Transcript Prezentacja programu PowerPoint

Quantum Dots in Photonic Structures
Lecture 13: Entangled photons from QD
Jan Suffczyński
Wednesdays, 17.00, SDT
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
Plan for today
1.
Reminder
2.
Entanglement
3. Entangled photons from
a single semiconductor QD
Correlation function g
I a (t ) I b (t   )
( 2)
gab ( ) 
I a (t ) I b (t )
( 2)
ab
( )
represents probability of detection of
the second photon at time t + , given
that the first one was detected at time t
Karta do pomiaru korelacji
Dioda „STOP”
Dioda
„START”
zliczeń n()
Liczba skorelowanych
Liczba zdarzen
Od źródła fotonów
6
5
4
3
2
1
0
-60 -40 -20
wejście
STOP
wejście
START
0
20
 ==t2t –-tt1
2
1
40
t1 = 0
t2 = 20
60
Correlation function g
Thermal light source:
( 2)
g ( 2) (0)  1
g()
2
1
0
time t
-40 -20
0
20
40
2
g()
Coherent light source (cw):
g ( 2) ( )  1
1
0
time t
-40 -20
0
20
40
2
g()
Single photon source (cw):
time t
Single photon source (pulsed):
T
g ( 2) (0)  0
1
0
-40 -20
00
20
40
g()
2
time t
g ( 2) (0)  0
T
1
0
( )
-40 -20
0
20
 = t2 – t1
40
Photon statistics
0.4
P(n)
0.3
0.2
0.1
Bose-Einstein distribution
0.0
0
1
2
0
1
2
0
1
2
3
4
5
6
3
4
5
6
3
4
5
6
n
0.3
P(n)
0.2
LASER
Poissonian distribution
0.1
0.0
n
1.00
P(n)
P(n)
0.75
Sub-poissonian distribution
0.50
0.25
0.00
n
Autokorelacja emisji z ekscytonu
neutralnego (X-X):
X
750
CX
XX
2210
2215
2220
2225
Photon Energy [m eV]
Zliczenia
-PL Intensity [arb. units]
Pojedyncze fotony z QD na żądanie
500
250
Od próbki
X
X
0
-60
START
STOP
• g( 2)(0) = 0.073 = 1/13.6
• Rejestrowane fotony pochodzą z
pojedynczej kropki
-40
-20
0
20
40
 = tSTOP- tSTART (ns)
START
X
60
STOP
X
czas 
500
Counts
X-CX crosscorelation
400
300
200
100
0
-60
-40
-20
0
20
 = t X -t C X [ns]
40
60
Three carriers capture
Single carrier capture
500
X after CX
CX after X
Counts
Single
carrier
capture
400
300
200
100
0
-60
 >0 ↔ X emission
after CX emission:
-40
-20
0
20
 = t X -t C X [ns]
40
60
STOP
START
CX
X
<0 ↔ CX emission
after X emission:
time
STOP
CX
time
START
X
XX-X crosscorrelation
STOP (H)
1000
X
H
V
XX CX
5.24
800
Counts
-PL Intensity [arb. units]
START (H)
H/H
600
400
200
2210
2215
0
2225
Photon Energy [meV]
START
XX
-40
-20
0
20
 = tX- tXX [ns]
40
STOP
X
• XX-X cascade
0
time
Origin of the emission within the caviy mode
Cavity mode
QD
PL
~1 meV
~15 meV
Energy
Why is emission at the mode wavelength observed?
Strong coupling in a single quantum
dot–semiconductor microcavity system,
Reithmaier et al., Nature (2004)
Quantum nature of a strongly coupled single quantum
dot–cavity system, Hennessy et al., Nature (2007):
Crosscorrelation QD - M
Time (ns)
Strong emission at the
mode wavelength even for
large QD-mode detunings
„Off-resonant cavity–exciton
anticorrelation demonstrates the
existence of a new, unidentified
mechanism for channelling QD
excitations into a non-resonant
cavity mode.”
Autocorrelation M - M
Time (ns)
„… the cavity is accepting multiple
photons at the same time - a
surprising result given the
observed g(2)(0)≈ 0 in crosscorrelation with the exciton.”
Dynamics of the emission of the coupled system
M
67K
Energy
M
pillar B
X
62K
57K
53K
44K
M
T = 53 K
X
Eimission Intensity (arb. units)
Photoluminescence (arb. units)
Pillar B, diameter = 2.3 m,
gM = 0.45 meV, Q = 3000,
Purcell factor Fp= 8
X
1344
1346
1348
Photon Energy (meV)
T = 53 K
M
X
670 ± 30 ps
710 ± 30 ps
pillar B
0.5
1.0
1.5
Time (ns)
 X and M decay constants similar
2.0
Statistics on different micropillars
 Strong correlation between exciton
and Mode decay constants
Mode Decay Time (ns)
2.0
1.5
slope = 1.02 ± 0.08
1.0
 The same emitter responsible for the
emission at both (QD i M) energies
0.5
0.0
0.0
0.5
1.0
1.5
QD Decay Time (ns)
2.0
-2
2
 QD-M detuning (< 3gM) does not crucial
for the QD→M transfer effciency
 M /  QD
1.5
1.0
0.5
0.0
0
Detuning /gM
J. Suffczyński, PRL 2009
Contribution from different emission lines
 When two lines are detuned similarly from the mode, the
contribution from more dephased one to the mode emission
is dominant
Mode Decay Time (ns)
2.0
1.5
slope = 1.02 ± 0.08
1.0
0.5
0.0
0.0
0.5
1.0
1.5
QD Decay Time (ns)
2.0
Phonons diatomic chain example
M
m
M
m
M
Solutions to the Normal Mode Eigenvalue Problem
ω(k) for the Diatomic Chain

