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

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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,

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Optical and Quantum Communications Group www.rle.mit.edu/qoptics November 22, 2016

6.453 Quantum Optical Communication Lecture 20 Jeffrey H. Shapiro

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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

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www.rle.mit.edu/qoptics 3

Second-Order Nonlinear Optics § Spontaneous Parametric Downconversion

§ Strong pump at frequency § No input at signal frequency § No input at idler frequency § Nonlinear mixing in crystal produces signal and idler outputs

pump signal idler

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Classical Electromagnetics in Nonlinear Medium § Maxwell’s Equations in a Dielectric Medium: § Constitutive Relation: § Wave Equation for -going Plane Waves:

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Pump, Signal, and Idler Plane-Wave Modes § Assume Monochromatic Pump, Signal, and Idler:

§ Non-depleting pump § Slowly-varying signal and idler complex amplitudes

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Linear and Nonlinear Polarization Terms § Constitutive Law for Second-Order Nonlinear Crystal:

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Coupled-Mode Equations for Downconversion § Photon Fission: § Signal and Idler Equations for :

dAS(z) dz = j ωSχ(2)AP 2cnS(ωS) A∗

I(z)ej(kP −kS−kI)z

dAI(z) dz = j ωIχ(2)AP 2cnI(ωI) A∗

S(z)ej(kP −kS−kI)z

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Conversion to Photon-Units Fields § Time-Average Powers on Photodetector Active Area : § Photon-Units Fields: § Photon-Units Coupled-Mode Equations:

c Sm(z) =

0nm(⇥m)A A

2 |

m(z)|2,

for m = S, I, P dAS(z) = jκA∗ dz

I(z)ej∆kz

dAI(z) = jκA∗ dz

S(z)ej∆kz

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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:

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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

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