Henini M. Handbook of Self Assembled Semiconductor Nanostructures for Novel devices in Photonics and Electronics
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Optically Driven Schemes for Quantum Computation Based on Self-assembled Quantum Dots 699
Under a “ 2 π pulse ” of σ
polarized laser radiation, the trion is created and then destroyed again,
resulting in a PHASE gate:
||
||
00
11
〉→ 〉
〉→ 〉 .
(23.12)
A general phase gate:
||
||
00
11
〉→ 〉
〉→ 〉e
iφ
(23.13)
can be performed using the same method, by either (a) introducing a detuning of the laser or (b)
introducing a phase difference between the pulse creating the exciton and the pulse destroying it
again. More details of these two approaches can be found in [38] .
The phase gate provides us with an arbitrary rotation about the z -axis of the Bloch sphere
(shown on the right-hand side of Fig. 23.3 ), but this is not enough for universal quantum com-
puting. We need to be able to do any rotation – and for this we require one more possible axis of
rotation to be available to us.
This second axis of rotation presents us with more diffi culty than the fi rst. This is because any
other axis of rotation (apart from the z -axis) must necessarily involve some transfer of population
between
|1〉
and
|0 〉
– and the tricks we have played so far with a circularly polarized laser excit-
ing a single exciton will no longer work. Instead, we must perform at least two different optical
transitions, in order to couple both spin levels to one or more higher lying trion states. In this
way a Raman -type transition can be realized, which allows population transfer. Let us refer again
to Fig. 23.10 . We know that our laser can couple |1〉
and
|X〉
, but it is also clear that
|0 〉
and
|X〉
cannot be coupled, no matter what the laser polarization is. This is because such a coupling
would involve an angular momentum change of two units. We must therefore take an alterna-
tive approach.
Light holes have a spin projection of
1
2
, and therefore light hole excitons have angular
momentum of 1 or 0 – and these are exactly what we need to perform a Raman-type manipu-
lation of our spin. Either spin qubit state (
|0 〉
or
|1〉
) can be excited to light hole trion state (two
electrons and a light hole, which has total angular momentum of
1
2
). This is because the angu-
lar momentum change in such a transition is always either 0 or 1. Such transitions are straight-
forwardly achieved by using laser light of different linear polarizations. Figure 23.11 shows more
detail.
+
|1/2> |1/2> |1/2> |1/2>
|1/2> |1/2>
1 to 0:
|1/2> |1/2>
Figure 23.11 Schematic diagram showing how two linearly polarized lasers can effect an optical Raman-type
transition between an “ up ” electron spin (qubit state |1) and a “ down ” electron spin (qubit state |0). Note that
two pathways occur in parallel for this transition, and both involve the creation of a light-hole trion state. The reverse
operation ( |0 to |1 ) also occurs, so this scheme forms a Pauli X gate for a single spin qubit. More details can be
found in [38] .
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700 Handbook of Self Assembled Semiconductor Nanostructures for Novel Devices in Photonics and Electronics
23.4.2 Two-qubit gates
The most obvious method of performing a two-qubit gate on a pair of spins would probably be to
control some sort of spin–spin interaction (for example, a Heisenberg exchange-type interaction).
Indeed, this sort of interaction can be controlled by gating a potential barrier between spin qubits
to tune wavefunction overlap (see Loss and Divincenzo’s well-known paper, [39] ). This method
is not as effective in self-assembled dots for two main reasons. First, the degree of wavefunction
overlap tends to be quite small since barrier regions are quite wide. Second, it is very hard to fab-
ricate electrodes between these sorts of dots. Hence, we turn again to optical methods for entan-
gling spin qubits, which, as we shall see shortly, also has the advantage of fast gate operation
times (on the order of a few picoseconds).
Optical methods for spin entanglement again rely on the Pauli blocking effect and so selectively
create trion states from the spin qubits. It is the interaction of the trions that indirectly couples
the spins.
