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MIT OpenCourseWare http://ocw.mit.edu 6.453 Quantum Optical Communication Spring 2009 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. November 25, 2008 6.453 Quantum Optical Communication Lecture 20 Jeffrey H. Shapiro Optical and Quantum Communications Group www.rle.mit.edu/qoptics 6.453 Quantum Optical Communication - Lecture 20 ! Announcements ! Pick up lecture notes, slides ! Nonlinear Optics of ! ! ! ! Interactions Maxwell’s equations with a nonlinear polarization Coupled-mode equations for parametric downconversion Phase-matching for efficient interactions Classical solutions 2 www.rle.mit.edu/qoptics Second-Order Nonlinear Optics ! Spontaneous Parametric Downconversion signal pump ! ! ! ! idler Strong pump at frequency No input at signal frequency No input at idler frequency Nonlinear mixing in crystal produces signal and idler outputs 3 www.rle.mit.edu/qoptics Classical Electromagnetics in Nonlinear Medium ! Maxwell’s Equations in a Dielectric Medium: ! Constitutive Relation: ! Wave Equation for -going Plane Waves: 4 www.rle.mit.edu/qoptics Pump, Signal, and Idler Plane-Wave Modes ! Assume Monochromatic Pump, Signal, and Idler: ! Non-depleting pump ! Slowly-varying signal and idler complex amplitudes 5 www.rle.mit.edu/qoptics Linear and Nonlinear Polarization Terms ! Constitutive Law for Second-Order Nonlinear Crystal: 6 www.rle.mit.edu/qoptics Coupled-Mode Equations for Downconversion ! Photon Fission: ! Signal and Idler Equations for : 7 www.rle.mit.edu/qoptics Conversion to Photon-Units Fields ! Time-Average Powers on Photodetector Active Area : ! Photon-Units Fields: ! Photon-Units Coupled-Mode Equations: 8 www.rle.mit.edu/qoptics Type-II Phase Matched Operation at Degeneracy ! Phase Matching for Efficient Coupling: ! Conservation of photon momentum: ! Type-II system: ! Operation at Frequency Degeneracy: ! Classical Input-Output Relation: 9 www.rle.mit.edu/qoptics Coming Attractions: Lectures 21and 22 ! Lecture 21: Nonlinear Optics of Interactions ! Quantum coupled-mode equations for parametric downconversion ! Two-mode Bogoliubov relation ! Gaussian-state characterization Quantum Signatures from Parametric Interactions ! Squeezed states from parametric amplifiers ! Lecture 22: Quantum Signatures from Parametric Interactions ! Photon twins from parametric amplifiers ! Hong-Ou-Mandel dip produced by parametric downconversion ! Polarization entanglement produced by parametric downconversion 10 www.rle.mit.edu/qoptics