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Pure-state, single-photon wave-packet generation by parametric down conversion in a distributed microcavity

Pure-state, single-photon wave-packet generation by parametric down conversion in a distributed microcavity. M. G. Raymer, Jaewoo Noh* Oregon Center for Optics, University of Oregon -------------------------------------- I.A. Walmsley, K. Banaszek, Oxford Univ.

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Pure-state, single-photon wave-packet generation by parametric down conversion in a distributed microcavity

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  1. Pure-state, single-photon wave-packet generation by parametric down conversion in a distributed microcavity M. G. Raymer, Jaewoo Noh* Oregon Center for Optics, University of Oregon -------------------------------------- I.A. Walmsley, K. Banaszek, Oxford Univ. ----------------------------------------------------------------- * Inha University, Inchon, Korea ----------------------------------------------------------------- ITR - NSF raymer@uoregon.edu

  2. Single-Photon Wave-Packet 1 Wave-Packet is a Superposition-state: (like a one-exciton state)

  3. Interference behavior of Single-Photon Wave-Packets At a 50/50 beamsplitter a photon transmits or reflects with 50% probabilities. 0 1 beam splitter Wave-Packet is a Superposition-state: 1

  4. Interference behavior of Single-Photon Wave-Packets At a 50/50 beamsplitter a photon transmits or reflects with 50% probabilities. 1 1 beam splitter Wave-Packet is a Superposition-state: 0

  5. Single-Photon, Pure Wave-Packet States Interfere as Boson particles 2 1 beam splitter 1 0

  6. Single-Photon, Pure Wave-Packet States Interfere as Boson particles 0 1 beam splitter 1 2

  7. Energy conservation: red red blue Spontaneous Parametric Down Conversion in a second-order nonlinear, birefringent crystal Signal V-Pol pump H-Pol Idler H-Pol kz V H Phase-matching (momentum conservation): P frequency phase-matching bandwidth

  8. optional Correlated Photon-Pair Generation by Spontaneous Down Conversion (Hong and Mandel, 1986) 0 or 1 IDLER Monochromatic Blue Light Perfect correlation of photon frequencies: Red photon pairs 2nd-order Nonlinear optical crystal SIGNAL 0 or 1 • Creation time is uncontrolled • Correlation time ~ (bandwidth)-1

  9. Correlated Photon-Pair Measurement (Hong, Ou, Mandel, 1987) Red photons 2 or 0 1 MC Blue light Time difference 1 0 or 2 Nonlinear optical crystal boson behavior Coincidence Rate Correlation time ~ (bandwidth)-1 Creation time uncontrolled Time difference

  10. 1 1 For Quantum Information Processing we need pulsed, pure-state single-photon sources. Create using Spontaneous Down Conversion and conditional detection: (Knill, LaFlamme, Milburn, Nature, 2001) Pulsed blue light trigger if n = 1 filter shutter nonlinear optical crystal

  11. For Quantum Information Processing we need pulsed, pure-state single-photon sources. Create using Spontaneous Down Conversion and conditional detection: (Knill, LaFlamme, Milburn, Nature, 2001) Pulsed blue light trigger if n = 1 filter shutter SIGNAL 1 nonlinear optical crystal

  12. Pulsed Pump Spectrum has nonzero bandwidth trigger Zero-Bandwidth Filter , w0 detect signal Pure-statecreation at cost of vanishing data rate

  13. Do single photons from independent SpDC sources interfere well? Need good time and frequency correlation. Pulsed blue light trigger 1 filter 1 random delay Coincidence Counts large data rate 1 filter 1 Time difference trigger vanishing data rate

  14. Goal : Generation of Pure-State Photon Pairs without using Filtering Want : (no entanglement) Single-photon Wave-Packet States: signal idler

  15. Decomposition of field into Discrete Wave-Packet Modes.(Law, Walmsley, Eberly, PRL, 2000) (Schmidt Decomposition) Single-photon Wave-Packet States:

