Quantum Dots in Photonic Structures

Wednesdays, 17.00, SDT

Jan Suffczyński

Projekt Fizyka Plus nr POKL.04.01.02-00-034/11 współfinansowany przez Unię Europejską ze środków Europejskiego Funduszu Społecznego w ramach Programu Operacyjnego Kapitał Ludzki

Lecture 12: Single photon correlations and cavity mode emission

Plan for today

1. Reminder 2.

Photon emissionstatistics

3. Origin of the emission with the cavity mode

Strong coupling –Rabi splitting

Ener

gy

Eigenstates :Entengled states emitter-photon

RabbiSplitting DR

(|0,1> + |1,0>)/ 2

(|0,1> |1,0>)/ 2

|0,1> ↔

In resonance:

Oscillationswith Rabi frequency = R / h

|1,0>

|0,1> :

|1,0> :

Emitter in ground state

Excitedemitter

Empty cavity

Photon inside cavity

Out of the resonence:

Weak vs strong coupling

Out of the cavity

Strong coupling regime

• At resonance QD- Cavity mode: anticrossing of the levels!

QD– Cavity mode detuning

Energy levels versus detuning:

4)( 22MQDRabi g Rabi splitting:

4)( 22MQDRabi g

Reithmaier et al., Nature (2004)

Weak coupling vs strong coupling

Equal intensity at resonance/X intensity increased at resonance

Anticrossing/no anticrossing

Exchange of linewidths/no lw exchange

CorrelationCorrelation (lat. correlation-, correlatio, from com-, „together, jointly”; and relation-, relatio, „link, relation”

Correlations macro in the world:

Correlations

Correlations

Correlations

Korelacje

A statistical effect!

Correlation function

)()(

)()()()2(

tItI

tItIg

ba

baab

represents probability of detection of the second photon at time t + , given

that the first one was detected at time t

)()2( abg

Od źródła fotonów

Dioda „START”

Dioda „STOP”

n( = tSTOP- tSTART)

Idea pomiaru korelacji między pojedynczymi fotonami

)()( )2( abgn

-60 -40 -20 0 20 40 600

1

2

3

4

5

6

Lic

zba

zdar

zen

= t2 - t

1

= t2 – t1

t1 = 0t2 = 20

wejścieSTART

wejścieSTOP

Karta do pomiaru korelacji

Dioda „START”

Dioda „STOP”

Licz

ba s

kore

low

anyc

h zl

icze

ń n(

)

Od źródła fotonów

-60 -40 -20 0 20 40 600

1

2

3

4

5

6

Lic

zba

zdar

zen

= t2 - t

1

= t2 – t1

t1 = 0, t2 = 0

wejścieSTART

wejścieSTOP

Karta do pomiaru korelacji

Od źródła fotonów

Skor

elow

anyc

h zl

icze

ń n(

)

Dioda „STOP”

Dioda „START”

Correlation function )()2( g

T

time t

0)0()2( g

-40 -20 0 20 400

1

2

g()

= t2 – t1

T

0

Single photon source (pulsed):

0)0()2( g

-40 -20 0 20 400

1

2

g()

0

Single photon source (cw):

time t

-40 -20 0 20 400

1

2

g() 1)()2( g

0

Coherent light source (cw):

time t

1)0()2( g

-40 -20 0 20 400

1

2

g()

0

Thermal light source:

time t

Photon statistics

Bose-Einstein distribution

Poissonian distributionLASER

0 1 2 3 4 5 60.0

0.1

0.2

0.3

P(n

)

n

0 1 2 3 4 5 60.0

0.1

0.2

0.3

0.4

P(n

)

n

Sub-poissonian distribution

0 1 2 3 4 5 60.00

0.25

0.50

0.75

1.00

P(n

)

n0 1 2 3 4 5 6

0.00

0.25

0.50

0.75

1.00

P(n

)

n

Single photon sources

– single atoms

– single molecules

– single nanocrystals

– NV in diamond

h

• highly efficient

• work with high repetition rates

• excited optically / electrically

• easy to integrate with electronics

• + more …

− single semiconductor quantum dots

(Koenraad et al.)

