Quantum dots:
Physics, technology and
applications
Andrea Fiore
QD
Ecole Polytechnique Fédérale de Lausanne
Outline:
• Self-assembled quantum dots
• Laser applications
• Single QDs
Quantum dots
QD
E
Electrons in GaAs, T=300K:
h
30 nm
∆E > kT ⇔ L < λ ≈
*
2m kT
λ
L
QD lasers:
Single QD devices:
electron
photon
100 nm
Andrea Fiore
Why care about QDs?
Or: The QD "dream"
Density of states and
carrier distribution
n(E) = g(E) f (E)
Fermi distribution
Density of states
Carrier distribution
Density of states
E
c
Energy
Bulk: g ( E ) ∝ E − Ec
QD
f(E)
g(E)
n(E)
≈kT
Energy
• Low peak gain
• Temperature sensitivity
Andrea Fiore
Heterostructures
QD
Semiconductors with different gap
Heterostructure potential for electrons
Schrödinger eq.:
 p2

 2m + Vcrist ( r ) + Vhet ( r ) ψ ( r ) = Eψ ( r )


ψ k ( r ) = uk ( r ) χ ( r )
uk : Bloch function
χ : envelope function
 p2

 2m * + Vhet ( r )  χ ( r ) = Eχ ( r )


Andrea Fiore
2D nanostructures:
Quantum Wells
ky
Density of states
z
2> E
2>
1>
1>
kx, ky
AlGaAs GaAs AlGaAs
E
E
1
Energy
2
Carrier distribution
kx
QD
g(E)
f(E)
n(E)
Energy
Only marginal improvement in the gain linewidth
Andrea Fiore
1D nanostructures:
Quantum Wires
2> E
2>
ky
1>
1>
ky
AlGaAs GaAs AlGaAs
1
ρc ( E ) ∝
E − En
E
E
1
Energy
2
Carrier distribution
Density of states
QD
g(E)
Narrower
population
distribution
f(E)
n(E)
Energy
Andrea Fiore
0D nanostructures:
Quantum Dots
QD
E
2>
1>
2>
1>
AlGaAs GaAs AlGaAs
E
E
1
Energy
2
Carrier distribution
Density of states
ρ c ( E ) ∝ δ ( E − En )
∆E>>kT
g(E)
f(E)
n(E)
Energy
All carriers at
the same energy
Andrea Fiore
Narrower gain makes
better lasers
QD
Gain calculation:
Arakawa, Sakaki 1982
Asada et al., 1986
E
• Lower threshold current
• Lower temperature sensitivity
• Larger modulation bandwidth
NB:
Idealized
picture !!!
Andrea Fiore
Real QDs
Or: The shattered dream?
Nanostructure fabrication:
Quantum Dots
QD
"Straightforward" approach: Fabrication on the nanoscale
• Need high-resolution lithography
• Etching ⇒ Nonradiative defects
"Self-organized" methods: Making Nature work for us !
• Growth on patterned substrates
substrate
• Strain-driven growth on planar
substrates
substrate
Andrea Fiore
Self-assembled growth
QD
Epitaxial growth: Interplay of surface energy and strain
"Standard" (Frank-van der Merve) 2D epitaxial growth:
GaAs
AlAs
substrate
Stranski-Krastanow 3D growth mode (strain-driven):
WL
QDs
substrate
Andrea Fiore
Self-assembled
quantum dots
QD
MBE growth of InAs on GaAs:
15 nm
200 nm
Atomic Force Microscopy
Transmission Electron Microscopy
☺ Simple growth technique, no
pre-growth patterning required
Random nucleation sites ⇒ no
control of island position
☺ High crystalline quality ⇒
High radiative efficiency at RT
Size dispersion ⇒ Emission energy
dispersion
☺ 1.3 µm operation possible
Andrea Fiore
Inhomogeneous broadening
QD
1 µm diameter:
11000
40K , 4 µ W
PL counts
8800
300 nm
6600
4400
2200
0
1170
25
20
15
10
Inh. broad.
E
FW H M =
31 m eV
5
0
0.95
1
1250
1.05
E nergy (eV )
1.1
1000
50K , 4 µ W
Gain FWHM:
∆EQDs≈∆EQWs
300 n m
800
P L counts
PL intensity (arb. un.)
ideal
meas.
E
30
1190
1210
1230
Wavelength (nm )
300 nm diameter:
