1. Technion – Israel Institute of Technology, Physics Department and Solid State Institute Entangled Photon Pairs from Semiconductor Quantum Dots Nikolay Akopian, Eilon Poem and David Gershoni The Solid State Institute and the Physics Department, Technion, Haifa 32000, Israel Netanel Lindner, Yoav Berlatzky and Joseph Avron The Physics Department, Technion, Haifa 32000, Israel Brian Gerardot and Pierre Petroff Materials Department, UCSB, CA 93106, USA

2. Technion – Israel Institute of Technology, Physics Department and Solid State Institute Outline Motivation: deterministic sources for entangled photons. Entanglement. Radiative cascades in semiconductor quantum dots. Entanglement by spectral projection. Why does it work in spite of inhomogeneous broadening. Conclusion: semiconductor quantum dots are practical sources for entangled photons on demand.

3. Technion – Israel Institute of Technology, Physics Department and Solid State Institute Motivation Entanglement is an essential resource of quantum information processing. Entangled photons are particularly attractive due to their non interacting nature, and the ease with which they can be manipulated. Quantum computing, quantum communication require “Event ready” entangled photon pairs. Therefore, deterministic sources of entangled photons are needed.

4. Technion – Israel Institute of Technology, Physics Department and Solid State Institute Entanglement Systems A and B, Hilbert space The combined state is not entangled (seperable) if

5. Technion – Israel Institute of Technology, Physics Department and Solid State Institute AliceBob i (not) Entanglement

6. Technion – Israel Institute of Technology, Physics Department and Solid State Institute Entanglement How can we tell if a general state is entangled? For two qubits, we have the Peres criterion: is entangled iff its partial transposition satisfies A. Peres, Phys. Rev. Lett. 77, 1413, 1996.

7. Technion – Israel Institute of Technology, Physics Department and Solid State Institute Example The state gives the density matrix The partial transpose gives a non –positive matrix

8. Technion – Israel Institute of Technology, Physics Department and Solid State Institute Strain induced Self assembled Quantum Dots 3D confinement of charge carriers with discrete spectrum of spin degenerate energy levels.

9. Technion – Israel Institute of Technology, Physics Department and Solid State Institute Single semiconductor quantum dot Off resonance excitation emission due to radiative recombination h S P P S

10. Technion – Israel Institute of Technology, Physics Department and Solid State Institute Right circular polarization S shell 2 e - Left circular polarization S shell 2 h + Entangled photon pairs from radiative cascades

11. Technion – Israel Institute of Technology, Physics Department and Solid State Institute Suggestion: Benson Yamamoto et al PRL 2000 Bi-exiton radiative casacade Isotropic QDAnisotropic QD RL LR

12. Technion – Israel Institute of Technology, Physics Department and Solid State Institute The anisotropic e-h exchange interaction The photon’s energy indicates the decay path No entanglement Classical correlations only HV H V + -

13. Technion – Israel Institute of Technology, Physics Department and Solid State Institute Polarization Momentum wave function Environment HH HV VH VV Reduced Density Matrix For Polarization

14. Technion – Israel Institute of Technology, Physics Department and Solid State Institute Maximal Bell inequality violation: M. Horodecki et. al., Phys. Lett. A 223,1 (1996) Peres criterion for entanglement: HH HV VH VV

15. Technion – Israel Institute of Technology, Physics Department and Solid State Institute Two photon polarization density matrix: In our case In our case : However, we can still make a measurement on the wave packet However, we can still make a measurement on the wave packet :

16. Technion – Israel Institute of Technology, Physics Department and Solid State Institute The experimental setup Nika Akopian

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

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

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

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

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

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

23. Technion – Israel Institute of Technology, Physics Department and Solid State Institute Is there any ‘which path’ information left in the degrees of freedom of the QD’s environment ? No remnant ‘which path’ witness in the enviroenment of the QD!!

24. Technion – Israel Institute of Technology, Physics Department and Solid State Institute Spectral Filtering in the presence of inhomogeneous broadening Energy of XX photon (1) Energy of X photon (2) Energy conservation

25. Technion – Israel Institute of Technology, Physics Department and Solid State Institute Spectral Filtering in the presence of inhomogeneous broadening

26. Technion – Israel Institute of Technology, Physics Department and Solid State Institute Conclusions: First demonstration of entangled photon pairs from the radiative cascade in SCQDs. No other “which path” information in the environment. Deterministic entangled photon pair devices based on SCQD are thus possible provided is increased such that no spectral filtering is needed. Akopian et al, Phys. Rev. Lett. 96, 130501 (2006) Lindner et al, quant-ph/0601200.

27. Technion – Israel Institute of Technology, Physics Department and Solid State Institute Intensity Cross--Correlation Function : D1 D2 correlator I i (t 2 ) I j (t 1 ) PL Energy I(t) - Intensity Second order Intensity Correlation Function. j i MC conditional probability of detecting photon from line j at time (t+  ) after photon from line i had been detected at time (t)

28. Technion – Israel Institute of Technology, Physics Department and Solid State Institute Polarization Sensitive Intensity Cross- Correlation Measurements Decay time of 0.8 nsec Γ=1.6μeV Time (nsec) number of correlated radiative cascades

29. Technion – Israel Institute of Technology, Physics Department and Solid State Institute Polarization Tomography Spectral window 200 μeV

30. Technion – Israel Institute of Technology, Physics Department and Solid State Institute 1.5 ns window no subtraction of events from distinct cascades! Largest negative eigenvalue of the partially transposed matrix:

31. Technion – Israel Institute of Technology, Physics Department and Solid State Institute 0.6 ns window no subtraction of events from distinct cascades! Largest negative eigenvalue of the partially transposed matrix:

32. Technion – Israel Institute of Technology, Physics Department and Solid State Institute 1.5 ns temporal window no subtraction of events from distinct cascades!

33. Technion – Israel Institute of Technology, Physics Department and Solid State Institute 0.6 ns temporal window no subtraction of events from distinct cascades!

34. Technion – Israel Institute of Technology, Physics Department and Solid State Institute Polarization Tomography Spectral window 25 μeV