Pojedyncze fotony z QD na żądanie

2210 2215 2220 2225

XX

CX

-P

L I

nte

ns

ity

[a

rb.

un

its

]

Photon Energy [meV]

X

-60 -40 -20 0 20 40 600

250

500

750

Zlic

zen

ia

= tSTOP

- tSTART

(ns)

Autokorelacja emisji z ekscytonu neutralnego (X-X):

START

X

czas

Od próbki

• Rejestrowane fotony pochodzą z pojedynczej kropki

• g( 2)(0) = 0.073 = 1/13.6

X

X

STOP

START

STOP

X

-60 -40 -20 0 20 40 600

100

200

300

400

500

Co

un

ts

= tX-t

CX [ns]

X-CX cross-corelation

-60 -40 -20 0 20 40 600

100

200

300

400

500

Co

un

ts

= tX-t

CX [ns]

Three carriers capture

Single carrier capture

STOP

Single carrier capture

<0 ↔ CX emissionafter X emission:

STOPX

START

time

XCX

START

time

CX

>0 ↔ X emission after CX emission:

X after CXCX after X

XX-X crosscorrelationSTOP (H)START (H)

-40 -20 0 20 400

200

400

600

800

1000

H / H

Cou

nts

= tX- t

XX [ns]

5.24

2210 2215 2225

X

CXXX

H V

-PL

Int

ensi

ty [

arb.

uni

ts]

Photon Energy [meV]

START STOP

XX X

time0

• XX-X cascade

Origin of the emission within the caviy mode

Energy

PL ~15 meV

Cavity mode

QD

~1 meV

Why is emission at the mode wavelength observed?

Strong coupling in a single quantumdot–semiconductor microcavity system, Reithmaier et al., Nature (2004)

Strong emission at the mode wavelength even for large QD-mode detunings

Quantum nature of a strongly coupled single quantumdot–cavity system, Hennessy et al., Nature (2007):

Time (ns)

Autocorrelation M - MCrosscorrelation QD - M

Time (ns)

„Off-resonant cavity–exciton anticorrelation demonstrates the existence of a new, unidentified mechanism for channelling QD excitations into a non-resonant cavity mode.”

„… the cavity is accepting multiple photons at the same time - a surprising result given the observed g(2)(0)≈ 0 in cross-correlation with the exciton.”

1352

1356P

hoto

n E

nerg

y (m

eV)

X

XX

CXM

T = 40 K

Dynamics of the QD emission – Purcell efect

1352 1356

XXCX

10 KXM

33 K

44 K

Pho

tolu

min

esce

nce

(arb

. uni

ts)

50 K

Photon Energy (meV)

0.5 1.0 1.5 2.0Time (ns)

0.5 1.0 1.5 2.0Time (ns)

1352

1356

Pho

ton

Ene

rgy

(meV

)

X

XX in resonanse with the Mode

CX T = 10 K

tXX = 140 ps when XX in resonanse with the mode - Purcell efect

Pillar A (diameter = 1.7mm, gM = 1.08 meV, Q = 1250,Purcell factor Fp= 7.2

10 20 30 40 500.0

0.5

1.0

Dec

ay ti

me

(ns)

Temperature (K)

XX

When XX-M detuning increases Purcell efect decreases XX decay longer

Emission dynamics at mode wavelength the same as XX emission dynamics !

Above T = 45 K – 50 K carrier lifetime in wetting layer increases excitonic decay gets longer

10 20 30 40 500.0

0.5

1.0

Dec

ay ti

me

(ns)

Temperature (K)

XX M

pillar A

Dynamics of the emission of the coupled system

0.5 1.0 1.5 2.0

710 ± 30 ps

M

Eim

issi

on Int

ensi

ty (ar

b. u

nits

)

Time (ns)

X

670 ± 30 ps

Pillar B, diameter = 2.3 mm,gM = 0.45 meV, Q = 3000,

Purcell factor Fp= 8

T = 53 K

T = 53 KX

M

1344 1346 1348

M

X

M

67K

57K

44K

62K

53K

Pho

tolu

min

esce

nce

(arb

. uni

ts)

Photon Energy (meV)

X

Ene

rgy

pillar B

pillar B

X and M decay constants similar

Dynamics of the emission of the coupled system

1.5 1.0 0.5 0.0 -0.5 -1.0 -1.50.0

0.5

1.0

Dec

ay ti

me

(ns)