MacroPL at 5K:
35
1 µm
600
400
200
0
1170
1190
1210
1230
Wavelength (nm )
1250
2
Andrea Fiore
Dot density: 300 dots/µm
Can we do better?
Controlling self-assembly
QD
• SK growth on prepatterned substrates
In adatoms
Kohmoto et al., J. Vac. Sci. Tech. B 2002
• Growth-rate
anisotropy driven
growth:
vs self-assembled
Site-controlled...
☺ Site control
☺ Improved unif.
Baier et al., APL 2004
GaAs
QD
4 µm
Courtesy: E. Pelucchi, E. Kapon, EPFL
Andrea Fiore
Homogeneous linewidth
Single-QD photoluminescence:
2
2
Γ=
=
+ Γ phon (T )
T2 τ life
Radiative dephasing Phonon scattering
QD
(Bayer et al., PRB 2002)
T<2 K: lifetime-limited
2 K<T<60 K: acoustic phonons
T>60 K: optical phonons
Andrea Fiore
Radiative properties
QD
Intensity (arb. un.)
MBE growth of InAs on GaAs:
7 10
-8
6 10
-8
5 10
-8
4 10
-8
3 10
-8
2 10
-8
1 10
-8
QD characteristics:
293 K
21 A/cm
2
• 1300 nm emission on GaAs
• Radiative efficiency ≈20% at RT
• Long carrier lifetime ≈ 1ns
0
1100
1200
1300
W avelen gth (n m )
1400
• Density: ≈3x1010 cm-2
A. Zunger, MRS Bulletin 1998
Intensity (arb. un.)
Excited states:
2 10
1.5 10
1 10
-7
ES2
ES1
-7
-7
7.2 kA/cm
GS
90 0 A/cm
5 10
11 0 A/cm
0.9
1
2
ES2
ES1
2
-8
0
WL
WL
GaAs
2
GS
1.1 1.2 1.3 1.4 1.5
E nergy (eV)
Andrea Fiore
QD lasers (1):
The physics of a different laser
QD lasers
EPFL QD lasers:
QD
Laser performance:
• Jth<200 A/cm2
• ηext=30-40%
• CW up to 80 C
7 10
-4
6 10
-4
5 10
-4
4 10
-4
3 10
-4
2 10
-4
1 10
-4
0
600 µm, HR coated 95%:
2
J (A/cm )
2 m m , 3 Q D layers, RT
147 A/cm2
136 A/cm2
0 10
110 0 1150 120 0 1250 130 0 1350 140 0
W avelength (nm )
35
Pow er (m W)
Intensity (a.u.)
As-cleaved, RT:
0
400
800
1200
1600
p ulsed
30
25
20
15
2 0C
3 0C
4 0C
5 0C
6 0C
7 0C
8 0C
10
5
0
0
0.2
0.4
0.6
0.8
1
Current (A)
HR coatings and measurements:
O. Gauthier-Lafaye, Opto+ Andrea Fiore
A summary of laser
performance
QD
To The Best Of My Knowledge:
1.3 µm
on GaAs
Jth at RT
T0
LEF
10 Gb/s
<30
A/cm2
>200 K
1.55 µm
on InP
<400
A/cm2
>84 K
<1
<3
YES
NO
Huang 2000, Park 2000
Saito 2001, Wang 2001
Shchekin 2002
Schwertberger 2002
several groups
Ukhanov 2002
Hatori 2004, Kuntz 2005
1.3 µm on GaAs is better mastered
Andrea Fiore
The quantum side of QDs
QD
Quantum Dots: Are they really different (better?) than QWs?
Fact:
Inhomog. + homog. broadening makes gain linewidth ≈QWs
... But still it is a different laser!
Confinement-related aspects:
• Discrete n. states
• Low Jtr
• Low max gain
• Excited states
• Intraband dynam.
• Localization
• Thermal equil.?
Andrea Fiore
The role of the density of
states
Transparency current:
Maximum gain per pass:
I tr ∝
g max
QD
ρ ( E)
τ
2
πe 2 xcv
ω
=
ρ ( E)
e0nc
E
QWs:
QDs: 2
QWs:
1300 nm QDs on GaAs:InAs ρQD GaAsπ
2g S
GaAs
≈ *
≈ 0.1
QDs
10
−2
InGaAs
GaAs
S = 3x10 cm , ∆Einh = 20meV ) ρ QW
( gGaAs
m ∆Einh
kt
*
gtransparency
QDs have ≈10mtimes
lower ρ (E•)Low
g S : areal dot
density
S
current
2
≈
ρ QW (E ) = 2
QD
∆Einh : inhom og. broad.
density of
states
• Low∆E
max
π
inh gain
Andrea Fiore
Room-temperature:
Jth=33 A/cm2
Jtr = 9 A/cm2
Theoretical estimate for Jtr:
(NQD=2, gS=3x1010 cm-2, τ=800 ps)
QD
8.4 µm x 4 mm
2 QD layers
y
n
a er
f
o las
tr r
J
t to
s
e uc
