Entangled photon pair generation by spontaneous parametric down
Entangled photon pair generation by spontaneous parametric down conversion Atsushi Yabushita Department of Electrophysics National Chiao-Tung University ?
Outline ØIntroduction ØOptical parametric processes ØOpt. param. amplifier (OPA) ØSpontaneous param. down conv. (SPDC) ØApplication | classical ØBroadband generation | for short pulse ØApplication | quantum ØEntangled photon pairs ØGhost imaging | wave vector ØGhost spectroscopy | frequency ØQuantum key distribution (QKD) | polarization ØMultiplex QKD | polarization and frequency ØEntangled photon beam ØConclusion Our work
Outline ØIntroduction ØOptical parametric processes ØOpt. param. amplifier (OPA) ØSpontaneous param. down conv. (SPDC) ØApplication | classical ØBroadband generation | for short pulse ØApplication | quantum ØEntangled photon pairs ØGhost imaging | wave vector ØGhost spectroscopy | frequency ØQuantum key distribution (QKD) | polarization ØMultiplex QKD | polarization and frequency ØEntangled photon beam ØConclusion Our work
Outline ØIntroduction | OPA and SPDC l. Light is … l. Light-matter interaction l. Frequency conversion • SHG and SPDC • SPDC OPA • OPA is …? l. Why OPA? l. Why SPDC?
Introduction Light gamma-ray X-ray Ultraviolet visible infrared radio wave => Electro-magnetic wave
Introduction Light-matter interaction Electric field make dielectric polarization Emission from dipole oscillating in vertical direction E : exp(-iwt) E*E : exp(-i 2 wt) Second harmonic generation (SHG) using a non-linear crystal within some limitation from physical law…
BBO crystal b-Ba. B 2 O 4 Introduction energy / momentum conservation in frequency mixing k 2, w k 1, w
Introduction Reversible? YES! Reverse process spontaneous parametric down conversion (SPDC) occur by itself 2=>1+1 2=>0. 8+1. 2 2=>1+1
seed | w/o amp Introduction How does SPDC occur? similar as OPA (optical parametric amplification) …what is OPA? Signal (amplified) pump seed idler process | difference frequency generation hnpump-hnsignal=hnidler Energy conservation hnpump=hnsignal+hnidler signal | amplified
Introduction How 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 hnpump-hnsignal=hnidler Energy conservation hnpump=hnsignal+hnidler #signal=#idler quite low efficiency ~10 -10
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
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)
Outline ØIntroduction ØOptical parametric processes ØOpt. param. amplifier (OPA) ØSpontaneous param. down conv. (SPDC) ØApplication | classical ØBroadband generation | for short pulse ØApplication | quantum ØEntangled photon pairs ØGhost imaging | wave vector ØGhost spectroscopy | frequency ØQuantum key distribution (QKD) | polarization ØMultiplex QKD | polarization and frequency ØEntangled photon beam ØConclusion Our work
Application | classical Broadband generation | for short pulse Shorter pulse needs broader spectrum
Application | classical Broadband generation | for short pulse Optical parametric amplifier (OPA) nondegenerate Non-collinear OPA (NOPA)
Application | classical Broadband generation | for short pulse WLC OPA (OPG with WLC) pulse width=~9 fs Spectrum diffracted by grating Visible broadband
Outline ØIntroduction ØOptical parametric processes ØOpt. param. amplifier (OPA) ØSpontaneous param. down conv. (SPDC) ØApplication | classical ØBroadband generation | for short pulse ØApplication | quantum ØEntangled photon pairs ØGhost imaging | wave vector ØGhost spectroscopy | frequency ØQuantum key distribution (QKD) | polarization ØMultiplex QKD | polarization and frequency ØEntangled photon beam ØConclusion Our work
Application | quantum SPDC generates photon pairs (low efficiency) w s , k s w p , k p NLC w i , k i correlated parameters (1) wave vector : k p = k s + k i (2) frequency : w p = w s + w i (3) polarization: (in case of Type-II crystal)
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!