Consider again the macromolecule formed by the stacked dots QD
a
and QD
b
and consider two
spin qubits driven by σ
laser pulses. These selectively create trion states
|
()
X
ab
〉
from the qubit
|
()
1〉
ab
only. The Hamiltonian of the system is:
Ht V Hc
ii ab
iab
ab F
i
i
() ( ..)
,
ω|X X| |XX XX| | X X |〉〈 〉 〈 〉〈
∑
Δ
Ω
e 11
aab
li i
tHc
,
cos ( ) . .)
∑
〉〈ω |X|1
(23.14)
where H.c . denotes the Hermitian conjugate, ω
a
(
b
)
is the trion creation energy for QD
a
(
b
)
, Ω
a
(
b
)
is
the time-dependent coupling between laser and QD
a
(
b
)
, and ω
la
(
b
)
is the frequency of the laser
addressing QD
a
(
b
)
. Two types of trion coupling have been included: the interdot Foerster cou-
pling strength V
F
, and the biexcitonic energy shift due to the exciton–exciton dipole interaction
Δ e
ab
[23] .
One possible way of performing an entangling gate is to exploit Δ e
ab
. We assume that the
energy difference between states
|0 〉
and
|1〉
is negligible on the exciton energy scales and that
the two dots are different, so that Foerster interaction is inhibited [23] . A CPHASE gate can be
implemented by fi rst applying a resonant exciting laser π pulse to each dot, which creates an exci-
ton if the dot spin state is
|1〉
. Now, after a time Δ t , another π pulse is applied to each dot, which
destroys any excitons that were created by the fi rst pulse. A phase θ Δ t Δ e
ab
will be accumu-
lated if and only if the system is initially in state
|11〉
[40] . This scheme can be adjusted to include
imperfect QD structures which present a relevant admixture of heavy-and light-hole states. This
is done by using chirped laser pulses [40] .
Another possibility is to use the Foerster interaction, which as we know is most effective for
resonant excitons. We therefore set ω
a
ω
b
, and this time we only need to use a single laser (of
frequency ω
l
) to excite excitons. We assume the laser couples equally strongly to each dot, with
strength Ω . Making these extra assumptions allows us to recast the Hamiltonian, Eq. 23.14, in
the following form:
Ht XX I I XX XXXX
VXX Hc
a
F
ab
() ( )
(..
ω
ε
|| || | |
|1|
〉〈 ⊗ ⊗ 〉〈 〉〈
〉〈
ˆˆ
Δ
1))
cos ( . .)Ω ω
l
tXII XHc
|| ||
11
〉〈
⊗⊗
〉〈
ˆˆ
(23.15)
This new Hamiltonian decouples into four separate subspaces each containing one of the four
computation basis states. The eigenstate energy level structure of these four subspaces is depicted
in Fig. 23.12 for the situation in which the laser is turned off.
|0 0 〉
is alone since it cannot couple to
the laser at all.
|10〉
and
|0 1〉
couple to
|X0〉
and
|0 X〉
respectively.
|11〉
couples to the symmetric and
antisymmetric combinations of
|X1〉
and
|1X〉
, which are split by the Foerster interaction. The high-
est energy eigenstate is
|XX〉
, which lies at an energy 2 ω
a
Δ e
ab
above
|11〉
.
Having established the rather complicated energy level structure of the system, it is now rather
simple to see how to perform an entangling gate. The laser is tuned to the energy of the
|11〉
to
()||/112XX〉〉
transition and a 2 π pulse is executed. This means
||11 11〉→ 〉
. The other three
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Optically Driven Schemes for Quantum Computation Based on Self-assembled Quantum Dots 701
computation states are unaffected by the pulse, since they are either uncoupled (for
|0 0 〉
) or off-
resonance (for
|10〉
and
|0 1〉
). Hence, the action of this pulse is to effect a CPHASE gate, which is
of course entangling and universal for quantum computing.
