radiative modes. However, the corrugation of

the surface or a grating structure can couple surface plasmons and propagating ﬁ elds. In this case,

strong light emission can be obtained. Such processes are at the origin of phenomena such as sur-

face enhanced Raman scattering (SERS) of second harmonic generation on a metallic surface.

In 2002, the group of M. Bawendi was the ﬁ rst to study the effect of a rough metal ﬁ lm on

the ﬂ uorescence of colloidal CdSe nanocrystals [97] . The gold ﬁ lm exhibits peaks ranging from

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Quantum Optics with Single CdSe/ZnS Colloidal Nanocrystals 741

10 to 50 nm measured by an atomic force microscope. Using far-ﬁ eld microscopy and time-

resolved single-photon detection, they observed a complete conversion of the emission to linear.

They observed a reduction factor of the exciton lifetime larger than 10

. At the same time, the

detected efﬁ ciency is multiplied by 5. Hence, radiative and non-radiative decay rates are strongly

modiﬁ ed. The usually dominant Auger rate is no longer so efﬁ cient. This enables the ﬂ uorescence

of charged quantum dots to be detected, which are usually not ﬂ uorescent (section 24.5). The

simultaneous acceleration of radiative and non-radiative decay rates illustrates the possibilities

offered by the use of metallic structures as well as their drawback. Absorption and emission of

the nanocrystal are increased by the coupling of the nanocrystal with the metal plasmons. At

the same time, non-radiative decay chanels are enhanced by energy transfer from the quantum

dot to the metal. As a result, the quantum yield of the nanocrystal is reduced while the ﬂ uores-

cence intensity is increased.

After the use of a rough metallic surface, Zhang et al . reported results concerning the modiﬁ -

cation of nanocrystal ﬂ uorescence obtained with a two-dimensional textured Ag grating [157] .

The periodicity of the metallic surface is on the scale of the quantum dot emission wavelength.

Then, the energy of the quantum dot can excite surface plasmons which can scatter off the metal

through the coupling by the grating of the surface plasmons and propagating modes. Using an

angular-resolved detection scheme, the authors demonstrated the redirection of the emission as

well as a modiﬁ cation of its polarization. Time-resolved photoluminescence experiments showed

the enhancement of non-radiative and radiative decay rates. They are due to the modiﬁ cation

of the electromagnetic mode’s density directly linked to the mode dispersion of the corrugated

surface plamons. The decrease in Auger processes efﬁ ciency results in the reduction of blinking.

Since the analysis is carried out on ensembles, the exact contribution of blinking reduction and

quantum yield reduction cannot be quantitatively measured but the results conﬁ rm qualitatively

the observations made on rough metallic surfaces.

Another scheme used to enchance colloidal quantum dot ﬂ uorescence consists in a gold nano-

pocket aperture [158] . The nanocrystals are partially encapsulated in a smooth Au ﬁ lm with an

aperture lower than the emission wavelength. The enhancement depends strongly on the plas-

mons ’ characteristics which can be controlled through the gold ﬁ lm thickness. It is maximum for

a 50 nm layer. The increase of the detection intensity is attributed to the enhancement of local-

ized ﬁ eld intensity at the sharp edge of the nanopocket aperture, the high density of states due to

surface plasmons and the subwavelength nanopocket aperture size which couples surface plas-

mons to propagating photons.

24.8.5 Perspectives

The results detailed in this section illustrate the potential applications of the coupling between

colloidal quantum dots and metallic or dielectric nanophotonic structures. Very promising for

the realization of optoelectronic devices or biomedical image probing, such structures could also

be very useful in the ﬁ eld of quantum information. First, an efﬁ cient single-photon source emit-

ting at room temperature which could be used for the implementation of quantum cryptography

protocols could be developed. Light conﬁ nement inside the photonic cavities will allow control of

the polarization and of the radiative pattern of the nanocrystal ﬂ uorescence. Due to the Purcell

effect, the radiative emission rate will be increased improving the rate of this single photon

source. The originality of the new devices will lie in the realization of photonic structures work-

ing at visible wavelengths, which requires very small patterns. Moreover, the great ﬂ exibility and

ease of utilization even at the single molecule level should be used to control the position of the

nanocrystals on a surface at nanometre-sized scale to optimize the coupling between the emitter

and the mode of the cavity. At the single nanoobject level, this phase of CQED experiments car-

ried on semiconductor structures remains a technical challenge.