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” )
Experimental result (quantum lithograph) quantum classical
Application | quantum ghost imaging | wave vector BBO coincidence count CC 1 CC 2 CC 3
Application | quantum ghost imaging | wave vector BBO coincidence count CC 1 CC 2 CC 3
Application | quantum ghost imaging measure the shape of an object Detector does NOT scan after object classical w s , k s w p , k p NLC w i , k i Y. Shih, J. Mod. Opt. 49, 2275 (2002)
Application | quantum ghost spectroscopy | frequency BBO coincidence count CC 1 CC 2 CC 3
Application | quantum ghost spectroscopy | frequency BBO coincidence count CC 1 CC 2 CC 3
experiment setup BBO : non-linear crystal M 1 : parabolic mirror M 2, 3 : plane mirror P 1 : prism (remove pump) P 2 : prism (compensate angular dispersion) PBS : polarizing beam splitter G : diffraction grating L 2, 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) L 1 : focusing lens (f=100 mm, 8 mm)
1. Broadband photon pairs Spectrum of photon pairs and absorption spectrum of the sample pump focusing lens (f=100 mm) more absorption in longer wavelength
1. Broadband photon pairs result : absorption spectrum calculate absorption spectrum from the ratio → agree with the result by a spectrometer
1. Broadband photon pairs result : absorption spectrum agree with the result by a spectrometer
summary of this section 1. Broadband photon pairs spectrum of SPDC photon pairs spherical lens → objective lens (f=100 → 8 mm) spectrum was broadened (11, 11→ 63, 69 nm) 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, 013806 (2004)
Outline ØIntroduction ØOptical parametric processes ØOpt. param. amplifier (OPA) ØSpontaneous param. down conv. (SPDC) ØApplication | classical ØBroadband generation | for short pulse ØApplication | quantum ØEntangled photon pairs ØGhost imaging | wave vector ØGhost spectroscopy | frequency ØQuantum key distribution (QKD) | polarization ØMultiplex QKD | polarization and frequency ØEntangled photon beam ØConclusion Our work
Application | quantum Outline for “Quantum Key Distribution (QKD)” ØBB 84 protocol | single photon lhow it works lcan it be safe? ØE 91 protocol | polarization entangled photon pair lpolarization entanglement? lhow it works lcan it be safe?
Application | quantum ØBB 84 protocol | single photon l. Purpose : to share a secret key lhow it works? • key at random 0 1 1 0 • base at random + + + + • base at random 0 + 1 + + + 0 1 0
Application | quantum 50% of keys can be shared (shared keys are same) complicated…But secure! ØBB 84 protocol | single photon l. Purpose : to share a secret key lhow it works? • key at random 0 1 1 0 • base at random + + + + • base at random 0 + 1 + + + 0 1 0 How can it be secure? ?
Application | quantum 0 1 1 0 ØBB 84 protocol | single photon l. Can it be secure? • key at random 0 1 1 0 • base at random + + + + base? (random try) + 0 • base at random 0 + 1 1 1 1 0 + + + 0 1 1
Security can be checked! Application | quantum ØBB 84 protocol | single photon l. Can it be secure? • key at random 0 1 1 0 • base at random + + + + base? (random try) + 0 • base at random 0 + 1 1 1 1 0 + + + 0 1 0 0 1 1 Error!
1. Broadband photon pairs polarization-entangled photon pairs Alice EPR-Bell source Bob
1. Broadband photon pairs Mixed state (statistical mixture) Alice HV and VH (50%-50%) Bob ? ?
QKD example (without Eve) Base select Alice 0 1 1 0 H V V H 1 R L If they use the same base, “ 100%” correlation (quantum key distributed!) Bob Base select V H H V 0 1 1 0 … … 0 EPR-pair L R 0 1
QKD example (with Eve) Base select Alice V H H V … … V H H V … 1 1 0 H V V H … 0 Bob Base select EPR-pair 0 1 1 0 Eve also share the key (NOT secure QKD…) How can it be improved? ?