23.5 General quantum computer architecture and related quantum devices
23.5.1 Quantum dot-based quantum bus
Most of the QD-based quantum computation schemes propose the use of vertically stacked dots
[7] . However, experiments show that the maximum length of such arrays is of the order of only
ten QDs [8] . To implement non-trivial computation, we need arrays (or array networks) of at
least a few tens of qubits, and possibly many more. Therefore, an important problem is how to
communicate between different vertically stacked arrays of QDs.
The communication between distant vertical arrays of QDs can be done using quantum buses
made by in-plane chains of quantum dots [41, 42] . Recent experimental progress has shown that
it is possible to grow in-plane chains of quantum dots, whose density and QD size can be inde-
pendently controlled [12] . Information could be transferred along this structure by, for exam-
ple, a sequence of SWAP gates acting on excitonic or spin qubits – but this would require a high
degree of external control over the quantum dynamics. A different approach is to implement
information transfer across the in-plane arrays (IPAs) by exploiting the natural dynamics of the
system [41, 42] . The key idea is that if we inject an excitation at one end of the chain, the natural
quantum evolution will transfer such an excitation to the opposite end in a known time, which
is determined by the chain characteristics (number of quantum dots, strength and sequence of
QD–QD couplings). This concept is exemplifi ed in Fig. 23.13 . Recently, there have been interest-
ing developments in the study of the natural dynamics of spin chains – see, for example, [43, 44] .
We can translate some of these ideas into the IPA system: the use of natural dynamics should
simplify the problem of transferring information across our QD-based quantum computer.
State-of-the-art in-plane QDs can be made monodisperse up to a few per cent. Let us assume
that the information is stored in exciton qubits:
|(|)01〉〉
ii
is the absence (presence) of a single
ground-state exciton in QD
i
. The Hamiltonian for an IPA of N QDs, in which we consider at most
a single exciton in the chain, is given by:
HE V Hc
iii
i
N
Fi i i i i i
i
N
|| ||| |11 10 0 1
111
1
1
〉〈 〉〈 ⊗ 〉 〈
∑∑
(..)
,
(23.16)
|0X〉
|XX〉
(|1X〉|X1〉)
1
2
|X0〉
|01〉|11〉 |10〉 |00〉
√
(|1X〉|X1〉)
1
2
√
Figure 23.12 Schematic diagram showing the energy level structure of the two quantum dot system discussed
in section 23.4.2. The Hamiltonian decouples into four separate subspaces, illustrated by different panels here. A
pulsed laser is tuned to the |||/11 1 1 2〉↔ 〉 〉()XX
transition (shown by the solid line). It has no effect in the other
subspace since it is either off-resonance or does not couple at all (shown by the dashed lines).
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702 Handbook of Self Assembled Semiconductor Nanostructures for Novel Devices in Photonics and Electronics
where V
Fi
,
i
1
is the Foerster coupling [45, 46] between nearby quantum dots discussed in sec-
tion 23.3.2. Single-particle tunnelling is again neglected. This Hamiltonian is isomorphic to the
Hamiltonian of a spin chain. We will focus on relatively short chains, with N 10, correspond-
ing to lengths of a few hundred nanometres: our purpose is to communicate between arrays of
stacked QDs, whose relative distance is greater than the diameter of the laser spot used to address
the single QDs.
From the general theory of spin chains it is known that, by applying a specifi c modulation to
the sequence of spin–spin coupling, it is possible to perform perfect transfer of a quantum state
across the chain [43] . When this scheme is considered for QD IPAs, the implementation of this
strict coupling sequence can in principle be done by growth or by tuning the interdot couplings
a posteriori , by applying in-plane electric fi elds [41, 42] . Our analysis though shows that both
methods are highly impractical and can lead to different systematic errors [41, 42] . We will
therefore consider IPAs of identical QDs, i.e. V
Fi
,
i
1
V and E
i
E , a relatively easier require-
ment to satisfy. We want to address the questions (i) if transfer of a state along the chain with a
high degree of accuracy is still possible by exploiting the natural dynamics of the chain and (ii)
how the results are affected by imperfections. We consider IPAs with N 1, … 9, and simulate
the evolution of the system after the fi rst QD has been populated.