w nd
o
l o
e
J
ic
h
T em
s
Voltage (V)
N quantum dots ⇒ 2N states
Single facet power (mW)
Record threshold current
density
Current (mA)
Huang et al., Electron. Lett. 2000
eg S
J tr = N QD
= 12 A/cm 2
τ
BUT: Modal gain per QD layer ≈ 3-4 cm-1
• Low-loss cavities
• Stack many layers
Andrea Fiore
QD stacking for max gain
10 nm spacing: QDs aligned
50nm
QD
25 nm spacing: QDs not aligned
50nm
5
100 K
Intensity (a.u.)
4
3 QDs
d=25 nm
1 QD
3
2
3 QDs
d=10 nm
1
0
1100
1200
Strain interaction between dot
layers produces vertical
alignment and PL broadening
1300
Wavelength (nm)
Andrea Fiore
Gain problem in QD lasers
Intensity (a.u.)
Ground state lasing only for low loss (L>1.5
mm):
N QD gth = α +
7 10
-4
6 10
-4
5 10
-4
4 10
-4
3 10
-4
2 10
-4
ES1
1 10
-4
GS
3 Q D layers
2 mm
ES2
0
L= 600µm, HR/ HR coa ted, P= 3 mW.
Device width= 3µm
-1 0
0
25°C
45°C
1200
1300
-2 0
Po we r (dBm )
W avelen gth (nm )
Wavelength (nm )
1 1
ln
L R
High T ⇒ Higher optical loss
⇒ Wavelength switch
600 µ m
0 10
1100
QD
1350
Ground state
1300
1250
65°C
-3 0
-4 0
-5 0
1200
-6 0
Excited state
1150
1100
0
2
4
Device length (m m )
-7 0
1150
1200
1250
1300
1350
Wa ve le ng th (nm )
Andrea Fiore
Dual-state lasing
QD
Markus et al., APL 2003
Violates population
clamping theory ???
light
population
bias
Andrea Fiore
Interpretation of
dual-λ lasing
QD
"Slow" intraband relaxation
(Benisty et al., PRB 1991)
τ0
τ0 ≈10 ps in our QDs (PL rise time)
Photoluminescence:
τ0
τspont
1
1
>>
τ0
τ spont
⇒ no relax.
bottleneck
Laser:
τ0
τstim
Behaviour predicted by Grundmann et al., APL 2000
1 − fGS
1
≈
τ0
τ stim
⇒ ES
population
Andrea Fiore
Modeling 2-λ lasing
Rate equation model:
fES
ES
τ0
Model
τ0 ≈ 8 ps
fGS
GS
Photon num ber
0.35
fWL
WL
QD
total
2 mm
0.3
0.25
0.2
GS
0.15
0.1
0.05
0
ES
0
8
16
24
32
40
C arrier injection rate (e/ τ )
2
Population
2 mm
1.5
1
GS
ES threshold
0.5
0
Exper.
ES
G S threshold
0
8
16
24
32
40
C arrier injection rate (e/ τ )
r
Integr. int. (arb. un.)
r
0.14
2 mm
0.12
total
293 K
0.1
0.08
0.06
GS
0.04
0.02
0
ES
0
200
400
600
800
C urrent (m A)
1000
Andrea Fiore
A more general view
Carrier accumulation in non-lasing states:
• Low differential gain
• Large gain compression
∆n
a=
QD
dg GS
dN tot
capture time from WL to QD ⇒ ∆nWL
WL
relaxation time from
ES to GS ⇒ ∆nES
capture into nonlasing QDs ⇒ ∆nnonlas QDs
∆nGS << ∆n tot
dg GS
small
⇒a=
dN tot
• Small frel in lasers
• High Psat in SOAs
Andrea Fiore
Differential gain
τc
WL
dg GS dg GS dNGS dNQD
a=
=
dN tot dNGS dNQD dN tot
ES
τ0
material
GS
10 Q D laye rs
500 µ m , HR co ated
0
2
4
2
15
2.5
cm )
dNGS
dNQD
6
8
10
Normalised injection rate
capture: τc
3
Differ. gain (x10
N ormal. differ. gain
dNQD
dN tot
relaxation: τ0
Relaxation
is the limit
τc=1 ps, τ0=8 ps:
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
QD
2
1.5
1
10 QD layers
500 µ m , H R coated
0
2
4
6
8
10
Norm alised injection
rate
Andrea
Fiore
Gain compression
g = g ( N tot , Nφ )
dg GS
ap =
dNφ
Nφ=0:
WL
τc
QD
Why???
N tot
Nφ large:
WL
τc
ES
ES
GS
GS
τ0
Increased stimul. em. rate
τ0
Relax. rate:
fES (1 − fGS )
τ0
Carrier re-distribution
Andrea Fiore
M odul. response (dB)
Gain compression in
QD lasers
5
Γap 

