MIT OpenCourseWarehttp://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.September 18, 2008Optical and Quantum Communications Groupwww.rle.mit.edu/qoptics6.453 Quantum Optical CommunicationLecture 5Jeffrey H. Shapiro2www.rle.mit.edu/qoptics6.453 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 statistics3www.rle.mit.edu/qopticsQuantum Harmonic Oscillator: Reprise! Operator-Valued Dynamics:! Hamiltonian and the Number Operator:! Heisenberg Uncertainty Principle:4www.rle.mit.edu/qopticsQuantum Harmonic Oscillator: Reprise! Number Kets:! Orthonormal:! Complete:! Diagonal representation of number operator:! Annihilation and creation operators:5www.rle.mit.edu/qopticsClassical versus Quantum Quadrature Behavior! Classical Oscillator: Noiseless ! Quantum Oscillator: NoisyHow can we get to the classical limit?6www.rle.mit.edu/qopticsQuadrature-Statistics of Number Kets! Quadrature-Measurement Mean Values:! Quadrature-Measurement Variances:! Non-Minimum Quadrature-Uncertainty Product:7www.rle.mit.edu/qopticsClassical versus Quantum Quadrature Behavior! Classical Oscillator: Noiseless ! Quantum Oscillator: StateHow can we get to the classical limit?8www.rle.mit.edu/qopticsCoherent States! Eigenkets of the Annihilation Operator:! Number-ket representation:! Normalized, non-orthogonal:! Overcomplete:9www.rle.mit.edu/qopticsCoherent-State Measurement Statistics! Number-Operator Measurement:! Quadrature-Operator Measurements:! Minimum Uncertainty-Product with Equal Variances10www.rle.mit.edu/qopticsClassical versus Quantum Quadrature Behavior! Classical Oscillator: Noiseless ! Quantum Oscillator: StateTHIS is how we get to the classical limit!11www.rle.mit.edu/qopticsComing 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
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