Figure 23.14 shows the time evolution of a fi ve QD chain, following state input to one end of
the chain. It presents the average fi delity of state transmission to the other end when the initial
state input is varied over the Bloch sphere. As can be seen, the time evolution as a whole presents
a periodic behaviour (within the numerical error), centred on the peak labelled with “ C ” . Within
this period many peaks are present, some of which correspond to a fi delity very close to 1. This is
a typical pattern for all the spin chains analysed, and in particular for N 9, the very fi rst peak
(labelled “ A ” in the fi gure) always corresponds to a fi delity F
Bl
95% [41, 42] . The time t
A
at
which resonance “ A ” occurs and the corresponding fi delity
〈〉F
Bl
A
present a weak linear depend-
ence with the length N of the chain (with the time getting longer for longer chains and the fi del-
ity getting smaller). t
A
remains below 2 ps for N 9 [41, 42] .
In-plane array (IPA)
QD1 QD2 ... QDN
In-plane array (IPA)
QD1 QD2 ... QDN
Time t
0
: exciton in
arbitrary state in QD1
Time t
0
δ
t
: exciton in
the same state in QDN
Natural evolution
Figure 23.13 At time t
0
an excitation is injected at one end of the IPA. After the known time δ t the same excitation
has been transferred to the other end of the IPA by the natural quantum evolution of the system.
AB C
<F>
Bl
0.6
0.7
0.8
0.9
1
10 20 300
0.5
t (ps)
Figure 23.14 F
Bl
as a function of time for N 5 and V
Fi
,
i
1
1 m e V.
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Optically Driven Schemes for Quantum Computation Based on Self-assembled Quantum Dots 703
In all cases analysed, at least one of the subsequent peaks (e.g. B and C in Fig. 23.14 , for
N 5) corresponds to an even higher fi delity of transmission – and in some cases it could be
worth waiting for these higher peaks.
In the case of imperfect chains, the exciton energies E
i
might have a random distribution.
Calculations have been performed in this case, assuming that the variation is bounded, and the
corresponding fi delity has been averaged over an appropriate number of such confi gurations.
Peak A is more robust to this random variation, i.e. peaks B and C tolerate a lesser amount of
noise in the distribution of the energies [41, 42] .
We underline that for comparable parameters, the IPA can transfer information faster than a
microcavity, the typical gating time for a microcavity-mediated two-qubit gate being greater than
100 ps [47] . The use of IPA is a promising alternative to microcavity for medium-distance com-
munication in QD-based quantum computation schemes.
23.5.2 Control arrays
For practical implementations, it is necessary to have the ability to switch the information trans-
fer across a quantum bus on and off. This can be achieved by the use of a “ control array ” (CA)
[42, 48] . A control array is a second IPA stacked on (or under) the IPA used as a quantum bus
(see Fig. 23.15 ). For experimentally reasonable parameters, it is possible to optically gener-
ate a single exciton in each QD of the CA by the use of a single laser pulse (or multiple, but in-
phase, laser spots) [48] . In this scheme the ground-state excitonic transition in the CA and in
the quantum bus must be different by at least a few meV, so that the CA can be energy selectively
addressed with respect to the quantum bus. This happens naturally in the stacking process itself,
as vertically stacked QDs tend to be different in size. The ground-state excitonic transitions in the
inner QDs of the bus can then be altered, as we now discuss.
ε
1
ε
3
ε
2
ε
N
...
Control array (CA)
ε
N
ε
1
(a) (b)
Quantum bus
ε
2
Δε
2
ε
3
Δε
3
...
Figure 23.15 Panel (a) : No excitons in the control array, inner QDs in the quantum bus are on resonance. Panel (b) :
One exciton in each QD of the control array, inner QDs in the quantum bus are off resonance due to the related
biexcitonic shift.
