Lecture 21 Jeffrey H. Shapiro Optical and Quantum Communications - - PDF document

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Optical and Quantum Communications Group www.rle.mit.edu/qoptics November 29, 2016

6.453 Quantum Optical Communication Lecture 21 Jeffrey H. Shapiro

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6.453 Quantum Optical Communication - Lecture 21 § Announcements

§ Pick up lecture notes, slides

§ Nonlinear Optics of Interactions

§ Coupled-mode equations for parametric downconversion § Phase-matching for efficient interactions § Classical and quantum solutions § Gaussian-state characterization

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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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Coupled Equations for Plane-Wave Modes § Monochromatic Pump, Signal, and Idler Electric Fields:

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

§ Photon-Units Coupled-Mode Equations:

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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Quantum Coupled-Mode Equations § Strong, Monochromatic, Coherent-State Pump § Positive-Frequency Signal and Idler Field Operators: § Quantum Coupled-Mode Equations:

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Quantum Input-Output Relation § Two-Mode Bogoliubov Relation

where

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Gaussian-State Characterization § Signal and Idler at are in Vacuum States § Signal and Idler at are in Zero-Mean Gaussian States § Baseband Signal and Idler Field Operators: § Non-Zero Covariance Functions:

• (n)

KSS (τ) =

(n)

dω KII (−τ) = ν 2π | (ω)|2ejωτ

• (p)

dω KSI (τ) =

• µ(

2π −ω)ν(−ω)ejω(τ+∆k l)

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Operation in the Low-Gain Regime § Low-Gain Regime: § Approximate Bogoliubov Parameters: § Normally-Ordered and Phase-Sensitive Spectra:

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Type-II Optical Parametric Amplifier § Doubly-Resonant Operation at Frequency Degeneracy § Normally-Ordered and Phase-Sensitive Covariances:

χ

(2) SIGNAL, ω

/2

P PUMP, ω P IDLER, ω

/2

P 50/50

PUMP, IDLER, SIGNAL,

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Quadrature Noise Squeezing § Homodyne Detection of 45° Polarization (Signal + Idler)

spectrum analyzer

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Quadrature Noise Squeezing: Quantum Efficiency 1 § Homodyne Detection of 45° Polarization (Signal + Idler)

G2 = 0.1

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Coming Attractions: Lecture 22 § Lecture 22: Quantum Signatures from Parametric Interactions

§ Hong-Ou-Mandel dip produced by parametric downconversion § Polarization entanglement produced by parametric downconversion § Photon twins from parametric amplifiers

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6.453 Quantum Optical Communication

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