K = 4π τ p  1 +

a 

9
2
γ Kfr f 3dBmax
K
∝ 1/ γ
f 3dBmax
0
2
-5
-10
-15
10 Q D layers
500 µ m , HR co ated
0
2
4
6
8
Frequency (GHz)
10
4
K factor (ns)
3.5
16
3
12
2.5
2
8
1.5
4
1
0.5
0
5
10
15
20
25
0
30
(G Hz)
Relaxation time fixes K
⇒ max f3dB
20
3dB
K ≈ 4π τp (1 + Aτ 0 )
10 Q D layers, 500 µ m , H R coated
M ax f
From rate equations:
2
QD
Relaxation time τ Andrea
(ps) Fiore
0
Modulation characteristics
Model
3 QD layers
2.5 Gb/s
QD
Exp: EPFL&Alcatel, 2003
100 ps
Exp.: Kuntz, EL 2005
Model
10 QD layers
10 Gb/s
Andrea Fiore
Quasi-thermal equilibrium?
3 Q D layers, 2 mm, pulsed
0.01
Intensity (arb. un.)
QD
4 00 m A
0.001
293 K
2 00 m A
1 00 m A
0.0001
40 m A
10
-5
10
-6
in creasing
current
10
-7
10
-8
10
-9
1150
-
-
-
-
hν2 hν3 hν1 hν2 hν3 hν1
1250
W avelength (nm )
1350
Inhomogeneous broadening +
absence of thermal equilibrium
⇒ Broad laser line = many ≈independent lasers!
Andrea Fiore
Non-equilibrium and
spectral-hole burning
Occupation factor
Occupation factor
1
QDs:
lasing line
0.8
τSHB
τact
0.4
k
Holes
0
10.85
0.9
0.8
0.95 1 1.05
Energy (eV)
1.1
real space
τact>100 ps
0.6
τSHB<1 ps
QDs more prone to nonequilibrium distribution
0.4
0.2
QWs:
E
0.6
0.2
QD
Electrons
0
0.85
0.9
0.95 1 1.05
Energy (eV)
1.1
Additional contribution
to gain compression
Andrea Fiore
QD lasers (2):
Prospects for application?
• Low threshold current
• Small linewidth enhancement factor
• Temperature performance
Lasers
• Broad gain, large saturation power
SOAs, SLEDs
Laser chirp
QD
Direct laser modulation:
01011...
01011...
Problem: Spectral broadening
laser mode
λm =
gain
∆I
λ
∆λ ∆n
2nLcav
⇒
=
λ
m
n
⇒
∆N ⇒
∆ g