Ekert 91 protocol Base select Alice 0 1 0 0 0 1 1 1 H L R H R L V V EPR-pair Base information (classical communication) “ 100%” correlation Bob Base select V H L R V R L H 0 1 0 1
Ekert 91 protocol Base select Alice 0 1 0 0 0 1 1 1 H L R H R L V V Base select EPR-pair Base information Bob can detect Eve (secure!) R V L V L H R H Bob OK V H L R V L R H 0 1 OK 0 1 NG! 0 0 0 OK 1
Experimental example of QKD T. Jennewein et. Al. , PRL 84, 4729 (2000)
Outline ØIntroduction ØOptical parametric processes ØOpt. param. amplifier (OPA) ØSpontaneous param. down conv. (SPDC) ØApplication | classical ØBroadband generation | for short pulse ØApplication | quantum ØEntangled photon pairs ØGhost imaging | wave vector ØGhost spectroscopy | frequency ØQuantum key distribution (QKD) | polarization ØMultiplex QKD | polarization and frequency ØEntangled photon beam ØConclusion Our work
Generation of photon pairs entangled in their frequencies and polarizations (for WDM-QKD) 2 w w - dw frequency-entangled w + dw BBO (type-II) e o/e polarization-entangled e/o polarization-entangled pair at many wavelength combinations light source for WDM-QKD
Standard : e o/e Multiplex : e polarization-entangled o/e polarization-entangled
experimental setup L 1 : focusing lens BBO : non-linear crystal M 1 : parabolic mirror M 2, 3 : plane mirror P 1 : prism (remove pump) P 2 : prism (compensate angular dispersion) G : diffraction grating L 2, 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 POL 1, 2 : linear polarizer
1. Broadband photon pairs simulation 45 o 0 o 135 o f=1 a=0 o 45 o 0 o 135 o f=1 a=60 o 90 o 135 o 0 o f=1 a=180 o 45 o 0 o f=1. 732 a=0 o 90 o 45 o 135 o 90 o
1. Broadband photon pairs polarization correlation (1 st diffraction@870 nm) 0 o 45 o 135 o phase shift (866 nm) < phase shift (870 nm) 90 o visibility < 100%
polarization correlation (1 st diffraction@870 nm) 0 o 45 o visibility relative phase 135 o 90 o 0 o 0. 75 45 o 0. 43 -25 o 135 o 0. 31 35 o 90 o -81 o 0. 50 phase shift (866 nm) < phase shift (870 nm) visibility<100%
no entanglement (iris open) entangled (iris 1 mm) phase shift (866 nm) < phase shift (870 nm) but phase shift<45 o to improve : walk-off compensation visibility<100% (866 nm, 870 nm) 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 polentanglement) A. Yabushita et. al, J. Appl. Phys. , 99, 063101 (2006)
Outline ØIntroduction ØOptical parametric processes ØOpt. param. amplifier (OPA) ØSpontaneous param. down conv. (SPDC) ØApplication | classical ØBroadband generation | for short pulse ØApplication | quantum ØEntangled photon pairs ØGhost imaging | wave vector ØGhost spectroscopy | frequency ØQuantum key distribution (QKD) | polarization ØMultiplex QKD | polarization and frequency ØEntangled photon beam ØConclusion Our work
Beam-like polarization entangled photon pair generation 羅信斌 (Hsin-Pin Lo) Department of Physics, NTHU 先 進 超 快 雷 射 研 究 中 心 超 快 動 力 學 研 究 室
Acknowledgement 籔下篤史 (Prof. A. Yabushita) Department of Electrophysics, National Chiao Tung University 羅志偉 (Prof. C. W. Luo) Department of Electrophysics, National Chiao Tung University 陳柏中 (Prof. P. C. Chen) Department of Physics, Nation Tsing Hua University 小林孝嘉 (Prof. T. Kobayashi) Department of Applied Physics and Chemistry and Institute for Laser Science The University of Electro-Communications, Tokyo, Japan 超 快 動 力 學 研 究 室 先 進 超 快 雷 射 研 究 中 心
SPDC photon image Beam-like photon pair H: Horizontal V: vertical Polarization Entangled photon pair Crystal optic axis
H V V H Generation rate ~ 32, 000 s-1
Main idea and experiment setup V 2 H 1 Coincidence measurement H 2 V 1 V 2 H 1 SPCM L 1 L 2 H 2 L 1=L 2=L 3 V 1 L 3 QWP
PRL 90, 240401 (2003) 2 by 2 fiber
HOM interference measurement HWP Pol. QWP L 1 L 3
Summary ØIntroduction ØOptical parametric processes ØOpt. param. amplifier (OPA) ØSpontaneous param. down conv. (SPDC) ØApplication | classical ØBroadband generation | for short pulse ØApplication | quantum ØEntangled photon pairs ØGhost imaging | wave vector ØGhost spectroscopy | frequency ØQuantum key distribution (QKD) | polarization ØMultiplex QKD | polarization and frequency ØEntangled photon beam Our work
Thank you for your attention!
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