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Entangled photon pair generation by spontaneous parametric down conversion Atsushi Yabushita

Entangled photon pair generation by spontaneous parametric down conversion Atsushi Yabushita Department of Electrophysics National Chiao-Tung University. ?. Outline. Introduction Optical parametric processes Opt. param. amplifier (OPA) Spontaneous param. down conv. (SPDC)

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Entangled photon pair generation by spontaneous parametric down conversion Atsushi Yabushita

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  1. Entangled photon pair generation by 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 • SHG and SPDC • SPDCOPA • OPA is …? • Why OPA? • Why SPDC?

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

  6. Introduction Light-matter interaction Electric field make dielectric polarization Emission from dipole oscillating in vertical direction E : exp(-iwt) E*E : exp(-i2wt) Second harmonic generation (SHG) using a non-linear crystal within some limitation from physical law…

  7. BBO crystal b-BaB2O4 Introduction energy / momentum conservation in frequency mixing k2,w k1,w

  8. Introduction Reversible? YES! Reverse process spontaneous parametric down conversion (SPDC) occur by itself 2=>1+1 2=>0.8+1.2 2=>1+1

  9. seed | w/o amp Introduction How does SPDC occur? similar as OPA (optical parametric amplification) …what is OPA? Signal (amplified) signal | amplified pump pump seed idler process | difference frequency generation hnpump-hnsignal=hnidler Energy conservation hnpump=hnsignal+hnidler

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

  11. Introduction Why OPA? complicated setup intense laser at different wavelength non-linear spectroscopy in UV/visible/IR… (ultrafast spectroscopy, Raman for vibration study, …) Other method? self phase modulation (SPM) | low efficiency

  12. 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)

  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 Shorter pulse needs broader spectrum

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

  16. Application | classical Broadband generation | for short pulse OPA (OPG with WLC) WLC pulse width=~9fs Spectrum diffracted by grating Visible 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. w s , k s w p , k p w i , k i NLC Application | quantum SPDC generates photon pairs (low efficiency) correlated parameters (1) wave vector :k p = k s + k i (2) frequency ：wp = ws + wi (3) polarization： (in case of Type-II crystal)

  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… Are there any other entanglements? Interference only in unknown case path entanglement Interference of “probability”, “wavefunction” different from statistics of classical phenomena=quantum Yes, we will see them in the following pages!

  20. Application | quantum Y. Shih, J. Mod. Opt. 49, 2275 (2002) quantum lithography | wave vector better resolution ( than classical limit ) ~ lp= l /2 Schematic set-up half! (Young’s : ) “SPDC photon pairs” v.s. “classical light”

  21. Experimental result (quantum lithograph) quantum classical

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

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

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

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

  26. BBO Application | quantum ghost spectroscopy | frequency CC1 CC2 coincidence count CC3 BBO BBO CC1 CC2 CC3 CC1 CC1 CC2 CC2 CC3 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 (Nd+3-doped glass) L1 : focusing lens (f=100mm, 8mm)

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

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

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

  31. 1. Broadband photon pairs summary of this section spectrum of SPDC photon pairs spherical lens → objective lens (f=100 → 8mm) spectrum was broadened (11,11→63,69nm) Nd3+ -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 photontransmitted through the sample A. Yabushita et. al., Phys. Rev. A 69, 013806 (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 0 1 0 1 1 0 • base at random +  +  + + • base at random  + +  + 0 0 0 1 1 0

  35. Application | quantum 50% of keys can be shared (shared keys are same) • BB84 protocol | single photon • Purpose : to share a secret key • how it works? • key at random 0 1 0 1 1 0 • base at random +  +  + + • base at random  + +  + complicated…But secure! How can it be secure?? 0 0 0 1 1 0

  36. Application | quantum 0 1 1 1 1 0 • BB84 protocol | single photon • Can it be secure? • key at random 0 1 0 1 1 0 • base at random +  +  + + • base at random  + +  + base? (random try) +    +  0 1 1 1 1 0 0 1 0 1 1 1

  37. Security can be checked! Application | quantum • BB84 protocol | single photon • Can it be secure? • key at random 0 1 0 1 1 0 • base at random +  +  + + • base at random  + +  + base? (random try) +    +  0 1 1 1 1 0 0 0 0 1 1 1 Error!

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

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

  40. H H 0 0 V V 0 0 V V H H 1 1 1 1 R L If they use the same base, “100%” correlation (quantum key distributed!) … … L R 0 0 1 1 QKD example (without Eve) Bob Base select Base select Alice EPR-pair

  41. ? H 0 V V V 0 V H H H 1 1 V H H H 1 1 H V V V 0 0 … … … … QKD example (with Eve) Bob Base select Base select Alice EPR-pair Eve also share the key (NOT secure QKD…) How can it be improved?

  42. H 0 V 0 Base information (classical communication) H L 1 1 L R 0 0 H R 0 1 R V 0 0 L R 1 1 V 1 L 0 V H 1 1 Ekert91 protocol Bob Base select Base select Alice EPR-pair “100%” correlation

  43. OK Base information R R H 0 V 0 H V V L 1 1 OK L L L R 0 0 V V H R 0 1 R L L V 0 0 H H L L 1 0 R R V 1 R 0 OK V H H H 1 1 Ekert91 protocol Base select Base select Alice Bob EPR-pair Bob can detect Eve (secure!) 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) w - dw 2w frequency-entangled w + dw BBO (type-II) o/e e polarization-entangled e/o polarization-entangled pair at many wavelength combinations light source for WDM-QKD

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

  48. L1 : focusing lens experimental setup 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. 1. Broadband photon pairs simulation 0o 45o 0o 135o 45o 135o f=1 a=0o f=1 a=60o 90o 90o 135o 0o 45o 0o f=1 a=180o 45o 135o f=1.732 a=0o 90o 90o

  50. 1. Broadband photon pairs polarization correlation (1st diffraction@870nm) 0o 45o phase shift (866nm) < phase shift (870nm) 135o 90o visibility < 100%

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