Schemes to generate entangled photon pairs via spontaneous parametric down conversion

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1 Schemes to generate entangled photon pairs via spontaneous parametric down conversion Atsushi Yabushita Department of Electrophysics National Chiao-Tung University?

2 Outline Introduction Optical parametric processes Opt. param. amplifier (OPA) Spontaneous param. down conv. (SPDC) Application classical Broadband generation for short pulse Application quantum Entangled photon pairs Ghost imaging wave vector Ghost spectroscopy frequency Quantum key distribution (QKD) polarization Multiplex QKD polarization and frequency Entangled photon beam Conclusion Our work

3 Outline Introduction Optical parametric processes Opt. param. amplifier (OPA) Spontaneous param. down conv. (SPDC) Application classical Broadband generation for short pulse Application quantum Entangled photon pairs Ghost imaging wave vector Ghost spectroscopy frequency Quantum key distribution (QKD) polarization Multiplex QKD polarization and frequency Entangled photon beam Conclusion Our work

4 Outline Introduction OPA and SPDC Light is Light-matter interaction Frequency conversion SG and SPDC SPDCOPA OPA is? Why OPA? Why SPDC?

5 Introduction Light gamma-ray X-ray Ultraviolet visible infrared radio wave => Electro-magnetic wave

vertical direction E : exp(-it) E*E : exp(-i2t) Second harmonic

6 Introduction Light-matter interaction Electric field make dielectric polarization Emission from dipole oscillating in vertical direction E : exp(-it) E*E : exp(-i2t) Second harmonic generation (SG) using a non-linear crystal within some limitation from physical law

7 Introduction BBO crystal -BaB 2 O 4 energy / momentum conservation in frequency mixing k 2, k 1,

8 Introduction SG (second harmonic generation) 2 Reversible? YES! Reverse process spontaneous parametric down conversion (SPDC) occur by itself 2=>+ 2=> =>+

vacuum noise (no seed for signal) pump idler process difference frequency

9 Introduction ow does SPDC occur? similar as OPA (optical parametric amplification) signal SPDC starts with vacuum noise (no seed for signal) pump idler process difference frequency generation h pump -h signal =h idler Energy conservation h pump =h signal +h idler #signal=#idler quite low efficiency ~10-10

10 Introduction Why SPDC? low conversion efficiency interesting character of entanglement never broken security quantum communication easy to transfer via optical fiber Other method? singlet (a pair of spin ½ particle)

11 Introduction OPA (optical parametric amplification) what is OPA? similar as SPDC, much higher efficiency pump Signal (amplified) pump seed w/o amp signal amplified seed idler process difference frequency generation h pump -h signal =h idler Energy conservation h pump =h signal +h idler

12 Introduction Why OPA? complicated setup intense laser at different wavelength non-linear spectroscopy in U/visible/IR (ultrafast spectroscopy, Raman for vibration study, ) Other method? self phase modulation (SPM) low efficiency 3 intensity (arb. units) w a v e le n g th ( nm )

13 Outline Introduction Optical parametric processes Opt. param. amplifier (OPA) Spontaneous param. down conv. (SPDC) Application classical Broadband generation for short pulse Application quantum Entangled photon pairs Ghost imaging wave vector Ghost spectroscopy frequency Quantum key distribution (QKD) polarization Multiplex QKD polarization and frequency Entangled photon beam Conclusion Our work

14 Application classical Broadband generation for short pulse 1 Shorter pulse needs broader spectrum

15 Application classical Broadband generation for short pulse Optical parametric amplifier (OPA) Non-collinear OPA (NOPA) nondegenerate degenerate

$diffracted by$

16 Application classical Broadband generation for short pulse WLC pulse width=~9fs OPA (OPG with WLC) Spectrum diffracted by grating isible broadband

17 Outline Introduction Optical parametric processes Opt. param. amplifier (OPA) Spontaneous param. down conv. (SPDC) Application classical Broadband generation for short pulse Application quantum Entangled photon pairs Ghost imaging wave vector Ghost spectroscopy frequency Quantum key distribution (QKD) polarization Multiplex QKD polarization and frequency Entangled photon beam Conclusion Our work

18 Application quantum SPDC generates photon pairs (low efficiency) p, k p s, k s NLC correlated parameters i, k i (1) wave vector : k p = k s + k i (2) frequency p s i (3) polarization (in case of Type-II crystal) 1 2 s i s i

19 Application quantum So, what is entanglement? Let s remind Young s double slit photon comes one by one if you block one of the slits Interference only in unknown case path entanglement Interference of probability, wavefunction different from statistics of classical phenomena=quantum Are there any other entanglements? Yes, we will see them in the following pages!

