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6.453 Quantum Optical Communication
Spring 2009
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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
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Classical Electromagnetic Fields in Free Space
! Maxwell’s Equations in Differential Form:
! Vector Potential
in Coulomb Gauge,
:
! 3-D Vector Wave Equation:
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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:
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Periodic Boundary Conditions Æ Plane Waves
! Periodic Boundary Conditions for
Cube:
! Plane Wave Solutions:
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Dimensionless Reformulation and the Hamiltonian
! Define:
! Electric and Magnetic Fields:
! Hamiltonian:
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Quantized Electromagnetic Field
! Field Operators:
! Commutators:
! Hamiltonian:
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Multi-Mode Number States and Coherent States
! Modal Number Operators:
! Modal Number States:
! Multi-Mode Number States:
! Modal Coherent States:
! Multi-Mode Coherent States:
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Coherent States are Field-Operator Eigenkets
! Classical Positive-Frequency Field Associated with
:
! Field Operator Eigenket Relation:
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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:
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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
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