1. Quantum Dots in Photonic Structures
Lecture 13: Entangled photons from QD
Jan Suffczyński
Wednesdays, 17.00, SDT
Projekt Fizyka Plus nr POKL /11 współfinansowany przez Unię Europejską ze środków Europejskiego
Funduszu Społecznego w ramach Programu Operacyjnego Kapitał Ludzki

2. 3. Entangled photons from a single semiconductor QD
Plan for today
Reminder 2.
Entanglement
3. Entangled photons from a single semiconductor QD

3. Correlation function
represents probability of detection of the second photon at time t + , given that the first one was detected at time t

4.  = t2 – t1 t1 = 0 t2 = 20 Karta do pomiaru korelacji
Od źródła fotonów
Karta do pomiaru korelacji
 = t2 – t1
Dioda „STOP”
Liczba skorelowanych zliczeń n()
Dioda
„START”
t1 = 0
wejście
STOP
t2 = 20
wejście
START

5. Correlation function Thermal light source: Coherent light source (cw):
Thermal light source:
time t
Coherent light source (cw):
time t
Single photon source (cw):
time t T
time t
 = t2 – t1
Single photon source (pulsed):

6. Photon statistics Bose-Einstein distribution LASER
Poissonian distribution
LASER
Sub-poissonian distribution

7. Pojedyncze fotony z QD na żądanie
Autokorelacja emisji z ekscytonu neutralnego (X-X):
Od próbki X
STOP
START
Funkcja korelacji drugiego rzędu
STOP X
START
g( 2)(0) = = 1/13.6 X
Rejestrowane fotony pochodzą z pojedynczej kropki
czas 

8. X-CX cross-corelation

9. Single carrier capture
Three carriers capture
Single carrier capture
CX after X
X after CX
Single carrier capture
START
time
CX
 >0 ↔ X emission
after CX emission:
STOP X
<0 ↔ CX emission
after X emission:
START
time X
STOP
CX

10. XX-X crosscorrelation
START (H)
STOP (H)
START
STOP
XX X
time
XX-X cascade

11. Origin of the emission within the caviy mode
Energy PL
~15 meV
Cavity mode QD
~1 meV

12. Why is emission at the mode wavelength observed?
Quantum nature of a strongly coupled single quantum
dot–cavity system, Hennessy et al., Nature (2007):
Time (ns)
Autocorrelation M - M
Crosscorrelation QD - M
„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.”
Strong coupling in a single quantum
dot–semiconductor microcavity system, Reithmaier et al., Nature (2004)
Strong emission at the mode wavelength even for large QD-mode detunings

13. Dynamics of the emission of the coupled system
Pillar B, diameter = 2.3 mm,
gM = 0.45 meV, Q = 3000,
Purcell factor Fp= 8 X
T = 53 K
Energy
pillar B M
T = 53 K
pillar B
 X and M decay constants similar

14. Statistics on different micropillars
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
J. Suffczyński, PRL 2009

15. 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

16. Phonons - diatomic chain example

17. Solutions to the Normal Mode Eigenvalue Problem
ω(k) for the Diatomic Chain л / a 2 –л k w A B C
ω+ = Optic Modes
ω- = Acoustic Modes
There are two solutions for ω2 for each wavenumber k. That is, there are 2 branches to the “Phonon Dispersion Relation” for each k.

18. Transverse optic mode for the diatomic chain
The amplitude of vibration is strongly exaggerated!

19. Transverse acoustic mode for the diatomic chain

20. ↔ + = a* c* b* Interpretation of the single photon correlation results
Crosscorrelation M - X = (X+CX+XX) - X =
X-X + CX-X + XX-X
X-X
CX-X
XX-X 1 + a* b* c*
g(2) (t) t ↔ 1 =
M-X
Hennessy et al., Nature (2007)
 g(2)(0) ~ 0
 Asymmetry of the M-X correlation histogram
g(2) (t) t
t (ns)

21. Quantum Entangled photons from a semiconductor QD

22. Crystals can produce pairs of photons, heading in different directions
Crystals can produce pairs of photons, heading in different directions. These pairs always show the same polarization. ?

