Schemes to generate entangled photon pairs via spontaneous parametric down conversion

Schemes to generate entangled photon pairs via 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) 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

Outline Introduction OPA and SPDC Light is Light-matter interaction Frequency conversion SG and SPDC SPDCOPA OPA is? Why OPA? 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(-it) E*E : exp(-i2t) Second harmonic generation (SG) using a non-linear crystal within some limitation from physical law

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

Introduction SG (second harmonic generation) 2 Reversible? YES! Reverse process spontaneous parametric down conversion (SPDC) occur by itself 2=>+ 2=>0.8+1.2 2=>+

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

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)

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

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) 2 1 0 400 600 800 w a v e le n g th ( nm )

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

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

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

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

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 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 : )

Experimental result (quantum lithograph) quantum classical

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

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)

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

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)

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

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

result : absorption spectrum 1. Broadband photon pairs 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 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, 013806 (2004)

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?

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 1 0 1 0 0 1 0

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 0 1 0 1 1 0 base at random + + + + base at random + + + + 0 1 0 1 0 0 1 0

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? (random try) + + result (bit) copy 0 1 1 1 1 0 base at random + + + 0 1 + 0 1 1 0 1 1

Application quantum BB84 protocol single photon Can it be secure? key at random 0 1 0 1 1 0 base at random + + + + base? (random try) + + result (bit) copy 0 1 1 1 1 0 Security can be checked! base at random + + + 0 1 + 0 1 0 0 1 1 Error!

EPR-Bell source Alice Bob 1. Broadband photon pairs polarization-entangled photon pairs 12 1 2 1 2 1 1 2 2 1 1 2 2 1 2 1 2

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

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

QKD example (with Eve) Alice Base select EPR-pair Base select Bob? 0 1 1 0 base/ get/ copy 0 1 1 0 Eve also share the key (NOT secure QKD ) ow can it be improved?

Ekert91 protocol Alice Base select EPR-pair Base select Bob Base information L (classical communication) R L 100% correlation R R L R L 0 0 0 1 1 0 0 0 1 0 0 1 1 1 1 1

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!

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

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

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 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

simulation f=1 =0 o coincidence counts (arb. units) 1 0.5 0 0 60 120 18 i (degree) f=1 =60 o s i f e 45 o 0 o 135 o 0o 90 o coincidence counts (arb. units) 1 0.5 1. Broadband photon pairs 45 o i 90 o s 0 0 60 120 18 i (degree) 135 o i 1 3 f=1 =180 o coincidence counts (arb. units) 0.5 135 o 0 o 45 o f=1.732 =0 o coincidence counts (arb. units) 2 1 45 o 0 o 135 o 90 o 0 0 60 120 18 i (degree) 90 o 0 0 60 120 18 i (degree)

1. Broadband photon pairs polarization correlation (1 st diffraction@870nm) 0 o s i f e i s i 45 o 135 o phase shift (866nm) < phase shift (870nm) 90 o f 1.7 1 visibility < 100% o 0,180

polarization correlation (1 st diffraction@870nm) 0 o s i f e i s i 45 o 135 o visibility relative phase 0 o 0.75 90 o 45 o 0.43-25 o 135 o 0.31 35 o 90 o 0.50-81 o phase shift (866nm) < phase shift (870nm) visibility<100% f 1.7 o 0,180 1

no entanglement iris open entangled iris 1mm phase shift (866nm) < phase shift (870nm) f 1.7 1 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, 063101 (2006)

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

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

Acknowledgement for $upport MOE ATU plan, Taiwan, ROC. National Science Council, Taiwan, ROC. NSC 98-2112-M-009-001-MY3, NSC 99-2923-M-009-004-MY3

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

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

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

OM interference measurement (adjust path length) WP Pol. QWP 600 L1 L3 Coincidence counts (1/s) 500 400 300 200 100 0-150 -100-50 0 50 100 150 Delay (m)

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

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 = 0.900.05 (highly entangled)

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, 022313 (2011)

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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

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