Quantum Dots in Photonic Structures

1. Lecture 12: Single photoncorrelations and cavitymodeemission 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. Photonemission statistics 3. Origin of the emission with the cavitymode

3. In resonance: Energy Rabbi SplittingDR (|0,1>|1,0>)/ (|0,1>+|1,0>)/ Eigenstates : Entengledstatesemitter-photon 2 2 ↔ |0,1> |1,0> Oscillations with Rabifrequency = R / h Strongcoupling –Rabisplitting Out of the resonence: |1,0> : Emptycavity Excited emitter |0,1> : Photon insidecavity Emitter in groundstate

4. Weak vs strongcoupling Out of the cavity

5. Strongcoupling regime Energylevels versus detuning: QD– Cavitymodedetuning • At resonanceQD- Cavitymode: anticrossingof the levels! Rabisplitting:

6. Weakcoupling vs strongcoupling Anticrossing/ no anticrossing Exchange of linewidths/ no lw exchange Equalintensityatresonance/ X intensityincreasedatresonance Reithmaieret al., Nature (2004)

7. Correlation Correlation (lat. correlation-, correlatio, from com-, „together, jointly”; and relation-, relatio, „link, relation” Correlations macro in the world:

8. Correlations

9. Correlations

10. Correlations

11. Korelacje A statisticaleffect!

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

13. Idea pomiaru korelacji między pojedynczymi fotonami Od źródła fotonów Dioda „STOP” Dioda „START” n( = tSTOP- tSTART)

14.  = 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

15.  = t2 – t1 t2 = 0 t1 = 0, Od źródła fotonów Karta do pomiaru korelacji Dioda „STOP” Skorelowanych zliczeń n() Dioda „START” wejście STOP wejście START

16. 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

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

18. h Single photon sources • single atoms • single molecules • single nanocrystals • NV in diamond

19. single semiconductor quantum dots • highly efficient • work with high repetition rates • excited optically / electrically • easy to integrate with electronics • + more … (Koenraad et al.)

20. 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 

21. X-CX cross-corelation

22.  >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:

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

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

25. 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

26. T = 10 K CX XX in resonanse with the Mode Photon Energy (meV) X T = 40 K CX M Photon Energy (meV) XX X Dynamics of the QD emission – Purcell efect Pillar A (diameter = 1.7mm, gM = 1.08 meV, Q = 1250, Purcell factor Fp= 7.2 tXX = 140 ps when XX in resonanse with the mode - Purcell efect

27. Dynamics of the emission of the coupled system WhenXX-M detuningincreases Purcell efectdecreases XX decaylonger Above T = 45 K – 50 K carrier lifetime in wetting layer increases  excitonic decay gets longer pillar A • Emission dynamics at mode wavelength the same as XX emission dynamics !

28. 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

29. Dynamics of the emission of the coupled system Temperatura (K) • X emissionintensityincreaseswhen X-M detuningdecreases: Evidence for Purcell effect 44 • T> 45 K : Shortening of the X lifetimewith decreasing X- M detuningimpossible to be observed  Purcell factordeterminationbasing on the emission dynamics not alwaysreliable pillar B Odstrojenie X - M (meV)  M i X decayconstantssimilar

30. Pillar A Exciton dynamics vs T, pillar A • BelowT=45 K temperaturedoes not affect the X emission dynamics. PL decaytimereflects exciton recombinationrate T< 45 K

31. Pillar A Exciton dynamics vs T, pillar A • Exciton emissiondecaylonger for T > 45 - 50 K • PL decaytimedoes not reflect exciton recombinationrate T> 45 K

32. 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

33. Dephasing rate : Naesby et al., Phys. Rev. A (2008) Influence of pure dephasing on emission spectra from single photon sources The role of QD state dephasing Pillar B, gM = 0.45 meV  Naesby et al.: effects of QD states dephasing responsible fort the emission at mode wavelength

34. 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

35. Phonons - diatomic chainexample M M M m m

36. 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.

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

38. Transverse acoustic mode for thediatomic chain

39. 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

40. XX-XX CX-CX X-X 1 1 1 1 +…= 0 0 0 XX-X CX-X CX-XX 0 ↔ 1 1 1 0 0 0 0 Time (ns)  g(2)(0) ≠ 0  Symmetry of the M-M correlation histogram Hennessy et al., Nature(2007) Interpretation of the single photon correlation results Autocorrelation M-M = 2*(X-X + CX-CX + XX-XX) + X-CX + CX-X + X-XX + X-XX + CX-XX + XX-CX: M-M M-M