∆ n
KramersKronig
I = I (t ) ⇒ n = n (t) ⇒ λ = λ (t)
Laser "chirp":
α
dn / dN
∆ν =
Γv g g1∆N with : α ≡ −
4π
dn i / dN
linewidth-enhancement
factor
Andrea Fiore
4π dneff / dN
α =
=0
λ
dg / dN
Gain
Ideally:
Current (mA)
Newell et al., PTL 1999
Energy
At high bias: Excited states!
12
ES
GS
8
6
4
ES
GS
2
0
5
10
G (el./dot/ τ
rad
)
Experiment
8
6
4
2
0
0
25 C
10
α -factor
α -factor
12
Model
10
QD
α
Refractive index
Linewidth enhancement
factor in QD lasers
15
0
10
20
30
Current (m A)
40
50
Markus et al., JSTQE 2003Andrea Fiore
Insensitivity to feedback
fcrit
2
+
α
1
∝ γ2
α4
α: linewidth enh. factor
γ: damping rate
QDs:
• α small
• γ large (gain compression)
feedback level (dB)
f
Coherence collapse threshold:
QD
I/Ith-1
O'Brien et al, Electron. Lett. 2003
Reduced feedback sensitivity
Potential for isolator-free modules
Andrea Fiore
Temperature characteristics
QD
∆E <kT
∆E v
Holes spread among
closely-spaced levels
Shcheckin
et al.,
APL 2002
No thermal
activation
Matthews
et al., APL 2002
if ∆E>>kT
Use p-doping
T-dependence fixed by
electron distribution
T0>200 K
(Shchekin EL 2002)
0.9
GS electrons
0.8
0.7
0.6
GS holes
0.5
0.4
10
Gain / Gmax
∆Ec>kT
Occupation factor
1
E
0.5
50 100 150 200 250 300
Temperature (K)
GS
0
ES
-0.5
-1
-1.5
0
50 100 150 200 250 300
Temperature (K)
Andrea Fiore
QDs as amplifiers
QD
Size dispersion
Broad gain
spectrum
Carrier reservoir
WL
Akiyama et al, OFC 2004
ES2
Large saturation
power & fast
recovery time
ES1
GS
Psat>19 dBm
over 120 nm
Polarisation sensitivity ? Preliminary evidence of
2004)
polarisation control by shape engineering (Jayavel, APLAndrea
Fiore
QD superluminescent diodes
Chirped QD multilayers
Current (mAmp.)
-4
-5
10
-6
10
800
500
300
200
100
50
GaAs
InGaAs
15% In
8 µm x 4mm ridge
13.5% In
12% In
10.5% In
9% In
-7
10
-8
10
1000 1100 1200 1300 1400
Wavelength (nm)
GS: 55 nm FWHM
ES: 45 nm FWHM
GS + ES: > 100 nm
120 nm
Output power (mW)
Intensity (a.u.)
10
QD
1.5
20 C pulsed
1
0.5
0
EPFL & EXALOS AG (Li et al, Electron. Lett. 2005)
0
0.2
0.4 0.6 0.8
1
Current (A)
Andrea Fiore
QD lasers: Real applications
coming up?
QD
QD lasers are different, in some cases better
Low chirp
Feedback insensitivity
Low-cost 10 Gb/s transmitters
Large T0
Broad gain
SOAs, tunable lasers, SLDs
Andrea Fiore
Single QDs
(as many QDs
as possible)
QD laser:
t
Single-photon emitter:
QD
(only 1 QD)
N. photons
Single photon emitters
Single-φ
emitter
QD
2
1
time
Application: Quantum cryptography
Bob
Alice
01011...
Single-φ
emitter
01011...
BB84
quantum key
distribution
Eve
Andrea Fiore
A close look at single
photons
QD
0,4
0,35
0,3
0,25
0,2
0,15
0,1
0,05
0
<n> =10
1
<n> =1
0,8
P(n)
σ n2 = n
P(n)
"Classical" light sources (e.g. a laser) are Poissonian:
0,6
0,4
0,2
0
0 2 4 6 8 10 12 14 16 18
n
