Lecture 20 Jeffrey H. Shapiro Optical and Quantum Communications - PDF document

November 22, 2016 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 1

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 2

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 3

Coupled-Mode Equations for Downconversion § Photon Fission: § Signal and Idler Equations for : j ω S χ (2) A P d A S ( z ) I ( z ) e j ( k P − k S − k I ) z = 2 cn S ( ω S ) A ∗ d z j ω I χ (2) A P d A I ( z ) S ( z ) e j ( k P − k S − k I ) z = 2 cn I ( ω I ) A ∗ d z 7 www.rle.mit.edu/qoptics Conversion to Photon-Units Fields § Time-Average Powers on Photodetector Active Area : 0 n m ( ⇥ m ) A A c � m ( z ) | 2 , S m ( z ) = | for m = S, I, P 2 § Photon-Units Fields: § Photon-Units Coupled-Mode Equations: d A S ( z ) I ( z ) e j ∆ kz = j κ A ∗ d z d A I ( z ) S ( z ) e j ∆ kz = j κ A ∗ d z 8 www.rle.mit.edu/qoptics 4

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 5

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