20 Application quantum quantum lithography wave vector better resolution ( than classical limit ) ~ p = Schematic set-up Y. Shih, J. Mod. Opt. 49, 2275 (2002) SPDC photon pairs v.s. classical light half! cos 2 [(2b / 2) ] (Young s : )

21 Experimental result (quantum lithograph) quantum classical

22 Application quantum ghost imaging wave vector BBO coincidence count CC1 CC2 CC3 CC1 CC2 CC3

23 Application quantum ghost imaging wave vector BBO coincidence count CC1 CC2 CC3 CC1 CC2 CC3

24 Application quantum ghost imaging measure the shape of an object Detector does NOT scan after object classical s, k s p, k p NLC i, k i Y. Shih, J. Mod. Opt. 49, 2275 (2002)

25 Application quantum ghost spectroscopy frequency BBO coincidence count CC1 CC2 CC3 CC1 CC2 CC3

26 Application quantum ghost spectroscopy frequency BBO coincidence count CC1 CC2 CC3 CC1 CC2 CC3

27 experiment setup BBO : non-linear crystal M1 : parabolic mirror M2,3 : plane mirror P1 : prism (remove pump) P2 : prism (compensate angular dispersion) PBS : polarizing beam splitter G : diffraction grating L2,3 : fiber coupling lens OF : optical fiber SPCM : single photon counting module TAC : time-to-amplitude converter Delay : delay module PC : computer S : sample L1 : focusing lens (f=100mm, 8mm)

28 Spectrum of photon pairs and absorption spectrum of the sample pump focusing lens (f=100mm) 1. Broadband photon pairs more absorption in longer wavelength

29 result : absorption spectrum 1. Broadband photon pairs calculate absorption spectrum from the ratio agree with the result by a spectrometer

30 result : absorption spectrum 1. Broadband photon pairs agree with the result by a spectrometer

31 summary of this section 1. Broadband photon pairs spectrum of SPDC photon pairs spherical lens objective lens (f=100 8mm) spectrum was broadened (11,1163,69nm) Nd 3+ -doped glass ( in the idler light path) coincidence resolving signal light s frequency absorption spectrum was measured fit well with the result measured by a spectrometer without resolving the frequency of photon transmitted through the sample A. Yabushita et. al., Phys. Rev. A 69, (2004)

32 Outline Introduction Optical parametric processes Opt. param. amplifier (OPA) Spontaneous param. down conv. (SPDC) Application classical Broadband generation for short pulse Application quantum Entangled photon pairs Ghost imaging wave vector Ghost spectroscopy frequency Quantum key distribution (QKD) polarization Multiplex QKD polarization and frequency Entangled photon beam Conclusion Our work

33 Application quantum Outline for Quantum Key Distribution (QKD) BB84 protocol single photon how it works can it be safe? E91 protocol polarization entangled photon pair polarization entanglement? how it works can it be safe?

34 Application quantum BB84 protocol single photon Purpose : to share a secret key how it works? key at random base at random base at random

35 Application quantum 50% of keys can be shared (shared keys are same) BB84 protocol single photon complicated But secure! Purpose : to share a secret key ow can it be secure?? how it works? key at random base at random base at random

36 Application quantum BB84 protocol single photon Can it be secure? key at random base at random base? (random try) + + result (bit) copy base at random

key at random 0 1 0 1 1 0 base at random + + + + base?

37 Application quantum BB84 protocol single photon Can it be secure? key at random base at random base? (random try) + + result (bit) copy Security can be checked! base at random Error!

38 EPR-Bell source Alice Bob 1. Broadband photon pairs polarization-entangled photon pairs

39 Mixed state (statistical mixture) and (50%-50%) Alice Bob 1. Broadband photon pairs??

40 QKD example (without Eve) Alice Base select EPR-pair Base select Bob If they use the same base, 0 100% correlation (quantum key distributed!) R L L R

41 QKD example (with Eve) Alice Base select EPR-pair Base select Bob? base/ get/ copy Eve also share the key (NOT secure QKD ) ow can it be improved?

42 Ekert91 protocol Alice Base select EPR-pair Base select Bob Base information L (classical communication) R L 100% correlation R R L R L

43 Ekert91 protocol Alice Base select EPR-pair Base select Bob Base information base/ get/ copy 0 R 1 L 0 R L 0 Bob can 0 R detect Eve L (secure!) 1 L 1 R 1 R L L R OK 0 1 OK L 0 R 1 0 L 0 R 0 OK 1 NG!

44 Experimental example of QKD T. Jennewein et. al., PRL 84, 4729 (2000)

45 Outline Introduction Optical parametric processes Opt. param. amplifier (OPA) Spontaneous param. down conv. (SPDC) Application classical Broadband generation for short pulse Application quantum Entangled photon pairs Ghost imaging wave vector Ghost spectroscopy frequency Quantum key distribution (QKD) polarization Multiplex QKD polarization and frequency Entangled photon beam Conclusion Our work

46 Generation of photon pairs entangled in their frequencies and polarizations (for WDM-QKD) 2 e BBO (type-ii) o/e e/o frequency-entangled polarization-entangled polarization-entangled pair at many wavelength combinations light source for WDM-QKD

47 Standard : e o/e polarization-entangled Multiplex : e o/e o/e o/e polarization-entangled polarization-entangled polarization-entangled

$experimental setup L1 : focusing lens BBO : non-linear crystal M1 : parabolic mirror M2,3 : plane mirror P1 : prism (remove pump) P2 : prism (compensate angular dispersion) G : diffraction grating$