0 1 2 3 4 5 6 7 8 9 10
n
"Nonclassical" light source:
1
<n> =1
Single quantum system:
P(n)
0,8
0,6
0,4
0,2
0
0 1 2 3 4 5 6 7 8 9 10
n Andrea Fiore
The quest for single-ϕ
sources
QD
The simplest single-ϕ sources:
• Single atoms
• Single ions
• Single molecules
• ...
Wish list for single-ϕ sources:
• Compact, electrically pumped
• Efficient
• Emitting at 1300-1550 nm
⇒ A semiconductor LED!
(Diedrich and Walther, PRL 1987)
electron
photon
Andrea Fiore
Isolating single QDs
QD
High areal density
15 nm
200 nm
Need very high spatial
resolution!
Nanomesas:
Shadow-mask apertures:
≈ 100 nm
≈ 1 QD
CNR-IFN Roma
Andrea Fiore
How many photons?
QD
A dot can accommodate many carriers ⇒ many photons!
Total energy
GaAs InAs GaAs
|1>
|0>
2E0+E1-∆E'corr
2E0-∆Ecorr
|0>
|1>
E0
0
useful
photon!
Kiraz et al., PRB 2002
Cascade process with emission of photons at different energies
⇒ Spectral selection of the last photon
Andrea Fiore
Measuring single photons
QD
Second-order correlation function:
<I(t)I(t+τ)>
PMT
classical
delay τ
PMT
Coincidence
counts
quantum
τ
Hanbury Brown and Twiss experiment (1956)
a
PMT
Photon anticorrelation on
single semiconductor
QDs:
delay τ
b
(Michler et al., Nature 2000)
1
Coincidence
PMT ψ =
a + b )
(
counts
2
Are you
SURE?
Andrea Fiore
Why single photons
QD
Quantum key distribution uses single photons:
Bob
Alice
01011...
Single-φ
source
01011...
Eve
• Two polarization coding sets:
=1
=0
=1
=0
1 1 0 0 0 1 0 1 1
• Alice chooses a polarization set randomly:
• Bob selects an analyzer set randomly:
• Only the bits where the same polarization
sets were used are kept
1 1
0 0
1 1
Andrea Fiore
Eavesdropping on single
photons
Bob
Alice
01011...
Single-φ
source
01011...
QD
A single photon
cannot be split!
Eve
To spy, Eve must intercept the photon and retransmit it:
photon
"wrong"
analyzer
error
By monitoring the error rate Alice and Bob can check
the channel security!
Andrea Fiore
Single-photon sources
QD
Q: Do I really need a single-photon source for QKD?
Answer: NO!
Present QKD systems use attenuated lasers
filters
laser
<n>≈0.1
< n >≈ 0.1 ⇒ P ( 2 ) ≈ 1%
Few 2-photon pulses
With "privacy amplification" ⇒ Totally secure key
PRICE TO PAY:
P (1) ≈ 10%
Most pulses empty!
To beat lasers, a single-φ source must be efficient!
Andrea Fiore
Extracting light from
semiconductors
QD
The problem of light extraction:
Outside
medium
(noutside)
Total internal reflection
n(GaAs)≈3.5
θc
Active region
(ninside)
η
extr
=
Ω
c ≈ 2%
4π
Need to change carrier-photon interaction
so that light is generated only in useful directions
Andrea Fiore
Back to basics
QD
Electron-photon interaction
described by perturbation theory:
H ' = − p i E 0 e jω t
Coupling to a density of optical modes (or a lossy mode):
Fermi golden
rule:
