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