Finally, let us mention that the colloidal nature of nanocrystals allows the addition of func-

tions by chemical reactions. This possibility is widely used in cellular imaging, where nanocrys-

tals are attached to biomolecules in order to be used as markers, but has been little explored in

single-emitter quantum optics. It might, however, offer ways to deposit nanocrystals on speciﬁ c

sites of a photonic structure.

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742 Handbook of Self Assembled Semiconductor Nanostructures for Novel Devices in Photonics and Electronics

24.9 Conclusions

Colloidal quantum dots are often called artiﬁ cial atoms since the three-dimensional conﬁ nement

results in a discrete, atomic-like energy spectrum. Since the observation of photon antibunch-

ing, these chemically synthesized quantum dots have emerged as very promising candidates for

investigating quantum optics using solid-state sources.

We ﬁ rst analysed in detail the generation of single photons by colloidal quantum dots. The ﬂ u-

orescence of an individual nanocrystal shows a perfect antibunching. This is due to the efﬁ ciency

of Auger processes in small quantum dots which renders the ﬂ uorescence of a nanocrystal simi-

lar to the one of a two-level system. Auger recombination enables one to work at room tempera-

ture, which makes the collection both simple and very efﬁ cient. The main drawback of colloidal

quantum dots is the blinking of their ﬂ uorescence. This phenomenon exhibits exotic characteris-

tics which bring to light the dynamics of charge exchange between the nanocrystal and its envi-

ronment. From a general point of view, this intermittency demonstrates the inﬂ uence of the close

environment of the nanocrystal on its ﬂ uorescence properties: the environment induces ﬂ uctua-

tions on many optical properties such as the radiative lifetime or the emission wavelength.

The spectral diffusion has been ﬁ rst studied through its correlation with the ﬂ uorescence

in-termittency. More recently, using a method called photon-correlation Fourier spectroscopy, it

has been possible to investigate the dynamics of the spectral diffusion at a timescale of around

1 0 μ s and to characterize the time coherence of the single photons emitted by the nanocrystals.

From the perspective of quantum computing, this characteristic is linked to the indistinguisha-

bility of photons and to the possibility of observing photon coalescence. By resolving the spectral

diffusion dynamics at short timescale, it has been proved that the time coherence of the zero pho-

non line is about 200 ps, a value much longer than the one obtained by standard spectroscopy.

Applying schemes used in atomic physics, and fast time-resolved detection, two photon interfer-

ences could be achieved.

The inﬂ uence of the environment on the time coherence of the emission of a solid-state source

makes tricky the observation of the coalescence of photons emitted by such devices. Like strong

coupling or spontaneous emission rate inhibition, quantum optics phenomena have often been

observed ﬁ rst on atomic physics systems and after on solid-state devices. However, beyond the

compatibility with modern electronics, solid-state physics offers an original scheme for the gen-

eration of particular quantum states of light. The recent observation of entangled photon pairs

obtained by the radiative desexcitation of biexcitons in epitaxially grown quantum dots shows

that such sources could be an alternative solution to the generation of polarization entanglement

by parametric down-conversion. In colloidal quantum dots, the Auger effect is more efﬁ cient

than in epitaxial quantum dots because of the very small size of the structure. It even prevents

any biexciton radiative recombination in quantum dots with a low radius. However, we reported

and analysed recent results showing that such a radiative cascade could be obtained for the larg-

est quantum dots or for quantum dots with alternative core–shell structures.

Finally, we discussed results concerning the control of colloidal quantum dots emission using

photonic structures following concepts of CQED. Using metallic or dielectric devices, many

groups have demonstrated the possibility of modifying the nanocrystal emission in terms of radi-

ation pattern or radiative lifetime. Compared to epitaxially grown structures, colloidal quantum

dots provide the opportunity to test new methods to control the position of emitters in photonic

structures. Moreover, the realization of such structures working at visible wavelengths represent

a technological challenge since they require very small patterns.

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