Consider the scheme illustrated in Fig. 23.15 . In panel (a) all ground-state excitonic transi-
tions are on resonance, and the information transfer can occur by Foerster coupling. In panel
(b) one exciton has been optically generated in each QD of the CA. The biexcitonic coupling Δ e
i
between each of these excitons and the computationally relevant transition in the correspond-
ing QD of the quantum bus detunes the inner QDs with respect to the QDs at the beginning and
end of the bus chain. This detuning inhibits the Foerster coupling and hence the exciton transfer
across the chain. Our calculations show that for Δ e
i
/ V
Fi
,
i
1
10, the overlap between the evolu-
tion of the state of the quantum bus and its initial state (one exciton in QD1) is greater than 96%
at all times [48] . We underline that the transfer time across a bus of nine QDs with a Foerster
coupling as low as 0.2 meV is still less than 10 ps, so fast transfer times, together with good trans-
fer blocking, are possible in the same device.
23.5.3 Quantum dot-based quantum computer architecture
In this section we discuss our own proposal for a quantum computer architecture which exploits
vertically stacked arrays (VSA) as quantum registers, and IPAs and CAs as switchable quan-
tum buses [41, 42] . The proposed hardware is composed of VSAs connected by IPA buses (see
Fig. 23.16 ). Each VSA can be individually discriminated by a laser spot spatially, for example by
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704 Handbook of Self Assembled Semiconductor Nanostructures for Novel Devices in Photonics and Electronics
near-fi eld techniques. QDs in different VSAs may be resonant with the same laser frequency. This
allows each VSA in principle to be formed by the same QD sequence. The combined spatial and
energy-selective addressability of this architecture strongly enhances the hardware fl exibility
with respect to schemes that use energy-selective addressing only.
This need for spatial separation sets a minimum length of the order of 100 nanometres for
the interconnecting IPAs. Interconnecting IPAs can both transfer qubits between different quan-
tum registers and entangle qubits in QDs belonging to different VSAs. For example, a pair of
entangled qubits in one VSA can be made using, e.g., the method described in section 23.3.2,
and then one of the qubits can be transferred across the IPA to a different VSA. If the computa-
tional degrees of freedom are encoded in electronic spins in the VSA, the swapping of informa-
tion between spin and excitonic qubits will be necessary before and after the transfer. This can be
done using optical means and on a picosecond timescale, by exploiting the Pauli-blocking effect,
as described in [48] .
By using the proposed architecture, gating between qubits in different VSAs can also be per-
formed, overcoming the problem that the physical register (the VSA) can at most be formed by
10–15 qubits (the QDs). This design allows compact implementation of a quantum computer:
in principle in fact the hardware can be confi ned to a single slab. This allows easier lateral access
(e.g. for wiring) and manipulation of each QD, which may be used to apply electric fi elds to spe-
cifi c dots in order to tune properties like biexcitonic shift or Foerster coupling. This architecture is
scalable, since the same basic structure (VSA plus related IPA), and the slab structure as a whole,
can be repeated at will.
23.5.4 Entanglement distributor
The results highlighted in previous sections show the feasibility of quantum communication
between separated quantum registers, based on quantum buses made from chains of in-plain
QDs and utilizing the natural dynamics of these systems. We will now discuss how the same
hardware elements and properties can be used to design an entanglement distributor, which pro-
vides a resource of distributed entangled states on demand [48] .
Entanglement is a fl exible resource. Our device can be utilized in a variety of approaches
to quantum processing, for example for teleportation of quantum states, to enable distributed
quantum gates, or to build distributed cluster states [49] . The purpose of the device is to gener-
ate maximally entangled qubits on demand and to distribute them to spatially separate regions.
Its structure is sketched in Fig. 23.17 . It is formed by two coupled dots, QDA and QDB, where the
entangled exciton pairs are produced. QDA and QDB are connected to the quantum buses BAA
and BAB, respectively. The transfer of exciton along the buses is controlled by the control arrays
CAA and CAB, as indicated. The buses connect QDA and QDB to QDC and QDD, respectively.
