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6.453 Quantum Optical Communication
Spring 2009
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September 18, 2008
6.453 Quantum Optical Communication
Lecture 5
Jeffrey H. Shapiro
Optical and Quantum Communications Group
www.rle.mit.edu/qoptics
6.453 Quantum Optical Communication — Lecture 5
! Announcements
! Turn in problem set 2
! Pick up problem set 2 solution, problem set 3, lecture notes, slides
! Quantum Harmonic Oscillator
! Number measurements versus quadrature measurements
! Coherent states and their measurement statistics
2
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Quantum Harmonic Oscillator: Reprise
! Operator-Valued Dynamics:
! Hamiltonian and the Number Operator:
! Heisenberg Uncertainty Principle:
3
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Quantum Harmonic Oscillator: Reprise
! Number Kets:
! Orthonormal:
! Complete:
! Diagonal representation of number operator:
! Annihilation and creation operators:
4
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Classical versus Quantum Quadrature Behavior
! Classical Oscillator: Noiseless
! Quantum Oscillator: Noisy
How can we get to the classical limit?
5
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Quadrature-Statistics of Number Kets
! Quadrature-Measurement Mean Values:
! Quadrature-Measurement Variances:
! Non-Minimum Quadrature-Uncertainty Product:
6
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Classical versus Quantum Quadrature Behavior
! Classical Oscillator: Noiseless
! Quantum Oscillator:
State
How can we get to the classical limit?
7
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Coherent States
! Eigenkets of the Annihilation Operator:
! Number-ket representation:
! Normalized, non-orthogonal:
! Overcomplete:
8
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Coherent-State Measurement Statistics
! Number-Operator Measurement:
! Quadrature-Operator Measurements:
! Minimum Uncertainty-Product with Equal Variances
9
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Classical versus Quantum Quadrature Behavior
! Classical Oscillator: Noiseless
! Quantum Oscillator:
State
THIS is how we get to the classical limit!
10
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Coming Attractions: Lectures 6 and 7
! Lecture 6:
Quantum Harmonic Oscillator
! Squeezed states and their measurement statistics
! Probability operator-valued measurement of
! Lecture 7:
Single-Mode Photodetection
! Direct Detection
! Homodyne Detection
11
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