1. Lecture 13: Entangledphotons from QD Quantum Dots in PhotonicStructures 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

2. Plan for today Reminder 2. Entanglement 3. Entangledphotons 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 Od źródła fotonów Karta do pomiaru korelacji Dioda „STOP” Liczba skorelowanych zliczeń n() Dioda „START” t1 = 0 wejście STOP t2 = 20 wejście START

5. Correlationfunction Thermal light source: 0 time t Coherent light source (cw): 0 time t Single photon source (cw): 0 time t Single photon source (pulsed): T T 0 time t  = t2 – t1

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

7. X START X STOP STOP X Pojedyncze fotony z QD na żądanie Autokorelacja emisji z ekscytonu neutralnego (X-X): Od próbki START X • g( 2)(0) = 0.073 = 1/13.6 • Rejestrowane fotony pochodzą z pojedynczej kropki czas 

8. X-CX cross-corelation

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

10. START STOP X XX time 0 XX-X crosscorrelation STOP (H) START (H) • XX-X cascade

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

12. Quantum nature of a strongly coupled single quantum dot–cavity system, Hennessy et al., Nature(2007): Crosscorrelation QD - M Autocorrelation M - M Time (ns) 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.” Why is emission at the mode wavelength observed? 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 T = 53 K X Energy M pillar B T = 53 K pillar B  X and M decay constants similar

14. Statistics on differentmicropillars • Strongcorrelationbetween exciton and Modedecayconstants • The same emitterresponsible for the emissionatboth (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 chainexample M M M m m

17. Solutions to the Normal Mode Eigenvalue Problem ω(k)for the Diatomic Chain w A B C ω+ = Optic Modes ω- = Acoustic Modes k –л / a 0 л / a 2 л / a There are two solutions forω2for 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 thediatomic chain

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

21. Quantum Entangledphotons from a semiconductor QD

22. ? 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. 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. 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? ?

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)

35. 4) What percentage agreement do you expect on average? • 0% • 25% • 75% • 100%

36. 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%

37. 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%

38. 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%

39. 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%

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%. Confirmation: Alain Aspect et al. 1983

41. Two-slitInterference Pattern No Two-slitInterference Pattern H V Turning InterferenceOn and Off

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. Biexciton Exciton Emptydot Enangledphotons from a QD The method: biexciton – excitoncascade Obstacle: anisotropy The energycarries the information on the polarization of the photon

44. Biexciton Exciton Emptydot Entangledphotons from a QD The method: biexciton – excitoncascade Anobstacle: anisotropy The energycarries the information on the polarization of the photon (in circularpolarizationbasis:)

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

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

47. START STOP X XX time 0 (No) entanglement test STOP (H) START (H) • XX-X cascade

48. ~ ~ ~ ~ Kaskadowa emisja pary fotonów Energia XX V H X AES H V pusta kropka • Brak splątaniafotonów w kaskadzie XX-X • Dodatniakorelacjazgodnych polaryzacjiliniowych fotonów w kaskadzie • Czas rozpraszania spinu X: TX ~ 3.4  0.6 ns

49. B = 0 XX H V X AES H V (No) entanglement test Conclusion: No entanglement, anisotropygoverns the polarization of the emission CdTe/ZnTeQDs Classicalpolarizationcorrelation of the photons in the XX-X cascade

50. Obstacle: anisotropy - solutions • Find QD with Δ≈0 • Tunesplitting to zero • Erase which‐path information with narrow filter • Erase which‐path information by time reordering