These are located at the ends of the stacked quantum registers QRA and QRB. Quantum compu-
tation can be performed in QRA and QRB according to any of the all-optical methods previously
Independent laser
spots
Quantum bus and related
control array (IPAs)
Quantum register (VSA)
Figure 23.16 Quantum dot-based quantum computer architecture. It exploits the different characteristics of
vertical and in-plane arrays of quantum dots. The fi rst are used as quantum registers, the second as both quantum
buses and to control the dynamics in the quantum buses. In this design different quantum registers can be resolved
spatially by different laser spots.
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Optically Driven Schemes for Quantum Computation Based on Self-assembled Quantum Dots 705
described. These quantum registers and the dot pair (QDA, QDB) can be addressed by different
laser spots.
The entanglement distribution process is as follows. (i) The quantum buses BAA and BAB
are set off-resonance. This is achieved through the creation of an exciton in each control array
(CAA and CAB) QD. The biexcitonic shift between these excitons and the excitonic transitions
of the related QDs in BAA and BAB inhibits Foerster coupling between QDA(B) and BAA(B).
(ii) The entangled pair is created in QDA and QDB by using the method described in section
23.3.2. IIIB based on the biexcitonic shift. (iii) The quantum buses BAA and BAB are set on reso-
nance through the annihilation of the excitons in control arrays CAA and CAB. (iv) The entan-
gled excitons propagate down the buses in opposite directions. Notice that each quantum bus is
connected to one of the central QDs only. (v) When the excitons reach QDC and QDD, the quan-
tum buses BAA and BAB are again set off resonance using the same method described above. (vi)
The entangled excitons are now trapped in QDC and QDD and the entanglement can be delivered
to the registers QRA and QRB.
Even if excitonic qubits are used to produce and deliver entanglement, actual quantum com-
putation in the quantum arrays QRA and QRB can be based on longer-lived spin qubits. By
means of the Pauli-blocking effect, the excitonic qubit can be swapped into a spin qubit. This is
done by all-optical means [48] . This swapping can be essential to create a long-lived entangled
resource.
The fi delity of our distribution scheme depends on several factors. By considering experimen-
tally relevant parameters, and taking into account the correct ratio between the various energy
scales (such as the ratio between biexcitonic shift and Foerster coupling discussed in section
23.5.2), we estimate that the total time for one entanglement distribution operation is no more
than 20 ps, whereas the exciton decay time is about 1 ns.Our estimate of the overall fi delity of
distribution is 91% [48] .
One of the very important features of our entanglement distributor is that it integrates with,
and thus enhances, many of the current QD-based quantum proposals. Given the impressive
progress with QD structures (see e.g. [9–12] ), we hope that some experimental group will pick
up the challenge to build this device which constitutes a route to scalable solid-state quantum
computation.
23.6 Conclusions
We have presented an overview of all-optical quantum computation schemes based on self-
assembled quantum dots. We have discussed the reasons why we think these structures represent
Independent laser
spots
BAB
CAB
QRB
QRA
BAA
CAA
QDB
QDD
QDC
QDA
Figure 23.17 Sketch of the entanglement distributor, from [48] .
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706 Handbook of Self Assembled Semiconductor Nanostructures for Novel Devices in Photonics and Electronics
a good hardware choice for quantum devices and how an overall, scalable architecture for a
quantum computer could be constructed starting from a few basic elements. This architecture
exploits the natural dynamics of spin chains and in this way allows us to reduce the amount of
gating – and related error sources – needed to implement information transfer across the various
elements of the quantum computer. Due to the vast improvement in the last few years of growth,
characterization and optical control techniques [13–20] , and the creation of complex and regu-
lar quantum dot structures [9–12] , we are confi dent that some of the devices proposed in this
chapter form a feasible experimental challenge in the very near future.
