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November 3-4, 2003 Optical-Fiber Entanglement Sources: Theoretical progress and development of associated technologies Xiaoying Li, Paul Voss, Jun Chen, Sarah Dugan, and Prem Kumar Center for Photonic Communication and Computing Northwestern University, Evanston, IL 60208-3118 Our Motivation • Provide theoretical understanding for optimization of polarization entanglement purity – Model Raman effect (noninstantaneous nonlinear response) – Model pulsed pump with realistic signal/idler filters • Cascaded four wave mixing in PPLN waveguide: alternate source of polarization entangled photons • Develop photon counting technology 2 Cause of Uncorrelated Photons in the Fiber λp = 1530nm, λ0 = 1535±2nm 40 30 1545.3nm 20 1515nm 10 0 0 5 10 3 1545.3nm 2 1 1515nm 0 15 0 *107 Pump photons/pulse λp = 1534nm, λ0 = 1537±2nm *103 4 Single counts(1s) Single counts(5s) *103 50 100 200 300 Length of DSF (m) It is Raman Scattering! S RS ∝ P p L DSF 800 Theory curve for two independent sources Coin(5s) 600 Improvements are possible! Suppress Raman scattering and optimize FWM: 400 • Optimize signal / idler wavelengths • Optimize filter bandwidth • Decrease temperature, although not desirable 200 0 0 20 40 Single A(5s) 60 *103 3 400 χ(3) Nonlinear Response • Noninstantaneous response due to back action of nuclei on electronic Kerr nonlinearity • Nonlinear coefficient from parallel Raman power gain profile (Dougherty, 94), power gain peak magnitude for DSF (Taylor, 01), Kramers-Kronig transform gives from , and from H(0) for DSF (Taylor, 94). 4 Quantum Model of FWM plus Raman Effect L. Boivin, F. X. Kärtner, and H. A. Haus, Phys. Rev. Lett. 73, 240 (1994). J. H. Shapiro and L. Boivin, Opt. Lett. 20, 925 (1995). • Envelope propagation for continuous-time temporal modes • After Fourier Transform, undepleted pump approximation, only looking at three modes 5 FWM plus Raman solution • Voss and Kumar, to appear in Opt. Lett. Solution is where and and Noise Figure is: 6 Excellent Agreement with Several Experiments • Addition of Raman noise can be treated analytically • Matches PIA noise figure data with no fitting parameters • Theory ok for twin beam noise reduction (TBNR) at low gains • At G>2, need Raman + higher order FWM theory for TBNR 7 Classical Equations of FWM: Start of pulsed theory • Degenerate FWM • Non-degenerate FWM • Heisenberg Equation of Motion 8 Interaction Hamiltonian for FWM in Optical Fibers • Hamiltonian for Degenerate FWM • Hamiltonian for Non-degenerate FWM where 9 Standard Approach: Pulsed fields • Electric Fields of Pump, Signal and Idler • First-Order Perturbation • Two-photon State 10 Coincidence Counting • Biphoton Amplitude • Coincidence Counting Rate • Gaussian Filter Approximation • Analytical Expression for Coincidence Counting Rate 11 Effect of filter bandwidth and filter frequency shift 60000 50000 Experimental Data Theoretical Prediction CC/sec 40000 30000 20000 10000 0 0 0.5 1 1.5 2 2.5 3 3.5 Pump Peak Power [W] 14000 Coincidence Counts sec 12000 4000 CC/sec 10000 8000 3000 6000 2000 4000 1000 2000 0 0 0.5 1 1.5 2 2.5 -1 ´ 10 Filter Bandwidth [nm] 12 -8 -5 ´ 10 -9 5´ 10 -9 1´ 10 -8 Dl Cascaded Four-Wave Mixing •Cascaded χ(2) process -- pump generates second harmonic which pumps down-conversion •Leading to mode-matched source of entangled photons Pump source: 20kHz, 10ns into 1542nm GS DFB 90/10 FPCs FC 1531nm PBS 2ω Det. Dichroic FC oscilliscope 13 Det. Tunable BPF (idl) Waveguide Signal Source: Tunable diode laser (Santac) Idler power vs. pump second-harmonic Coincidence counting with conversion 14 10GHz Amplitude modulator Pump 1551nm DFB Variable Attenuator WG1, gen. FPC Grating2 WG2, conv. •The two waveguides have 10GHz BERT similar modes, so coupling is 10MHz 100ps, easier clock 10MHz •Use one pump for both processes – improve coupling, signal and idler need 20nm separation •Pump requirements are same as earlier signal – pulsed, 100ps, <0.2nm – but now also <10kHz InGaAs/InP •First (shorter) waveguide has PCM larger BW, may have to filter WDM unconverted light •Detection efficiency is the average of the two detectors (~45%) •Coordinate coincidence measurements between Si DAQ detector and InGaAs/InP detector card Dichroic Grating1 Si PCM 14 MHz InGaAs/InP APD Photon Counters • Highest rate operation to date Detectors • Possible because of room temperature operation • Good suppression of afterpulses • Relatively high dark count rate Avalanche pulse Fast amplifiers A/D Digital thresholding logic • Previous system limited to <1 MHz because of: • Delay Generator DG535 rate limit (1 MHz) • Data Acquisition card (NI PCI6010E) • Avtech Pulse Generator rate limit (1 MHz) • Upgrade includes • Delay line based on phase shifter at 14 MHz • Avtech Pulse Generator (25 MHz) • Fast A/D to sample photocurrent (AD9033) • Digital thresholding for auto-recalibration and programmability • NI PCI5102 data acquisition (20 MHz) 15 Optical Clock Detection & Recovery Adjustable Delay Line 14 MHz results: Bias Scanned • Threshold constant • APD A scanned from 48.8 to 51.2 V. • APD B scanned from 49.4 to 51.0 V. • Scanned in 200 mV increments. • 800 ps, 12 V gate 16 14 MHz results: decision threshold scanned • Decision threshold scanned for each bias • 800 ps, 12 V gate • Q.E. ~ 10-15% for dark count probability of 0.2% • Fluctuations due to timing drift in phase shifting circuit • Conclusion: Most bias settings equivalent • Conclusion: threshold scanning or bias scanning are roughly equivalent 17 Threshold determination capacitive “ringing” light + dark count distribution Note: 1 ns capacitive “ringing” slowed down by 100 MHz bandwidth of amplifier dark counts capacitive “ringing” dark count distribution • Dark and light counts have different voltage distributions light + dark counts • Similar to PMT • There is an optimum threshold level 18 Afterpulsing at room temperature • 1 ns, 10 V gate Bias: 49 V asterisks 50 V squares 51 V circles • Afterpulsing increases with bias voltage (larger breakdown currents fill more trapping centers) • Afterpulsing prob ≈ dark count rate at 50 V bias, 14 MHz operation 19 Accomplishments and Work in Progress • Observed polarization entanglement / biphoton interference • Violation of Bell’s inequalities demonstrated • Observation of polarization entanglement over long distances (25/50 km) • Continuing studies on background photons • Coincidence counting in the 800 nm region • Progress on high-rate photon counting • Progress in quantum frequency conversion using PPLN waveguides 20