Wif ∝ r12
2
g ( E 2 − E1 )
V
g(E): Opt. density of
states per unit energy
V: Mode volume
Andrea Fiore
Microcavities & QDs
Wif ∝ r12
2
g ( E 2 − E1 )
free space:
cavity:
QD
V
8π E 2
gFS ( E ) = 3 3 V
hc
1
max
gcav =
∆Ecav
Energy
free space
E 2- E 1
∆Ecav
0
g
Sp. em. rate enhancement: (Purcell, 1946)
Wcav
1
1
λ3
∝
∝Q
FP =
2
WFS ∆EcavV E
V
FP>>1
η ≈ 100%
(all photons emitted
in cavity mode)
Andrea Fiore
Purcell effect
in micropillars
QD
Micropillars: (Gérard et al., PRL 1998)
Decreased PL lifetime:
Factor x5 increase in sp. em. rate under optical pumping
Andrea Fiore
Promising candidates for
high-Q microcavities
QD
Silica toroid: Q≈108 !
(Armani et al., Nature 2003)
Photonic crystal µ-cavity
(Vuckovic, APL 2003,
Vahala, Nature 2003)
Andrea Fiore
A single QD in a 3D
µ-cavity
Micropillars with
single QDs:
QD
Purcell
effect:
Single-φ
generation:
Pelton et al., PRL 2002
Vuckovic et al., APL 2003
Andrea Fiore
Single QDs: Applications?
QD
Quantum cryptography needs:
• 1.3 - 1.55 µm emission for fibers (problem with
detectors)
• Room temperature operation (very difficult)
• Electrical injection (demonstrated only with very low
efficiency: Yuan et al., Science 2002)
Andrea Fiore
Single QDs at telecom
wavelengths
Wavelength (nm)
1306 1304 1302 1300 1298 1296 1294
QD1
QD1
Very low growth rate:
Low density + long-λ
0.002 µ/h
XXX
-
+
PL Intensity (cps)
X
QD
X
50µW
XX
XX X
21µW
2 µm
X
8.3µW
x2
5.3µW
x2
2.5µW
x3
XX X
XX
X
x10
760nW
300nW
952
956
Energy (meV)
960
Preliminary anticorrelation
experiments at Fujitsu,
Toshiba Europe, EPFL
Alloing, APL 2005
Andrea Fiore
Temperature dependence
QD
Single QD emission above 77 K:
x40
Counta/sec (arb)
xx x
94K
78K
• Population of charged exciton
states at high T
• Homogeneous broadening of
lines due to phonon scattering
• Single lines can be isolated up
to T>77K
xx x
x20
xx x
70K
x15
62K
x10
x
52K
xx
x4
xx
x
42K
xx
Towards LN2-cooled singlephoton sources at 1300 nm
x
31K
936
940
944
Energy (m eV)
948
Andrea Fiore
Fabrication of nano-LEDs
< 1 µm
Al2O3
Au
GaAs
AlGaAs
QDs
QD
Etching:
Defects ⇒ NR recombination
Needs high-res. lithography
QD
300 nm current aperture
oxid. edge
oxid. edge
Oxidation:
☺ Does not create defects
☺ Smaller dimensions (<100 nm
with optical lithography)
Fiore et al., APL 2002
Andrea Fiore
Single QDs:
Perspectives
Single QDs: What next?
QD
• Entangled photon generation:
EC
EV
Two electrons ⇒ two photons
(orthogonally polarized and
entangled)
ψ =
1
(0
2
A
1
B
± 1
A
0
B
)
• Single-photonics (towards quantum computing?):
Identical single photons
"stick together"
Quantum optics
w/ single photons
(Santori et al., Nature 2002)
Andrea Fiore
Quantum interference of
two photons
QD
Lossless symmetric beamsplitter: Input-output relations
Classical:
Quantum:
2
1
1 †

