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QuickTime™ and a Photo - JPEG decompressor are needed to see this picture. 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 [email protected] QuickTime™ and a Photo - JPEG decompressor are needed to see this picture. Single-Photon Wave-Packet 1 Wave-Packet is a Superposition-state: 1 d ( ) 1 (like a one-exciton state) QuickTime™ and a Photo - JPEG decompressor are needed to see this picture. 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 d ( ) 1 1 QuickTime™ and a Photo - JPEG decompressor are needed to see this picture. 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: 1 d ( ) 1 0 QuickTime™ and a Photo - JPEG decompressor are needed to see this picture. Single-Photon, Pure Wave-Packet States Interfere as Boson particles 2 1 1 beam splitter 0 QuickTime™ and a Photo - JPEG decompressor are needed to see this picture. Single-Photon, Pure Wave-Packet States Interfere as Boson particles 0 1 1 beam splitter 2 QuickTime™ and a Photo - JPEG decompressor are needed to see this picture. Spontaneous Parametric Down Conversion in a second-order nonlinear, birefringent crystal kS Signal V-Pol H-Pol pump kP L kI Idler H-Pol Energy conservation: S I P red red blue Phase-matching (momentum conservation): r r kS kI kP / L phase-matching bandwidth kz V H P frequency optional Correlated Photon-Pair Generation by Spontaneous Down Conversion (Hong and Mandel, 1986) IDLER Monochromatic Blue Light 0 or 1 Red photon pairs 2nd-order Nonlinear optical crystal 2P d QuickTime™ and a Photo - JPEG decompressor are needed to see this picture. Perfect correlation of photon frequencies: ' P SIGNAL 0 or 1 C( ) 1SIGNAL 1IDLER P • Creation time is uncontrolled • Correlation time ~ (bandwidth)-1 P ' QuickTime™ and a Photo - JPEG decompressor are needed to see this picture. Correlated Photon-Pair Measurement (Hong, Ou, Mandel, 1987) 1 Red photons 2 or 0 MC Blue light 1 Time difference 0 or 2 Nonlinear optical crystal Coincidence Rate Correlation time ~ (bandwidth)-1 Creation time uncontrolled boson behavior Time difference QuickTime™ and a Photo - JPEG decompressor are needed to see this picture. 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 1 trigger if n = 1 filter 1 nonlinear optical crystal shutter QuickTime™ and a Photo - JPEG decompressor are needed to see this picture. 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 1 nonlinear optical crystal SIGNAL QuickTime™ and a Photo - JPEG decompressor are needed to see this picture. Pulsed Pump Spectrum has nonzero bandwidth 1IDLER ' trigger ZeroBandwidth Filter , 0 P ' 1SIGNAL 2P d ' d C( , ') 1IDLER ' 1SIGNAL detect signal d C( 0 , ) 1SIGNAL Pure-state creation at cost of vanishing data rate Pulsed blue light trigger 1 filter Do single photons from independent SpDC sources interfere well? Need good time and frequency correlation. QuickTime™ and a Photo - JPEG decompressor are needed to see this picture. 1 random delay Coincidence Counts 1 large data rate filter 1 trigger Time difference vanishing data rate QuickTime™ and a Photo - JPEG decompressor are needed to see this picture. Goal : Generation of Pure-State Photon Pairs without using Filtering Want : C(, ') 0 () 0 ( ') 2P d ' 1 I0 d C ( , ') 1IDLER ' 1SIGNAL 1 S0 (no entanglement) Single-photon Wave-Packet States: 1 S0 d 0 ( ) 1 S signal 1 I0 d 0 ( ) 1 I idler QuickTime™ and a Photo - JPEG decompressor are needed to see this picture. Decomposition of field into Discrete Wave-Packet Modes. (Law, Walmsley, Eberly, PRL, 2000) vac d' d C(, ' ) 1 S 1 I ' vac j 1 Sj 1 j Single-photon Wave-Packet States: 1 Sj d () 1 Ij d j 1 S j () 1 I Ij (Schmidt Decomposition) QuickTime™ and a Photo - JPEG decompressor are needed to see this picture. The Schmidt Wave-Packet Modes are perfectly correlated. vac j 1 Sj 1 Ij d j () 1 I j 1 Sj d () j 1 S 1 Ij But typically it is difficult to measure, or separate, the Schmidt Modes. CS1 ( ) Mode Amplitude Functions: Mode spectra overlap. No perfect filters exist, in time and/or frequency. C S 2 ( ) filter C S 3 ( ) frequency QuickTime™ and a Photo - JPEG decompressor are needed to see this picture. Why does the state generally NOT factor? 