48 experimental setup L1 : focusing lens BBO : non-linear crystal M1 : parabolic mirror M2,3 : plane mirror P1 : prism (remove pump) P2 : prism (compensate angular dispersion) G : diffraction grating L2,3 : fiber coupling lens OF : optical fiber SPCM : single photon counting module TAC : time-to-amplitude converter Delay : delay module PC : computer IRIS : iris diaphragms BS : non-polarizing beam splitter POL1,2 : linear polarizer

49 simulation f=1 =0 o coincidence counts (arb. units) i (degree) f=1 =60 o s i f e 45 o 0 o 135 o 0o 90 o coincidence counts (arb. units) Broadband photon pairs 45 o i 90 o s i (degree) 135 o i 1 3 f=1 =180 o coincidence counts (arb. units) o 0 o 45 o f=1.732 =0 o coincidence counts (arb. units) o 0 o 135 o 90 o i (degree) 90 o i (degree)

50 1. Broadband photon pairs polarization correlation (1 st 0 o s i f e i s i 45 o 135 o phase shift (866nm) < phase shift (870nm) 90 o f visibility < 100% o 0,180

51 polarization correlation (1 st 0 o s i f e i s i 45 o 135 o visibility relative phase 0 o o 45 o o 135 o o 90 o o phase shift (866nm) < phase shift (870nm) visibility<100% f 1.7 o 0,180 1

52 no entanglement iris open entangled iris 1mm phase shift (866nm) < phase shift (870nm) f but phase shift<45 o visibility<100% (866nm, 870nm) to improve : walk-off compensation o 0,180 to improve : group velocity compensation frequency resolved photon pairs are entangled in polarization (light source for WDM-QKD) future : compensations of walk-off and group velocity (improve pol-entanglement) A. Yabushita et. al, J. Appl. Phys., 99, (2006)

53 Outline Introduction Optical parametric processes Opt. param. amplifier (OPA) Spontaneous param. down conv. (SPDC) Application classical Broadband generation for short pulse Application quantum Entangled photon pairs Ghost imaging wave vector Ghost spectroscopy frequency Quantum key distribution (QKD) polarization Multiplex QKD polarization and frequency Entangled photon beam Conclusion Our work

54 Beam-like photon pair generation for 2photon interference & polarization entanglement

Luo) Department of Electrophysics, National Ch

55 Department of Physics, NTU (Prof. A. Yabushita) Department of Electrophysics, National Chiao Tung University (Prof. C. W. Luo) Department of Electrophysics, National Chiao Tung University (Prof. P. C. Chen) Department of Physics, Nation Tsing ua University (Prof. T. Kobayashi) Department of Applied Physics and Chemistry and Institute for Laser Science The University of Electro-Communications, Tokyo, Japan

56 Acknowledgement for $upport MOE ATU plan, Taiwan, ROC. National Science Council, Taiwan, ROC. NSC M MY3, NSC M MY3

57 SPDC photon image Beam-like photon pair : orizontal : vertical 1 [ Polarization Entangled photon pair 2 ] Crystal optic axis

58 Main idea (2photon interference) 1 l P1 P1 BBO B B O l S1 S1 l I1 I1 l 1 FC S pump l 1 L FC I l P2 P2 BBO l S2 S2 FC S 2 l I2 I2 l 2 l 2 FC I

59 Main idea (polarization entanglement) ] ) (e [ e i 2 1 i ] [ /4 /4 adjust phase

60 OM interference measurement (adjust path length) WP Pol. QWP 600 L1 L3 Coincidence counts (1/s) Delay (m)

61 2photon interference by photon pair beams 400nm (/2) classical lithography resolution~ 2-photon interference (quantum lithography) 2 times higher resolution

62 polarization entanglement by photon pair beams rotate polarization 90 degrees by QWP plates 1 > 1 >+e i 2 > 2 > 1 > 1 >+e i 2 > 2 > (max entangle at =n ) measure coincidence scanning visibility = (highly entangled)

63 Our new scheme to generate photon pair beams for two purposes two-photon interference polarization entanglement Our new scheme resolution of 2-photon interference () 2 times higher than classical limit () all photon pairs can be polarization entangled efficient generation of polarization entangled pairs cf.) traditional method : only crossing points of light cones sin-pin Lo et al., Beamlike photon-pair generation for two-photon interference and polarization entanglement, Phys. Rev. A 83, (2011)

64 You can find more detail information in this paper.

65 Summary Introduction Optical parametric processes Opt. param. amplifier (OPA) Spontaneous param. down conv. (SPDC) Application classical Broadband generation for short pulse Application quantum Entangled photon pairs Ghost imaging wave vector Ghost spectroscopy frequency Quantum key distribution (QKD) polarization Multiplex QKD polarization and frequency Entangled photon beam on-going in National Chiao-Tung University Our work

66 Thank you for your attention!

Beamlike photo-pair generation by femtosecond pulse laser

Beamlike photo-pair generation by femtosecon pulse laser Chih-Wei Luo ( 羅志偉 ) Department of Electrophysics National Chiao Tung University, Taiwan Ultrafast Dynamics Lab March, 0 in NTHU Acknowlegements