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. 1 1 Wave-Packet is a Superposition-state: 0 beam splitter

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

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

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

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

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

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

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

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

12. trigger Pulsed Pump Spectrum has nonzero bandwidth Zero- Bandwidth Filter,  0 detect signal Pure-state creation at cost of vanishing data rate

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

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

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

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

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

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

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

20. 0 =800 nm K G = 25206/mm  n/n ~ 6x10 -4 (  = 2/mm) 4 mm DBR 99% mirror SIMPLIFIED MODEL: Half-DBR Cavity Reflectivity frequency/10 15 DBR band gap 0.2 mm cavity cavity mode

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

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

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

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

25. PP  I  S 0 k S k I k P  S =  I =  P /2 Birefringent Nonlinear Crystal, Collinear, Type-II, Bulk Phase Matched, with Double-Period Grating: K GS /2 K GI /2 k S + k I = k P KTP -->

26. 0 L 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 KTP Crystal with Double Gratings 95% mirror

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

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

29. Schmidt-Mode Decomposition

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

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. no spectral entanglement 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. cavity 1 cavity 2 beam splitter photon pair weak single-mode squeezed Alternative Scheme: Single-mode squeezers combined at a beam splitter