Beamlike photo-pair generation by femtosecond pulse laser

Transcription

1 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

2 Acknowlegements Taiwan National Science Council Mr. Hsin-Pin Lo Prof. Yabushita Prof. Kobayashi Prof. Chen

3 Outline. Introuction quantum information. Introuction femtosecon (fs) laser pulses 3. Down conversion principle 4. Beamlike photon-pair generation

4 Introuction Quantum information ψ = α 0 + β * Superposition. Spee. Density 3. Communication cf. :

5 Introuction Quantum information Beam Us Up! Teleportation oesn't work for humans yet but it works over long istances! Free-space implementation of quantum teleportation over 6 km. Star Trek Ref.: X. M. Jin, et al, Nature Photonics 4, 376 (00).

6 Outline. Introuction quantum information. Introuction femtosecon (fs) laser pulses 3. Down conversion principle 4. Beamlike photon-pair generation

7 Introuction fs laser pulses What is the ultrashort pulse? ~0-6 s ~0-9 s ~0 - s ~0-5 s

8 Introuction fs laser pulses Timescales 0 fs light pulse Computer clock cycle Camera flash minute One month Age of pyramis Human existence Age of universe femtosecon picosecon Time (secons) a pulse : minute ~ minute : age of universe

9 Introuction fs laser pulses Which one is true? / min / 0.5 min / sec Iea from 石訓全

10 Introuction fs laser pulses Ultrafast camera!!

11 Introuction fs laser pulses The possibility for nuclear fusion! Short pulse = intense peak power 00 mj, 00 fs = TW 0 8 φ = 0 μm (0 0 V/cm) Institute of Laser Engineering Osaka University See Pump Veri Mira Long pulse, high energy Pump Evolution Short pulse, low energy Amplifier Legen Short pulse, high energy USA National Ignition laser beams

12 Introuction fs laser pulses USA National Ignition Facility Output power ~ 300 TW

13 Outline. Introuction quantum information. Introuction femtosecon (fs) laser pulses 3. Down conversion principle 4. Beamlike photon-pair generation

14 Down conversion principle Secon-orer susceptibility the first nonlinear optical effect P () ( ) ( 3 ) ( χ E + χ EE + + ) = ε EEE 0 χ The polarization of a material can be written as P i P P P x y z ( ) ( ) = ε χ E ( ) E ( ) = 3 0 j, k 3 ijk j k E E E E E E In a centrosymmetric (inverse sym.) crystal ijk =0 no SHG In non-centrosymmetric (no inverse-sym.) crystal ijk 0 SHG 6 z z x x y z E E E y x y

15 Down conversion principle Secon-orer susceptibility The energy conservation The momentum conservation ( ) = + k = = k + k = k Δk = k k 0 ( ) After propagation over a istance l in the meium, ( ) k ( ) k k Δ Δ ( k k ) l 0 kl = = ( k k ) l 0 kl = The two contributions a constructively The two interfere estructively If it satisfies above conitions, the intensity of SHG can be calculate by I 7 π 3 eff ( ) = I ( ) n 3 c χ 3 l sin Δ kl Dephasing must be overcome for SHG!! ( Δ kl ) I( Δkl) I( Δkl) Δkl

16 Down conversion principle Secon-orer susceptibility Inex-of-refraction ispersion ata on KH PO 4 Phase matching conition Δk = k c ( ) ( ) k = ( n n ) = 0 Get maximum signal of SHG Coherent length l π π λ = = = c Δk k ( ) ( ) k c( n n ) If λ= μm an n -n ~0.0 l c ~ 00 μm (n -n ) 0, l c, I() In normally ispersive materials the inex of refraction increases with. This makes it impossible to satisfy phase matching when both the an beams are of the same type. For birefringent crystal, n e n o Can satisfy the phase matching conition

17 Secon-orer susceptibility Birefringent crystal Positive birefringence (n e >n o ): Quartz Negative birefringence (n e <n o ): Calcite ( ) ( ) ( ) ( ) cos sin = + = θ θ θ θ o o e e n n n n ( ) ( ) ( ) ( ) = sin θ o e o o n n n n Calculate the phase-matching angle θ between the propagation irection an the optical axis For negative birefringent crystal, the polarization shoul be ( ) ( ) ( ) θ θ θ Type II : // Type I : e o e e o o n n n n n n = + = + E E E E Banwith of SHG ± = λ λ π λ λ.39 e n o n l Limit by crystal thickness [30μm KDP(KH PO 4 6fs] Down conversion principle