23. These are said to be entangled photons
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

25. 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

26. Niels Bohr and Einstein argued for 30 years about how to interpret quantum measurements like these.

27. 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.

28. Einstein felt that the filters were like a sieve
Einstein felt that the filters were like a sieve. The photons must contain characteristics that determine what they will do.

29. The information from the measurement of one can’t possibly fly instantaneously to its partner.

30. He referred to this as ‘spukhafte Fernwirkungen’
which is usually translated as ‘spooky action-at-a-distance’.

31. Then in 1964 John Bell devised a test.
He looked at what happens if the filters are in different orientations.

32. 2)Four entangled pairs of photons head toward two vertical polarizers.

33. If four make it through on the left, how many make it through on the right?
If four make it through on the left, four will make it through on the right.
In this situation, there is 100% agreement between the two photon groups.
The amount of agreement is the focus of Bell’s analysis.

34. 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)
b) The photon on the left is a vertical photon, so its entangled partner should be one too. The filter is 30 degrees away from vertical, so on average ¾ of the photons will get through.

35. 4) What percentage agreement do you expect on average? 0% 25% 75% 100%
b) There will be 75% agreement, therefore 25% disagreement.

36. 5) If the right filter is vertical and the left is placed at –30o, what agreement would you expect?
b) 25%
c) 75%
d) 100%
b) This situation is really the same as the previous one if you tilt your head by 30 degrees.

37. How much agreement is expected? 25% b)50% 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?
25% b)50% c)75% d)100%
c) Each shows 75% passing. In the left case, this results the minimum number of agreements, 50% match. In the right case, none match. Usually we’d get something in between the two possibilities.
Agreements could be from 50% to 100%.

38. 7) How much agreement does quantum mechanics predict
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%
d) They agree ½ x ½ = 25%

39. 7) How much agreement does quantum mechanics predict
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%
d) They agree ½ x ½ = 25%

40. 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%.
The results were conclusively in support of quantum mechanics, not Einstein.
The entanglement of photons has been demonstrated with the photons separated by over 20 km.
Somehow, measuring one photon, instantly affects its partner 20 km away.
Confirmation: Alain Aspect et al. 1983

41. Turning Interference On and Off
Two-slit Interference
Pattern
No Two-slit Interference
Pattern H V

42. “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.

43. 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

44. Entangled photons from a QD
The method: biexciton – exciton cascade
An obstacle:
anisotropy
Biexciton
Exciton
The energy carries the information on the polarization of the photon
Empty dot
(in circular polarization basis:)

45. X Xdark X Neutral exciton X Formed by: heavy hole and electron
Jz = ±3/2
Jz = ±1/2
4 possible spin states of X
Xdark X
Jz = -1
Jz = +1
Jz = -2
Jz = +2

46. Fine structure of neutral exciton
( + )/ 2 X
δ1~0.1meV
( – )/ 2 X
Anisotropic exchange
δ0~1meV
Isotropic exchange
( + )/ 2
δ2 ≈0
Xdark
( – )/ 2

47. (No) entanglement test
START (H)
STOP (H)
START
STOP
XX X
time
XX-X cascade

48. Kaskadowa emisja pary fotonów
Energia ~ XX V H
AES X V H
pusta kropka
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

49. (No) entanglement testH V
B = 0 XX
AES X
Conclusion: No entanglement, anisotropy governs the polarization of the emission
CdTe/ZnTe QDs
Classical polarization correlation of the photons in the XX-X cascade

50. 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

51. Influence of the in-plane electric field on the photoluminescence of individual QDs
Kowalik et al., APL’2005
InAs/GaAs Quantum Dots

52. Evolution of the anisotropy exchange splitting with the applied voltage
Kowalik et al., APL’2005

53. Influence of the in-plane magnetic field on the photoluminescence of individual QDs
Magnetic field [T]
AES [meV] 2 4 6
0.10
0.14
0.18
1.8904
1.891
Energy [eV]
m -PL
B=0
experiment
model 2 4 6 8 10
Magnetic Field [T]
[meV]
0.45 p
Angle J-2f [rad]
Increase or decrease of the anisotropy splitting, depending on the magnetic field direction
K. Kowalik et al., PRB 2007