A
ω+ =
Optic Modes
B
C
ω- =
–л/a
0
л/a
2л/a
Acoustic Modes
k
There are two solutions for ω2 for each wavenumber k. That is, there are 2
branches to the “Phonon Dispersion Relation” for each k.
Transverse optic mode for the diatomic chain
The amplitude of vibration is strongly exaggerated!
Transverse acoustic mode for the
diatomic chain
Interpretation of the single photon correlation results
Crosscorrelation M - X = (X+CX+XX) - X =
CX-X +CX-X
XX-X g(2) ()
(2) ()
g(2) ()
X-XX-X g+
XX-X
1
1
1
a*

0
+ b*
0
+ c*

0
M-X
M-X
g(2) ()
1
↔
=
0

 (ns)
Hennessy et al., Nature (2007)

~0
 Asymmetry of the M-X correlation histogram
g(2)(0)

Quantum Entangled photons
from a semiconductor QD
Crystals can produce pairs of photons,
heading in different directions. These pairs
always show the same polarization.
?
These are said to be entangled photons. If
one is measured to be vertically polarized,
then its partner kilometers away will also
be vertical.
?
Entanglement
1) Does a polarizing filter act by
a)
selecting light with certain
characteristics, like a sieve selects
grains larger than the hole size
or by
changing the light and rotating its
polarization, like crayons and a grid
Measurement-Reality
Niels Bohr and
Einstein argued
for 30 years about
how to interpret
quantum
measurements
like these.
Niels Bohr codified what
became the standard
view of quantum
mechanics.
The filter is like a grid for
crayons - the photon has
no polarization until it is
measured. It is in a
superposition of states.
Einstein felt that the
filters were like a
sieve. The photons
must contain
characteristics that
determine what they
will do.
The information from
the measurement of
one can’t possibly fly
instantaneously to its
partner.
He referred to this as
‘spukhafte
Fernwirkungen’
which is usually
translated as ‘spooky
action-at-a-distance’.
Then in 1964 John Bell devised
a test.
He looked at what happens if
the filters are in different
orientations.
2)Four entangled pairs of photons head
toward two vertical polarizers.
If four make it through on the left, how many
make it through on the right?
?
Next, we put the filter on the right at 30o.
3) Which of the following would you expect to
see if all 4 made it through on the left?
a)
b)
c)
d)
4) What percentage agreement do you
expect on average?
a) 0%
b) 25%
c) 75%
d) 100%
5) If the right filter is vertical and the left is
placed at –30o, what agreement would you
expect?
a) 0%
b) 25%
c) 75%
d) 100%
Next we combine the two experiments. The left
polarizer is at –30 and the right at +30.
How much agreement is expected?
a) 25% b)50%
c)75%
d)100%
7) How much agreement does quantum
mechanics predict? Hint: The two filters are at
60 degrees to each other.
a) 0%
b) 25%
c) 50%
d) 75%
7) How much agreement does quantum
mechanics predict? Hint: The two filters are at
60 degrees to each other.
a) 0%
b) 25%
c) 50%
d) 75%
The photons have a
polarization before
measuring - the
agreement will be
between 100% and 50%.
Just apply the rules of
quantum mechanics - the
agreement should be
25%.
Confirmation: Alain Aspect et al.
1983
Turning Interference
On and Off
Two-slit
Interference
Pattern
H
V
No Two-slit
Interference
Pattern
41
“Ghost” Interference
In their 1994 “Ghost Interference”
