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6.453 Quantum Optical Communication
Spring 2009
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December 2, 2008
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
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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
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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:
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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:
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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
PUMP, w
PUMP,
P
c
SIGNAL,
w P /2
IDLER,
w P /2
IDLER,
(2)
50/50
SIGNAL,
! Normally-Ordered and Phase-Sensitive Covariances:
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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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