55. Polarization sensitive photoluminescence
Spectral diffusion!!
Technion – Israel Institute of Technology, Physics Department and Solid State Institute

56. Polarization density matrix without spectral projection
Technion – Israel Institute of Technology, Physics Department and Solid State Institute

57. Spectral projection – Elimination of the ‘which path’ Information.
Photons from both decay paths
Technion – Israel Institute of Technology, Physics Department and Solid State Institute

58. Off diagonal matrix element
Spectral filtering
N,γ
Relative Number of
photon pairs
Off diagonal matrix element
Technion – Israel Institute of Technology, Physics Department and Solid State Institute

59. Density matrix – spectral window of 25 μeV (closed slits)
Density matrix – spectral window of 200 μeV (open slits)
Technion – Israel Institute of Technology, Physics Department and Solid State Institute

60. Density matrix – spectral window of 25 μeV (closed slits)
Bell inequality violation
Technion – Israel Institute of Technology, Physics Department and Solid State Institute

64. QD in a pillar molecule:
an ultrabright source of entangled photons
10 mm
5 mm

65. 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

66. QD as an entangled photons source
Distance R R
Radius D = 1 µm
Distance CC’= 0.7µm
PL Intensity (arb. units) DE E
A disk centered on the QD is exposed in the resist. The sample is moved by a distance CC’ and a
second disk is defined. The exposure time is adjusted to obtain the desired pillars diameter D.
1.315
1.320
1.325
1.330
1.335
Energy (eV)
E - controlled by pillar radius
DE – controlled by pillar distance

67. QD as an entangled photons source
Distance R R
Radius = 1 µm XX
Distance = 0.7 µm DE
PL Intensity (arb. units) DE X E E
A disk centered on the QD is exposed in the resist. The sample is moved by a distance CC’ and a
second disk is defined. The exposure time is adjusted to obtain the desired pillars diameter D.
Ground state
1.315
1.320
1.325
1.330
1.335
Energy (eV)
E - controlled by pillar Radius
DE – controlled by pillar Distance

68. Pillar molecules Radius R Distance Electronic lithography R = 2 µm
1,315
1,320
1,325
1,330
1,335
PL Intensity (arb. units)
Energy (eV)
Radius
Electronic lithography
Radius
Distance
R = 2 µm

69. Pillar molecules Radius R Distance Electronic lithography R = 1.75 µm
1,315
1,320
1,325
1,330
1,335
PL Intensity (arb. units)
Energy (eV)
Radius
Electronic lithography
Radius
R = 1.75 µm
Distance
R = 2 µm

70. Pillar molecules Radius R Distance Electronic lithography R = 1.5 µm
1,315
1,320
1,325
1,330
1,335
PL Intensity (arb. units)
Energy (eV)
Radius
Electronic lithography
Radius
R = 1.5 µm
R = 1.75 µm
Distance
R = 2 µm

71. Pillar molecules Radius R Distance Electronic lithography R = 1.25 µm
1,315
1,320
1,325
1,330
1,335
PL Intensity (arb. units)
Energy (eV)
Radius
Electronic lithography
R = 1.25 µm
Radius
R = 1.5 µm
R = 1.75 µm
Distance
R = 2 µm

72. Pillar molecules Photon Energy (meV) R Distance Electronic lithography
1,315
1,320
1,325
1,330
1,335
PL Intensity (arb. units)
Energy (eV)
Electronic lithography
Radius
Distance

73. 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

74. Characterization of the source - entanglement
Density matrix of the two-photon state
 67 % degree of entanglement
 Entanglement criteria fullfilled

75. Characterization of the source - brightness
Jaka wydajnosc : 10 MHZ do 80 MHZ
 Increased photon collection/extraction efficiency (~30 %)
 10 MHz rate of entangled photon pairs collected on the first lens