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

November 29, 2016 6.453 Quantum Optical Communication Lecture 21 Jeffrey H. Shapiro Optical and Quantum Communications Group www.rle.mit.edu/qoptics 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 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 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: 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 4 www.rle.mit.edu/qoptics 2

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: 5 www.rle.mit.edu/qoptics Quantum Coupled-Mode Equations § Strong, Monochromatic, Coherent-State Pump § Positive-Frequency Signal and Idler Field Operators: § Quantum Coupled-Mode Equations: 6 www.rle.mit.edu/qoptics 3

Quantum Input-Output Relation § Two-Mode Bogoliubov Relation where 7 www.rle.mit.edu/qoptics 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: d ω � ( n ) ( n ) 2 π | ( ω ) | 2 e j ωτ K SS ( τ ) = K II ( − τ ) = ν d ω � ( p ) � − ω ) ν ( − ω ) e j ω ( τ + ∆ k l ) K SI ( τ ) = µ ( 2 π 8 www.rle.mit.edu/qoptics 4

Operation in the Low-Gain Regime § Low-Gain Regime: § Approximate Bogoliubov Parameters: § Normally-Ordered and Phase-Sensitive Spectra: 9 www.rle.mit.edu/qoptics Type-II Optical Parametric Amplifier § Doubly-Resonant Operation at Frequency Degeneracy SIGNAL, ω /2 P IDLER, � (2) χ PUMP, ω P PUMP, � IDLER, ω /2 P 50/50 SIGNAL, � § Normally-Ordered and Phase-Sensitive Covariances: 10 www.rle.mit.edu/qoptics 5

Quadrature Noise Squeezing § Homodyne Detection of 45° Polarization (Signal + Idler) spectrum analyzer 11 www.rle.mit.edu/qoptics Quadrature Noise Squeezing: Quantum Efficiency 1 § Homodyne Detection of 45° Polarization (Signal + Idler) G 2 = 0.1 � 12 www.rle.mit.edu/qoptics 6

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 13 www.rle.mit.edu/qoptics 7

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