Notes
1. In this chapter we will refer to existing computers as “ classical computers ”
2. The entanglement of formation measures the number of Bell states required to cre-
ate the state of interest and for a two-qubit state it is given by:
Eh
F
() (( )/)ρτ121
,
where h ( x ) x log
2
( x ) ( 1 x )log
2
(1 x ) is the Shannon entropy function. τ is the “ tangle ” or
“ concurrence ” squared: τ C
2
[max { λ
1
λ
2
λ
3
λ
4
, 0 } ]
2
. The λ s are the square roots of the
eigenvalues, in decreasing order, of the matrix
ρρ ρ σ σ ρ σ σ
y
A
y
B
y
A
y
B
⊗⊗*
, where ρ * denotes the
complex conjugation of ρ in the computational basis 100 |10 |1 1 [37] .
References
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Quantum Optics with Single CdSe/ZnS Colloidal Nanocrystals
L. Coolen ,
1
X. Brokmann ,
2
and J.P. Hermier
1,
3
1
Laboratoire Kastler Brossel, Ecole normale supérieure, Université Pierre et Marie Curie Paris 6,
CNRS, 24 rue Lhomond 75231 Paris Cedex 05, France;
2
Institut d’Electronique de Microélectronique et de Nanotechnologies,
avenue Poincaré, 59652 Villeneuve d’Ascq, France;
3
Groupe d’Etudes de la Matière Condensée, UMR 8635 (CNRS), Université de Versailles
Saint-Quentin-en-Yvelines 45, avenue des Etats-Unis 78035 Versailles, Cedex.
24.1 Introduction
CdSe colloidal semiconductor nanocrystals illustrate the spectacular progresses made during the
last few years in the synthesis of nanostructures. They are small crystalline objects containing
between 1000 and 100 000 atoms. Their properties are dominated by quantum confi nement
effects and depend crucially on their size. Using processes fi rst developed by three pioneer groups
directed by P. Alivisatos (Berkeley), M. Bawendi (MIT), and P. Guyot-Sionnest (Chicago), their
size can be tuned from 2 to 10 nm by adjusting the temperature, the concentration of chemical
precursors or the duration of the reaction. The size dispersion of the nanocrystals is lower than
5%. Controlling the size during synthesis the wavelength in the visible spectrum can be tuned
over several hundred of nanometres. Nanocrystals can be used at room temperature and present
high photo-stability and high quantum effi ciency. All these properties make them very attractive
solid-state light sources, which have already been used in a wide range of applications such as
the realization of optoelectronic devices as thin fi lm LEDs or for biological labelling.
At the single molecule level, CdSe colloidal nanocrystals exhibit very remarkable properties. The
fl uorescence is known to display fl uorescence intermittency resulting in the alternation of dark
and bright periods and showing exotic statistical properties. Single-photon emission has also been
demonstrated using the fl uorescence of individual nanocrsytals. In the fi eld of quantum informa-
tion processing, single photons could be used for optical quantum computation or quantum cryp-
tography. Single-photon emission has been observed for other solid-state sources such as organic
molecules in a matrix, (epitaxially grown) “ self-assembled ” quantum dots and nitrogen vacancy
centres or NE8 defects in diamond. Compared to these sources, colloidal nanocrystals exhibit spe-
cifi c phenomena such as strong interactions between charge carriers known as Auger processes.
The aim of this chapter is to discuss the distinctive optical properties of colloidal quantum
dots from the perspective of realizing quantum optics experiments. Nanocrystals with a CdSe
core show the best optical properties in terms of photostability, radiative quantum effi ciency
and photostability. We focus our discussion here on these nanocrystals. However, we also expose
the perspectives offered by other materials such as PbSe, PbS, InP or CdTe. In section 24.2, we
present the theoretical aspects on quantum optics used here for the characterization of a single-
photon source. Then we summarize the basic optical properties of CdSe colloidal quantum
CHAPTER 24
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