18 Down conversion principle Secon-orer susceptibility Ex. BBO (β-barium Borate, BaB O 4 ) (eoe) (ooe)

19 Down conversion principle The energy & momentum conservation in frequency mixing (i) 800 nm (iii) 400 nm (i) (ii) (iii) ( ) = +, k = k + k ( ) = +, k = k + k ( ) = +, k = k + k Type I : E Type II : E (ii) // E E nm Spontaneous Parametric Down-Conversion (SPDC) Signal, s (800 nm) BBO Iler, i (800 nm) Pump, p (400 nm)

20 Outline. Introuction quantum information. Introuction femtosecon (fs) laser pulses 3. Down conversion principle 4. Beamlike photon-pair generation

21 Beamlike photon-pair generation SPDC photon generation pump θ H V H V V H pump θ Ψ = [ H V + V H Polarization Entangle photon pair ] H. P. Lo, A. Yabushita, C. W. Luo, P. C. Chen, T. Kobayashi, PRA 83, 033 (0)

22 Beamlike photon-pair generation Entangle photons generation Pump beam λ= 400nm θ e-ray θ=0 o Type II BBO crystal H state θ=5 o θ= 0 o o-ray P V state etector P etector

23 Beamlike photon-pair generation EPR-Bell states Generation rate ~ 500 s -

24 Beamlike photon-pair generation H V V H Generation rate ~ 3,000 s -

25 Beamlike photon-pair generation Our iea V H V H L L H V Coincience measurement TAC Coincience photon pair Star Stop Signal SPCM # PC CC elay V H Ψ = e If L=L=L3 iφ [ H V + L3 (e QWP iϕ V ) H ] SPCM # Time elay (electrical) Ψ = [ H V V H ]

26 Beamlike photon-pair generation Hong-Ou-Manel(HOM) ip interference measurement for light path ajustment Pol. QWP 50 0 HWP L coincince counts (/s) Pol. QWP elay (μm) Pol. Pol. HWP L L3 QWP QWP coincience counts (/s) elay (μm)

27 Beamlike photon-pair generation The coincience count rate of the photon pairs R C can be calculate as The normalize correlation functions of the pump an the signal-iler fiels p Δ = ( Δ ) γ ( L) exp - L l γ ( ΔL ) = exp - ( ΔL l ) If ΔL = 0 coh coh Ref.: R. W. Boy, PRA 77, 080(R) (008).

28 Beamlike photon-pair generation Two-photon interference of beamlike photon pairs SHG FC s FC I Coincience coincience counts (/s) IF POL S POL I IF BBO OSC QWP I QWP S M I M s M p QWP i =0 QWP s =0 coincience counts (/s) elay (μm) elay (μm)

29 Beamlike photon-pair generation Polarization entanglement of beamlike photon pairs Ψ SHG Coincience = V S FC s FC I H IF POL S POL I IF I BBO + exp i k OSC QWP I QWP S M I M s QWP i =45 QWP s =45 P0 ΔL + k M p S0 - k I0 coincience counts (/s) ΔL + ΔΦ H + = ( H + V ),- = ( H - V ), k k Φ = kp ΔL + S0 - I0 ΔL 0 + ΔΦ iφ iφ Ψ = ( + e )( ) + ( - e )( ) S I S I S I S I The coincience count rate of the photon pairs R + iφ - Ψ + + = - e = S Ref.: W. K. Wootters, PRL 80, 45 (998). I ( - cosφ) S V I elay (μm) coincience counts (/s) Entanglement + E( Ψ ) = h where 0 - C elay (μm) The concurrence was calculate to be 0.9±0.05

30 Summary coincience counts (/s) elay (μm) In this stuy, we prove the new iea can generate the beamlike photon for the twophoton interference an polarization entanglement. The concurrence of the pair was calculate to be 0.90 ± 0.05, which efines the egree of entanglement of the generate photon pairs. This confirms that the generate beamlike photon pair is highly entangle in its polarization. H. P. Lo, A. Yabushita, C. W. Luo, P. C. Chen, T. Kobayashi, PRA 83, 033 (0)

31 Acknowlegements Cooperators: Hsin-Pin Lo, Prof. A. Yabushita, Prof. T. Kobayashi, Prof. P. C. Chen, Thank you for your attention!!