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Ultrafast Spectroscopy of Quantum Dots (QDs)
Experimentelle Physik IIb
FB Physik, Universität Dortmund
Ulrike Woggon
With thanks to: M.V. Artemyev, P. Borri, W. Langbein, B. Möller, S. Schneider
Fruitful cooperations: calculations: R. Wannemacher, Leipzig, samples:D. Bimberg and coworkers, Berlin
D. Hommel and coworkers, Bremen A. Forchel and coworkers, Würzburg
• 1. Types of QDs and Techniques of Ultrafast Spectroscopy
Outline:
• 2. Application Aspects: Dynamics of Amplification in QD-Lasers
Outline:
D. Bimberg and coworkers, TU Berlin
predicted advantages of QD-lasers:
• low threshold current density • high characteristic temperature• high differential gain • large spectral tunability, from NIR to UV
Monitoring of high-frequency optical operation in semiconductor nanostructures by
ULTRAFAST SPECTROSCOPY
• 3. Fundamental aspects: Semiconductor QDs as artificial atoms
Outline:
L.Banyai, S.W. Koch, Semiconductor Quantum Dots
Monitoring of the „discrete-level“ - structure of semiconductor nanostructures by
ULTRAFAST SPECTROSCOPY
size energy
Quantum Dots: Nanocrystals and epitaxially grown Islands
Part 1: Types of QDs and Techniques...
Lattice-mismatch inducedisland growth
Precipitation of spherical nanocrystals in colloidal solutionor glass, polymer etc. matrix
CdSe QDs emitting in the visible (nanocrystals)
500 550 600 650 7000
0.5
1.0
1.5
CdSe QDsR = 1.5 nmT = 300 K
PL In
tensity (a
rb. u
nits)
Optic
al D
ensi
ty
Wavelength (nm)
2.4 2.2 2 1.8
Photon Energy (eV)
500 550 600 650 700
0.2
0.4CdSe QDsR = 2 nmT = 300 K
Opt
ical
Den
sity
Wavelength (nm)
PL Intensity (arb. units)
2.4 2.2 2 1.8
CdSe in glass
5 nm
InGaAs self-assembled islands emitting in the NIR
Grundmann, Bimberg et al., TU Berlin
D. Gerthsen et al., Karlsruhe
Calculated confined eh-pair energiesfor InAs assuming pyramidal shape
Femtosecond Heterodyne Technique
2 probe
22-1 four-wavemixing (FWM)
waveguidepumpprobe
12 signal
t
Part 1: Types of QDs and Techniques...
Ti:Sa + OPO, 80 fs ... 2 ps
Femtosecond Ultrafast Spectroscopy
Usually:
J. Shah, Ultrafast Spectroscopy
Femtosecond Heterodyne FWM- and PP-Spectroscopy
Usually:
Here:
AOM1
AOM2
pump beam
probebeam
+
_
HF-Lock-in
delay
delay
sample
reference beam 76MHz
laser
4MHz3MHz
probe pumpFWM
2MHz
79MHz
80MHz
Idet refsignal
electric field
150fs76MHz
AOM-Acousto-Optical Modulator
Gain Dynamics in Quantum Dots
InAs/InGaAs QDs3 x stack,20nm GaAs barrier
Part 2: Applied aspects: QD-laser...
Gain Dynamics of InGaAs QDs
1.1 1.2 1.3 1.4 1.5
+
_
n-GaAs
n-AlGaAs GaAs GaAs
p-AlGaAsp-GaAs
InGaAs QDs
ES
GS
laser
65meV
A
SE
(a.
u.)
Energy (eV)
Ground State Emission (GS): 1070nm @ 25K, 1170nm @ 300K
Sample from TU Berlin,Prof. Bimberg
ridge waveguide 5x500m, 3 stacked QD layers
areal dot density ~2x1010cm-2
optical density ~ 1.5 (~30cm-1)
Carrier injectionelectrically (0...20 mA)0.5 mA
20 mA
Gain Dynamics of InGaAs QDs
P. Borri et al., J. Sel. Topics Q. El. 6, p. 544 (2000); Appl. Phys. Lett. 76, p.1380 (2000).
Pump-inducedgain change in a heterodyne pump-probe experiment at maximum gain(20 mA) and without electricalinjection (0 mA)
Gain recovery in< 100 fs at 300 K !
Gain Dynamics of CdSe QDs
Ground State Emission (1): 605 nm @ 6K
CdSe nanocrystalsin glass matrixR ~ 2.5 nm
1.9 2.0 2.1 2.2 2.3 2.4
PL
Inte
nsity
(ar
b. u
nits
)
Photon Energy (eV)
0.03 I0
I0
(4)
(3)(2)
(1)
0
2
d
T=6KR~2.5 nmI0=5 mJ/cm
2
Woggon et al., Phys. Rev. B 54, 17681 (1996), J. Lum. 70, 269 (1996).
...
.....
onepair
twopairs
1se1sh
1se2sh
1pe1ph...
1se1sh 1se1sh
1se1sh 2se1sh
1pe1ph 1pe1ph...
(1),(2)
(4)
(3)
Gain Dynamics of CdSe QDs
Optics Lett. 21, 1043 (1996).
Gain recovery time spectrally varying, <1...100ps
Excitonic and biexcitonic contributions to optical gain
Gain Dynamics of CdSe QDs
Chem. Phys. 210, 71 (1996)
Gain spectrum inhomogeneously broadened:Spectral hole burning in gain spectrum with two fs-pump and one fs-probe beam
Spectral hole widthof a single
gain process ~20 meV
Intrinsic limitof gain recoverybelow 100 fs !
