1. Parametric Down-conversion and other single photons sources December 2009 Assaf Halevy Course # 77740, Dr. Hagai Eisenberg 1

2. Outline: Single photon sources Parametric Down Conversion – inside look Entanglement from PDC 2

3. Number of photons in a typical laser beam 3 Each photon carries energy of For the energy is A laser beam with power of Emits How can we create single photons?

4. Atoms as a single photons source 4 Sodium atoms prepared as A two level system System contains few atoms in each given moment Laser frequency tuned to the Energy gap between levels Coincidence counts recorded As a function of time

5. 2 nd order correlation function 5 Antibunching demonstrated After each emission The atom has to be stimulated Again – low probability For two fold coincidence Experimental difficulty to Ensure only one photon Exists in the system

6. Imperfect diamond as a single photon source 6 Diamond is an allotrope of carbon In every diamond some of the carbons are replaced with Nitrogen and a lattice vacancy The Nitrogen-vacancy pairs are well located In random points of the lattice

7. Experimental results 7

8. 8 All measurements presented here were made on a single NV center! emission events recorded From the same center Key parameter – mean time between Excitations: Low power – lower excitation rate – the System is ready after each excitation to Emit a photon High power – bigger probability of the System to be in an intermediate level

9. Theoretical model 9 Three level system - Intermediate level necessary Saturation as a function of pump rate K 12

10. 10 Fluorescence from a single molecule Problem: molecules posses rotational and internal degrees of freedom, as well as electronic levels Solution: placing single Pentacene molecules in a p-Terphenyl lattice Pentacene – consists of 5 Benzene (C 6 H 6 ) rings

11. Experimental results 11

12. Quantum dot as a single photon source 12 Bulk semiconductors – band gap is fixed Energy levels in the valence and conduction bands are continuous Applying stimulus on the bulk can create excitons – electron hole pairs When the exciton decays – it emits a photon with the fixed band gap energy

13. Quantum confinement 13 De Broglie wavelength In bulk semiconductor is much smaller than crystal size When one or more dimension are at this scale the motion is quantized This behavior is called Quantum confinement

14. Quantum dot 14 Consists of tens of semiconductor atoms (up to 50 nm) Quantum confinement causes energy levels to be discrete Engineering the quantum dot structure allows control of the band gap Control over the emission spectrum

15. Experimental results 15 Finite response time Of the detector causes All events in the time Frame to up 0.5ns to Contribute to the value At causing

16. Linear optics – the classical description 16 Light frequency is fixed and cannot be changed Light cannot interact with light polarization- expresses the density of permanent or induced electric dipole moments in a dielectric material. Linear susceptibility To create new frequencies we need non-linear optics Parametric Down-Conversion - introduction

17. Non-linear optics 17 Polarization depends on higher powers of the Electric field Focus on the second order susceptibility: Applying a field of results in Nonlinear process New frequencies generated

18. Sum frequency generation  (2) 33 11 22 L 18       Classically – two wave mixing creates a wave with new frequency Quantum description: two photons are annihilated, while one is created

19. - k 1 – k 2 Δk=k 3 Wavevector mismatch Motivation for Δk = 0 Intensity of the resulting wave 19

20. Parametric Down-Conversion 20 Quantum description: One photon annihilates, two photons created Interaction Hamiltonian - We assume the non depleting pump approximation: PDC SHG Energy and momentum conservation:, is the polarization mode

21. Fock representation 21 Our input state is, represent the coherent pump beam First order approximation of the wave function: We get Or depends also on the interaction time with the crystal PDC output is linear with pump power

22. 22 Heralded single photon source from PDC Herald - One that gives a sign or indication of something to come Emission from a two level quantum system can produce Single photons which do not posses any preferred direction PDC process is a quantum phenomena in which two photons are emitted in Defined spatial modes Measurement of one photon ensures us his twin existence

23. 23 Detection of the signal photon in A triggers measurement in B for 20ns resulting in an integer m If m occurs N(m) times in N cycles then If every down-converted photon is detected (quantum efficiency 1) and no dark counts then In the experiment: Signal to noise ratio is 1/5 Quantum efficiency is small Defining the probability to produce n Idler photons

24. 24 Accounting for probability to detect m background Photons If is small for then also In this case we can invert the equation and get M Linear equations in

25. Methods for achieving phase matching condition 25 Temperature tuning: refractive index changes with temperature - LiNbO 3 Quasi phase-matching: Periodically poling of the nonlinearity - LiTaO 3 Angle tuning: the use of birefringence – BBO, BiBO Phase matching condition: Δk = 0

26. Normal materials In a degenerate collinear case : Impossible because of dispersion K Signal K Idler K Pump 26

27. Δk = 0 Achieved with Birefringence Index of refraction in anisotropic crystals depends on polarization  n e (2  )  = n e (  )  + n o (  ) possible! How to do it? 27

28. The index ellipsoid – a measure for crystal symmetry Ѳ Ф n slow n fast k pump nznz nxnx nyny For every propagation direction there are 2 normal modes of polarization Δk = 0 Achieved with Birefringence 28

29. PDC processes Collinear Non-Collinear Type I – PDC products posses same polarization Type II – PDC products posses orthogonal polarization 29 K Signal K Idler K Pump K Signal K Idler K Pump

30. Scheme of non-collinear type II PDC process Nonlinear crystal Pump beam H polarized V polarized Momentum and Energy conservation: 1 2 K Signal K Idler K Pump 30 Degenerate case - Signal and Idler with the same wavelength

31. Experimental setup Rep. rate – 76MHZ Pulse duration Low noise Camera Band pass filter Low pass filter Dichroic mirror Ti:Sapphire laser Crystal 31 Residual pump Why pulsed laser? 31 1. Knowledge of the arrival times of the down-converted photons within the pulse duration 2. Improved probability of higher order events Broadband spectrum of the pump beam and the PDC photons Pulsed laser drawback

32. Angular dependency in the pump beam propagation direction 32

33. Comparing simulation to experimental results with BBO 33 ExperimentSimulation

34. Polarization of the down-converted circles Vertical polarization Horizontal polarization 34

35. Quantum entanglement Separable state Entangled state Entangled photons states are essential for quantum optics experiments 35

36. Generated Wave function Polarization entangled state The photons are labeled by their spatial mode and their polarization 36 12

37. :References M. Fox, Quantum optics – An inroduction, Oxford university press (2006) H.J. Kimble et al., “Photon antibunching in resonance fluorescence”, Phys. Rev. Lett. 39, 691- 695 (1977) T. Basche et al., “Photon antibunching in the flouescence of a single dye molecule trapped in a solid”, Phys. Rev. Lett. 7, 1516-1519 (1992) K. Kurtseifer et al., “Stable solid-state source of single photons”, Phys. Rev. Lett 85 (2000) 290-293 P. Michler et al.,”A quantum dot single photon turnstile device, Science 290 2282-2285 (2000) (R.W Boyd, Nonlinear optics, 2 nd edition, Elsevier (2003 M. Rubin et al., “Theory of two-photon entanglement in type-II optical parametric down-conversion”, Phys. Rev. A 50 5122-5133 (1994) C. Hong and L. Mandel, “Experimental realization of a localized one-photon state”, Phys. Rev. Lett. 56, 58-60 (1986) P. G. Kwiat et al., “New high intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75, 4337-4341 (1995) 37