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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 13, 2008 6.453 Quantum Optical Communication Lecture 17 Jeffrey H. Shapiro Optical and Quantum Communications Group www.rle.mit.edu/qoptics 6.453 Quantum Optical Communication - Lecture 17 ! Announcements ! Pick up graded mid-term exam, lecture notes, slides ! Quantization of the Electromagnetic Field ! Maxwell’s equations ! Plane-wave mode expansions ! Multi-mode number states and coherent states 2 www.rle.mit.edu/qoptics Classical Electromagnetic Fields in Free Space ! Maxwell’s Equations in Differential Form: ! Vector Potential in Coulomb Gauge, : ! 3-D Vector Wave Equation: 3 www.rle.mit.edu/qoptics Classical Electromagnetic Waves in Free Space ! Separation of Variables in the 3-D Vector Wave Equation: ! Separation Condition and Separation Constant: ! Helmholtz Equation and Harmonic Oscillator Equation: 4 www.rle.mit.edu/qoptics Periodic Boundary Conditions Æ Plane Waves ! Periodic Boundary Conditions for Cube: ! Plane Wave Solutions: 5 www.rle.mit.edu/qoptics Dimensionless Reformulation and the Hamiltonian ! Define: ! Electric and Magnetic Fields: ! Hamiltonian: 6 www.rle.mit.edu/qoptics Quantized Electromagnetic Field ! Field Operators: ! Commutators: ! Hamiltonian: 7 www.rle.mit.edu/qoptics Multi-Mode Number States and Coherent States ! Modal Number Operators: ! Modal Number States: ! Multi-Mode Number States: ! Modal Coherent States: ! Multi-Mode Coherent States: 8 www.rle.mit.edu/qoptics Coherent States are Field-Operator Eigenkets ! Classical Positive-Frequency Field Associated with : ! Field Operator Eigenket Relation: 9 www.rle.mit.edu/qoptics Simplified Model: Photodetection Theory Prelude ! ! ! ! ! ! Assumption 1: Only one polarization is excited Assumption 2: Only -going plane wave is excited Assumption 3: Only narrow bandwidth about is excited Assumption 4: Work with photon-units baseband operator Assumption 5: Quantization interval Fourier-integral field operator relationships ! Field-Operator Commutators: 10 www.rle.mit.edu/qoptics Coming Attractions: Mid-Term + Lectures 18, 19 ! Lectures 18, 19: Continuous-Time Photodetection ! Semiclassical theory: Poisson-distributed shot noise ! Quantum theory: Photon-flux operator measurement ! Continuous-time signatures of non-classical light 11 www.rle.mit.edu/qoptics