Quantum dots as active media in optical microcavities
5 m
CdSe QDs linked to microspheres
Picture: M.V.Artemyev, I. Nabiev
Part 2: Applied aspects: QD-laser...
„Dot - in - a - Dot“ - Structure
=619.22nm
R=2.77m
CdSenanodot
136 TM
R=2.5m
R=2.2 nmGlassmicrosphere
R=3.1 m
Artemyev et al., APL 78, p.1032 (2001), Nano Lett. 1, 309 (2001).
Cavity Modes of a CdSe-doped Microsphere
RPD = 2.5 m RQD = 2.5 nm
Nano Lett. 1, p. 309 (2001), Appl. Phys. Lett. 80, p.3253 (2002)
WGM
TM, =36, n=1
TM, =36, n=2
Optical Pumping of a CdSe-doped Microsphere
RPD ~ 15 m
Excitation spot size40 m2
cw-Ar laser, 488 nm
10 mW
14 mW
T = 300 K520 nm < em < 640 nm
CdSe nanocrystals(not on microsphere)
See also: Artemyev, Woggon et al. Nano Letters 1, 309 (2001)
Rabi Oscillations in Quantum Dots
Part 3: Fundamental aspects: Artficial atoms...
Bloch-sphere:population oscillation
Rabi-Oscillations in Atoms
Simple model: two coupled oscillators
R
|g>|e>
|g>|e>
|3>|2>|1>|0>
|3>|2>|1>|0>
photon field
0
RE
Rabi frequency
Ea
Eb
atom states
Two-level system in resonance with photon field
E0 == Eb - Ea
: transition dipole moment
: transition energy
E0 : electromagn. field vector
...
...
Rabi Oscillations versus Pulse Area
Pulse area: time-integrated Rabi frequency
Here pulsed excitation !
dtE
0
0 2 4 6 8 100
1
2
3
4
t0=1ps (E
HWHM=0.75meV)
pulse area ()
detu
ning
(m
eV)
Population oscillationblue = -1red = +1
No dephasing!
Initial conditions:for t << -t0 in ground state
0 2pulse area (
4 6 8 10
detu
ning
(m
eV)
Occupation probability of the ground (excited) state
(~ input field intensity)
Effect of Dephasing T2 on Rabi oscillations
The effect of a damping =1/T2 of polarization:
0 2 4 60.0
0.5
1.0
R=1
R=1/9
|b|2
Rt/2
=0
Population flopping over many periods is possible in systems with long dephasing times and large transition dipole moments: / R<<1.
Dephasing time T2 of InGaAs quantum dots
P. Borri et al., Phys. Rev. Lett. 87, 157401 (2001)
From 300K to 100K the FWMdecay is dominated by a short dephasing time < 1ps
Below T=10 K a slow dephasing time > 500 ps is observed (suppression of LO-phonon scattering!)
-1 0 1 2 3 200 400
500ps
T=10K
TI F
WM
fiel
d am
plitu
de (
a.u.
)
Delay time (ps)
Is the observed dephasing time T2 large enough to observe population flopping, i.e. Rabioscillation in QDs ?????
InGaAs - QDs
Rabi Oscillations in InGaAs Quantum Dots
Use of spectrally shaped ps-pulses
a sharpened distribution of the spectral intensity improves the visibility of the oscillations.
Rabi oscillation: two oscillation maxima can be clearly distinguished
0 4 8
1.146 1.149 1.152
T = 10 K
DT
fiel
d am
plitu
de (
a.u.
)
Pulse area (a.u.)
Inte
nsity
(a.
u.)
Energy(eV)
Experiment
Borri et al., Phys. Rev. B (Rapid Comm.), in press
Distribution in Transition Dipole Moments
2
20
22
2
1
eP
dfEdPdrrEdT
TpumpTEprobe ,,,,
0
22
0
0 2 4 60
T2
=0.25
0.2
0.15
0
T/T
(ar
b. u
nits
)
Pulse area ()0 2 4 6
T2=1.5ps
Pulse area ()
in average = 35 D = 20%
Borri et al., Phys. Rev. B (Rapid Comm.), in press
Quantum Beats in Quantum Dots
0 500 1000
tbeat
= 168 fs
E = 25 meV
Delay Time (fs)
FW
M-I
nten
sity
(lo
g. u
nits
)
Part 3: Fundamental aspects: Artficial atoms...
E
|0>
|1>|2>
Discrete Level-System E can be derived from beat period
Exciton-Biexciton Quantum Beats in QDs
|2x>|xx> Ebin
|x+> |x_>
|G>
|G>
|x> |xx>
|G>
|1e,1h>
Quantum Beats betweentwo optical transitions:
|G> |x> with EX
|x> |xx> with EXX
EX - EXX = Ebin (biexciton binding)
|G>
uncorr.electronand hole Coulomb interaction
exciton |x>biexciton |xx>formation
Exciton-Biexciton Quantum Beats in QDs
0 500 1000 1500
ExxFW
M In
tens
ity (
log.
u.)
B=208 fs
Delay Time t12 (fs)
2.45 2.5
FW
M (
log.
)
E (eV)
Exx Ex
20meV
Gindele, Woggon et al., Phys. Rev. B 60, p. 8773 (1999).
Determination of biexciton bindingenergy in CdSe/ZnSe QDs byfemtosecond quantum beat spectroscopy
Biexciton bindingenergy E = 21 meV
CdSe QDs in microspheres
InGaAs QDs in waveguides
2m
Summary
Fundamental aspects: Semiconductor Quantum Dots as Artficial Atoms
Application Aspects: Dynamics of Amplification in Quantum Dot Lasers
Types of Quantum Dots and Techniques of Ultrafast Spectroscopy