2P d ' 1 S0 d C ( , ') 1SIGNAL 1ID LER ' 1 I0 C(, ') ' Energy conservation and phase matching typically lead to frequency correlation need to engineer the state to make it factor QuickTime™ and a Photo - JPEG decompressor are needed to see this picture. Spontaneous Parametric Down Conversion inside a Single-Transverse-Mode Optical Cavity 1 mm kI pump kP Nonlinear optical crystal with wave-guide kS the problem: DOES NOT WORK cavity FSR ~ 1/L phase-matching BW ~ 10/L Spontaneous Parametric Down Conversion inside a Distributed-Feedback Cavity • large FSR = c /(2x0.2 mm) • small phase-matching BW: 0.2 mm cavity 4 mm ~ 10 c /(4 mm) 4 mm H-Pol pump Linear-index wave-guide QuickTime™ and a Photo - JPEG decompressor are needed to see this picture. H-Pol idler V-Pol signal Linear-index Distributed-Bragg Reflectors (DBR) second-order nonlinear-optical crystal SIMPLIFIED MODEL: Half-DBR Cavity 4 mm DBR QuickTime™ and a Photo - JPEG decompressor are needed to see this picture. 0.2 mm cavity 99% mirror Reflectivity 0 =800 nm KG = 25206/mm Dn/n ~ 6x10-4 (k = 2/mm) DBR band gap cavity mode frequency/1015 QuickTime™ and a Photo - JPEG decompressor are needed to see this picture. Quantum Generation in a Dielectric-Structured Cavity: Phenomenological Treatment E(x,t) D(x,t) J(x,t) Ep (x,t)E *(x,t) 2 x 2 t Signal NL Source Pump Frequency Domain: space and frequency dependent electric permeability: (x, ) (x)n 2 ( ) % ) J(x, % ) x2 (x, ) 2 E(x, x2 (x, ) 2 u(x, ) 0 (modes) E˜ p E˜ S (x, ) 0 L QuickTime™ and a Photo - JPEG decompressor are needed to see this picture. x † ˜ ˜ ˆ E S (x, ) EVAC (x, ) uout(x, ) d ' C( ,') aI ( ') two-photon amplitude C(,') NL ˜ (x', ') u *(x',)u * (x',') dx' E p S I 0 L interaction pump field internal Signal, Idler modes QuickTime™ and a Photo - JPEG decompressor are needed to see this picture. Heisenberg Picture Schrodinger Picture vac d' d C(, ' ) 1 S 1 I ' Amplitude for Photon Pair Production: C(, ') p ( ') (, ') pump spectrum (,') NL L 0 Cavity Phase-Matching dx' uP (x', ')uS *(x',)uI * (x',') pump mode internal Signal, Idler modes QuickTime™ and a Photo - JPEG decompressor are needed to see this picture. Type-II Collinear Spontaneous Parametric Down Conversion in a second-order nonlinear, birefringent crystal H-Pol pump kP L kS Signal V-Pol kI Idler H-Pol Phase-matching (momentum conservation): r r kS kI kP / L k V H Energy conservation: S I P P red red blue phase-matching bandwidth frequency Birefringent Nonlinear Crystal, Collinear, Type-II, Bulk Phase Matched, with Double-Period Grating: S = I = P/2 QuickTime™ and a Photo - JPEG decompressor are needed to see this picture. kS + kI = kP P I,S 0 kS kI KGS/2 KGI/2 kP KTP --> KTP Crystal with Double Gratings 95% mirror 0 L 4 • grating index contrastDn / n 5 10 • crystal length L = 4 mm, giving kG 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 QuickTime™ and a Photo - JPEG decompressor are needed to see this picture. Two-Photon Amplitude C(, ’) No Grating, No Cavity ’ QuickTime™ and a Photo - JPEG decompressor are needed to see this picture. Two Gratings ’ Two Gratings ’ with Cavity ’ Two-Photon Amplitude C(, ’) Two Gratings with Cavity ’ QuickTime™ and a Photo - JPEG decompressor are needed to see this picture. ’ x Pump Spectrum ’ (hi res) ’ QuickTime™ and a Photo - JPEG decompressor are needed to see this picture. Schmidt-Mode Decomposition C(, ') NL ˜ (x', ') u * (x',)u * (x',') dx' E p S I 0 L vac d' d C(, ' ) 1 S 1 I ' vac j 1 Sj Ij 1 Ij j 1 Sj d () j 1 S 1 d j () 1 I Schmidt-mode eigenva lues for dif ferent values of cavity-mirror reflectivity 2 j=1 j=2 j=3 j=4 j=5 2 0.95 0.99 0.951 0.998 0.0196 0.0007 0.0196 0.0007 0.0044 0.0002 0.0044 0.0002 QuickTime™ and a Photo - JPEG decompressor are needed to see this picture. First Four Schmidt Modes for 95% Cavity Mirror amplitude j=1 j=2 DBR j=3 frequency j=4 frequency 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. QuickTime™ and a Photo - JPEG decompressor are needed to see this picture. QuickTime™ and a Photo - JPEG decompressor are needed to see this picture. 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 singlephoton 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 singlephoton state. • Waveguide development at Optoelectronics Research Center (Uni-Southampton, Peter Smith) QuickTime™ and a Photo - JPEG decompressor are needed to see this picture. Alternative Scheme: Single-mode squeezers combined at a beam splitter cavity 1 photon pair weak single-mode squeezed beam splitter cavity 2