X

1.5 1.0 0.5 0.0 -0.5 -1.0 -1.50.0

0.5

1.0

Dec

ay ti

me

(ns)

X M

50 60 70

X E

mis

sion

Inte

nsity

(arb

. uni

ts)

44Temperatura (K)

Odstrojenie X - M (meV)

pillar B

X emission intensity increases when X-M detuning decreases: Evidence for Purcell effect

T> 45 K :Shortening of the X lifetime with decreasing X- M detuning impossible to be observed

Purcell factor determination basing on the emission dynamics not always reliable

M i X decay constants similar

Dynamics of the emission of the coupled system

Below T=45 K temperature does not affect the X emission dynamics. PL decay time reflects exciton recombination rate

10 20 30 40 500.0

0.5

1.0

1.5

2.0

2.5

Dec

ay T

ime

(ns)

Temperature (K)

X,meza APillar A

T< 45 K

Exciton dynamics vs T, pillar A

Exciton emission decay longer for T > 45 - 50 K

PL decay time does not reflect exciton recombination rate

T> 45 K

10 20 30 40 500.0

0.5

1.0

1.5

2.0

2.5

Dec

ay T

ime

(ns)

Temperature (K)

X,meza APillar A

Exciton dynamics vs T, pillar A

0.0 0.5 1.0 1.5 2.00.0

0.5

1.0

1.5

2.0

Mod

e D

ecay

Tim

e (n

s)

QD Decay Time (ns)

slope = 1.02 ± 0.08

Strong correlation between exciton and Mode decay constants

The same emitter responsible for the emission at both (QD i M) energies

QD-M detuning (< 3gM) does not crucial for the QD→M transfer effciency

-2 0 20.0

0.5

1.0

1.5

M / Q

D

Detuning /M J. Suffczyński, PRL 2009

Statistics on different micropillars

Naesby et al., Phys. Rev. A (2008) Influence of pure dephasing on emission spectra from single photon sources

Dephasing rate :

The role of QD state dephasing

0.0

0.5

1.0

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

Rel

ativ

e M

ode

Int

ensi

ty

X-M Detuning (meV)

Naesby et al.: effects of QD states dephasing responsible fort the emission at mode wavelength

X M

Em

issi

onIn

tens

ity

(arb

. uni

ts)

Pillar B, gM = 0.45 meV

Contribution from different emission lines

0.0 0.5 1.0 1.5 2.00.0

0.5

1.0

1.5

2.0

Mod

e D

ecay

Tim

e (n

s)QD Decay Time (ns)

slope = 1.02 ± 0.08

When two lines are detuned similarly from the mode, the contribution from more dephased one to the mode emission is dominant

Phonons - diatomic chain example

M m M m M

Solutions to the Normal Mode Eigenvalue Problemω(k) for the Diatomic Chain

There are two solutions for ω2 for each wavenumber k. That is, there are 2 branches to the “Phonon Dispersion Relation” for each k.

0 л/a 2л/a–л/a k

wA

BC

ω+ = Optic Modes

ω- = Acoustic Modes

Transverse optic mode for the diatomic chain

The amplitude of vibration is strongly exaggerated!

Transverse acoustic mode for thediatomic chain

Interpretation of the single photon correlation results

Crosscorrelation M - X = (X+CX+XX) - X = X-X + CX-X + XX-XX-X CX-X XX-X

1

0

1

0

1

0

+ +a* b* c*

g(2) (t) g(2) (t) g(2) (t)

t t t

↔

1

0

=

M-X

Hennessy et al., Nature (2007) g(2)(0) ~ 0 Asymmetry of the M-X correlation histogram

M-Xg(2) (t)

tt (ns)

Autocorrelation M-M = 2*(X-X + CX-CX + XX-XX) + X-CX + CX-X + X-XX + X-XX + CX-XX + XX-CX:

Time (ns)0

Hennessy et al., Nature (2007)

+…=

CX-CX1

0

X-X1

0

XX-XX1

0

1

0

CX-XX1

0

CX-X1

0

XX-X

g(2)(0) ≠ 0 Symmetry of the M-M correlation histogram

↔

1

0

M-M

M-M

Interpretation of the single photon correlation results