experiment, the Shih Group at the
University of Maryland in Baltimore
County demonstrated that causing
one member of an entangled-photon
pair to pass through a double slit
produces a double slit interference
pattern in the position distribution of
the other member of the pair also.
If one slit is blocked, however, the
two slit interference pattern is
replaced by a single-slit diffraction
pattern in both detectors.
Note that a coincidence was
required between the two photon
detections.
42
Enangled photons from a QD
The method: biexciton
– exciton cascade
Obstacle:
anisotropy
Biexciton
Exciton
Empty dot
The energy carries the
information on the
polarization of the photon
Entangled photons from a QD
The method: biexciton
– exciton cascade
An obstacle:
anisotropy
Biexciton
Exciton
Empty dot
(in circular polarization basis:)
 | RX LXX   | LX RXX 
The energy carries the
information on the
polarization of the photon
Neutral exciton X
• Formed by: heavy hole and electron
Jz = ±3/2
Jz = ±1/2
• 4 possible spin states of X
Jz = -1
Jz = +1
Jz = -2
Jz = +2
Fine structure of neutral exciton
X
( + )/ 2
δ1~0.1meV
( – )/ 2
X
δ0~1meV
Isotropic
exchange
Anisotropic
exchange
( + )/ 2
Xdark
( – )/ 2
δ2 ≈0
(No) entanglement test
STOP (H)
1000
X
H
V
XX CX
5.24
800
Counts
-PL Intensity [arb. units]
START (H)
H/H
600
400
200
2210
2215
0
2225
Photon Energy [meV]
START
XX
-40
-20
0
20
 = tX- tXX [ns]
40
STOP
X
• XX-X cascade
0
time
Kaskadowa emisja pary fotonów
1000
5.24
H/H
600
400
200
0
V/V
XX
750
500
~~
250
-40
-20
0
20
 = tX- tXX [ns]
1000
0.46
0
40
-40
600
-20
750
500
0
20
 = tX- tXX [ns]
V/H
0.36
Counts
Counts
Energia
1000
Counts
Counts
800
5.20
1250
V
40
H
1
 1  1 
2
AES
H/V
X
1
 1  1 
2
400
~~
200
V
H
250
0
-40
-20
0
20
 = tX- tXX [ns]
40
0
-40
-20
0
20
 = tX- tXX [ns]
40
• Brak splątania fotonów w kaskadzie XX-X
• Dodatnia korelacja zgodnych polaryzacji liniowych fotonów w kaskadzie
• Czas rozpraszania spinu X: TX ~ 3.4  0.6 ns
pusta
kropka
Normalized counts in peak
(No) entanglement test
6
H/H : 5.24
V/V : 5.20
H/V : 0.36
V/H : 0.46
5
4
XX
3
V
2
H
1
0
-60
-40
6
Normalized counts in peak
B=0
-20
0
20
 = tX- tXX (ns)
40
60




5
4
1
 1  1 
2
X
AES
1
 1  1 
2
V
H
3
2
Conclusion: No
1
0
-60
CdTe/ZnTe QDs
entanglement, anisotropy
-40
-20
0
20
 = tX- tXX (ns)
40
60
governs the polarization of
the emission
Classical polarization correlation of the photons in the XX-X cascade
Obstacle: anisotropy - solutions
•
•
•
•
Find QD with Δ≈0
Tune splitting to zero
Erase which‐path information with narrow filter
Erase which‐path information by time reordering
Influence of the in-plane electric field
on the photoluminescence of individual QDs
InAs/GaAs Quantum Dots
Kowalik et al., APL’2005
Evolution of
the anisotropy
exchange
splitting with
the
applied
voltage
Kowalik et al., APL’2005
Influence of the in-plane magnetic field
on the photoluminescence of individual QDs
• model
• experiment
 -PL
Angle Jf [rad]
B=0
AES [meV]
1.8904
1.891
Energy [eV]
[meV]
0.45
p
2
0
0.18
0.14
0
0
2
4
6
8
Magnetic Field [T]
10
0.10
0
2
4
Magnetic field [T]
6
Increase or decrease of the anisotropy
splitting, depending on the magnetic field
direction
K. Kowalik et al., PRB 2007
Polarization sensitive
photoluminescence
  27  eV