 †
†
3
=
+
=
+
E
E
E
a
a
a
(
)
1
2
(
3
1
2)
 3

2
2

1


1
1 † †
†


4
E4 =
E1 − E 2 )
a4 =
a1 − a 2 )
(
(


2
2
2-photon input:
classical fields
photon creation operators
1 †
a 3 + a†4 )( a†3 − a†4 ) 00 =
(
2
1 †2 †2
1
2 3 04 − 0 3 24 )
= ( a 3 − a4 ) 00 =
(
2
2
Both photons from the same port
Andrea Fiore
(entangled state)
1112 = a1†a†2 00 =
2-photon interference:
Experiment
QD
"Mandel's dip":
A non-classical interference effect
Andrea Fiore
Using quantum interference
for quantum gates
QD
Asymmetric beamsplitter (R=33%, T=67%):
2
3
1
4
 †
2 †
a
a1 +
=
 3
3


a † = 1 a † −
1
 4
3
2
1112 = a a 00 =
2 3 04 − 0 3 24
(
3
† †
1 2
1
3
a†2
2 †
a2
3
1
) − 3 1314
Sign shift induced by the
photon collision
Andrea Fiore
CNOT quantum gate
Photonic quantum bits:
O'Brien et al., Nature 2003:
QD
0 = photon in upper branch
1 = photon in lower branch
control bit
target bit
Balanced interferometer:
If C=0: Tin=0→Tout=0, Tin=1→Tout=1
If C=1: Phase shift at 1/3 beamsplitter
Tin=0→Tout=1, Tin=1→Tout=0
NB: Works
with only 1/9
probability!
Andrea Fiore
Quantum computing with
linear optics
QD
"Probabilistic" quantum gates are possible using single
photons, beamsplitters and phase shifters
The probability of success can be increased arbitrarily by
using teleportation and entanglement
"Efficient" quantum computation (Knill et al., Nature 2001)
Linear optics quantum computation needs "perfect"
single-photon sources and detectors (plus a few
hundred optical elements….)
In the meantime, interesting
quantum optics experiments:
Andrea Fiore
Conclusion
QD
Today:
• QD lasers for telecom
• QD broad gain SOAs and SLEDs
Tomorrow:
• "Quantum" applications
Current (mAmp.)
0.14
-4
2 mm
0.12
10
total
293 K
0.1
Intensity (a.u.)
Integr. int. (arb. un.)
QDs: A different light source
0.08
0.06
GS
0.04
0.02
0
ES
0
200
400
600
800
C urrent (m A)
1000
-5
10
-6
10
800
500
300
200
100
50
8 µm x 4mm ridge
-7
10
-8
10
1000 1100 1200 1300 1400
Wavelength (nm)
Andrea Fiore
Acknowledgements
QD
• Simulations: Alexander Markus
• QD lasers: M. Rossetti, L.H. Li
• Single QDs: B. Alloing, C. Monat, C. Zinoni
• Collaborations with Alcatel CIT and EXALOS AG
Funding:
• For this tutorial: ePIXnet NoE
• For QD research at EPFL:
Andrea Fiore