  16. The Schmidt Wave-Packet Modes are perfectly correlated. But typically it is difficult to measure, or separate, the Schmidt Modes. filter Mode Amplitude Functions: Mode spectra overlap. No perfect filters exist, in time and/or frequency. frequency

  17. Why does the state generally NOT factor? Energy conservation and phase matching typically lead to frequency correlation need to engineer the state to make it factor

  18. the problem: cavity FSR ~ 1/L phase-matching BW ~ 10/L DOES NOT WORK Spontaneous Parametric Down Conversion inside a Single-Transverse-Mode Optical Cavity 1 mm pump Nonlinear optical crystal with wave-guide

  19. Spontaneous Parametric Down Conversion inside a Distributed-Feedback Cavity • large FSR = c /(2x0.2 mm) • small phase-matching BW: ~ 10 c /(4 mm) 0.2 mm cavity 4 mm 4 mm H-Pol idler H-Pol pump V-Pol signal Linear-index wave-guide Linear-index Distributed-Bragg Reflectors (DBR) second-order nonlinear-optical crystal

  20. SIMPLIFIED MODEL: Half-DBR Cavity 4 mm 0.2 mm cavity l0 =800 nm KG = 25206/mm Dn/n ~ 6x10-4 (k = 2/mm) DBR 99% mirror Reflectivity DBR band gap cavity mode frequency/1015

  21. Frequency Domain: space and frequency dependent electric permeability: (modes) Quantum Generation in a Dielectric-Structured Cavity: Phenomenological Treatment Signal Source Pump

  22. 0 L two-photon amplitude interaction internal Signal, Idler modes pump field

  23. Heisenberg Picture Schrodinger Picture Amplitude for Photon Pair Production: Cavity Phase-Matching pump spectrum pump mode internal Signal, Idler modes

  24. Type-IICollinear Spontaneous Parametric Down Conversion in a second-order nonlinear, birefringent crystal pump V-Pol Signal H-Pol Idler H-Pol Phase-matching (momentum conservation): k V H Energy conservation: P red red blue frequency phase-matching bandwidth

  25. Birefringent Nonlinear Crystal, Collinear, Type-II, Bulk Phase Matched, with Double-Period Grating: wS = wI = wP/2 kS + kI = kP wP wI, wS 0 kS kI kP KTP --> KGS/2 KGI/2

  26. 0 L KTP Crystal with Double Gratings 95% mirror • grating index contrast • crystal length L = 4 mm, giving G L = 8 • cavity length ~ 0.2mm • signal and idler fields are phase matched at degeneracy wavelength SI = 800 nm • pump wavelength = 400 nm • pump pulse duration 10 ps

  27. Two-Photon Amplitude C(w, w’) No Grating, No Cavity Two Gratings w’ w’ zoom in Two Gratings with Cavity w’ w’ w w

  28. Two-Photon Amplitude C(w, w’) zoom in Two Gratings with Cavity w’ w’ x Pump Spectrum w’ (hi res) w w’ w

  29. Schmidt-Mode Decomposition

  30. First Four Schmidt Modes for 95% Cavity Mirror amplitude j=2 j=1 DBR j=4 j=3 frequency frequency

  31. Unfiltered Measurement-Induced Wave-function Collapse • For cavity-mirror reflectivity = 0.99, the central peak contains 99% of the probability for photon pair creation, without any external filtering before detection. • If any idler photon is detected, then the signal photon will be in the first Schmidt mode with 99% probability. • Promising for high-rate production of pure-state, controlled single-photon wave packets.

  32. CONCLUSIONS & DIRECTIONS: • Spontaneous Down Conversion can be controlled by modifying the density of states of vacuum modes using distributed cavity structures. • One can engineer the vacuum to create single-photon pairs in well defined, pure-state wave packets, with no spectral entanglement. • In the absence of detector filtering, detection of one of the pair leaves the other in a pure single-photon state. • Waveguide development at Optoelectronics Research Center (Uni-Southampton, Peter Smith)

  33. Alternative Scheme: Single-mode squeezers combined at a beam splitter cavity 1 photon pair weak single-mode squeezed beam splitter cavity 2

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