Technion – Israel Institute of
Technology, Physics
Department and Solid State
Spectral
diffusion!!
Polarization density matrix
without spectral projection
Technion – Israel Institute of
Technology, Physics
Department and Solid State
Spectral projection – Elimination of the ‘which
path’ Information.
Photons from
both decay
paths
Technion – Israel Institute of
Technology, Physics
Department and Solid State
Spectral
| A (, ) | filtering
| AH (, ) |2
2
V
Δ = 27μeV
Γ = 1.6μeV
*
Relative Number of
photon pairs
N,γ
AH AV
N
Off diagonal matrix element
Technion – Israel Institute of
Technology, Physics
Department and Solid State

(| AH |  | AV | )d 
2
2
spectral  window
1
*
g
AH AV d

N spectral window
Densitymatrix
matrix–– spectral
spectral window
μeVμeV
Density
windowofof25200
(closed
slits)
(open slits)
Technion – Israel Institute of
Technology, Physics
Department and Solid State
Density matrix – spectral window of 25 μeV
(closed slits)
γ = 0.18 ± 0.05
2 1 + 4 γ = 2.13 ± 0.07 > 2
2
Bell inequality violation
Technion – Israel Institute of
Technology, Physics
Department and Solid State
QD in a pillar molecule:
an ultrabright source of entangled photons
10 m
5 m
QD as an entangled photons source
The idea: obtain polarization entangled photon pairs from biexciton-exciton cascade
Main obstacle: anisostropy of the QD  exciton level splitting
Hindrance: low collection efficiency (a few %)
Energy
XX
X
Ground state
The solution: coupling of the X and XX to the modes of the photonic molecule
 When exciton level homogeneous linewidth larger than exciton anisotropy
splitting: polarization entangled photons emitted in XX-X cascade
 Increased extraction efficiency due to photon funneling into cavity mode
QD as an entangled photons source
PL Intensity (arb. units)
Distance
R
R
1.315
E - controlled by pillar radius
DE – controlled by pillar distance
Radius D = 1 µm
Distance CC’= 0.7µm
DE
E
1.320
1.325
1.330
Energy (eV)
1.335
QD as an entangled photons source
XX
E
X
E
Ground state
PL Intensity (arb. units)
Distance
R
R
1.315
E - controlled by pillar Radius
E – controlled by pillar Distance
Radius = 1 µm
Distance = 0.7 µm
E
E
1.320
1.325
1.330
Energy (eV)
1.335
Pillar molecules
R
Distance
PL Intensity (arb. units)
1.326
1,325
Energy (eV)
Electronic lithography
1,330
1,335
Energy (eV)
1,320
Radius
1,315
1.325
1.324
1.323
1.322
1.321
1.320
0.7
0.8
0.9
1.0
Radius
Distance (µm)
Distance
R = 2 µm
1.1
Pillar molecules
R
Distance
PL Intensity (arb. units)
1.326
1,325
Energy (eV)
Electronic lithography
1,330
1,335
Energy (eV)
1,320
Radius
1,315
1.325
1.324
1.323
1.322
1.321
1.320
0.7
0.8
0.9
1.0
Radius
Distance (µm)
R = 1.75 µm
Distance
R = 2 µm
1.1
Pillar molecules
R
Distance
PL Intensity (arb. units)
1.326
1,325
Energy (eV)
Electronic lithography
1,330
1,335
Energy (eV)
1,320
Radius
1,315
1.325
1.324
1.323
1.322
1.321
1.320
0.7
0.8
0.9
1.0
Distance (µm)
Radius
R = 1.5 µm
R = 1.75 µm
Distance
R = 2 µm
1.1
Pillar molecules
R
Distance
PL Intensity (arb. units)
1.326
1,325
Energy (eV)
Electronic lithography
1,330
1,335
Energy (eV)
1,320
Radius
1,315
1.325
1.324
1.323
1.322
1.321
1.320
0.7
0.8
0.9
1.0
Distance (µm)
R = 1.25 µm
Radius
R = 1.5 µm
R = 1.75 µm
Distance
R = 2 µm
1.1
Pillar molecules
R
1,315
1,320
1,325
Energy (eV)
Radius
Electronic lithography
Distance
1,330
1,335
Photon Energy (meV)
PL Intensity (arb. units)
Distance
Experimental realization
 Purcell effect evidenced on X and XX transitions
 The proof of entanglement:
polarization resolved second order XX-X crosscorrelations
A. Dousse, at al. Nature 2010
Characterization of the source - entanglement
Density matrix of the twophoton state
 67 % degree of entanglement
 Entanglement criteria fullfilled
Characterization of the source - brightness
 Increased photon collection/extraction efficiency (~30 %)
 10 MHz rate of entangled photon pairs collected on the first lens