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.October 2, 2008Optical and Quantum Communications Groupwww.rle.mit.edu/qoptics6.453 Quantum Optical CommunicationLecture 8Jeffrey H. Shapiro2www.rle.mit.edu/qoptics6.453 Quantum Optical Communication — Lecture 8! Announcements! Pick up problem set 3 graded, lecture notes, slides! Quantum Harmonic Oscillator! Positive operator-valued measurement (POVM) of! Reconciling POVMs and observables! Single-Mode Photodetection! Direct Detection — semiclassical versus quantum! Homodyne Detection — semiclassical versus quantum3www.rle.mit.edu/qopticsMeasuring the Operator: Definition! Definition: Measurement of the Operator! yields an outcome that is a complex number! joint probability density for getting this outcome is! Consistency Checks:4www.rle.mit.edu/qopticsMeasuring the Operator: Characteristic Function! Joint Characteristic Function for the Measurement! Anti-Normally Ordered Characteristic Function of the State5www.rle.mit.edu/qopticsMeasuring the Operator: Examples! Number State :! Coherent State :! Squeezed State :6www.rle.mit.edu/qopticsMeasuring the Operator: Summary7www.rle.mit.edu/qopticsReconciling POVMs with Observables for! Measure Two Commuting Observables on! Signal in State , Ancilla in Vacuum State! Commuting Observables are Real and Imaginary Parts of:8www.rle.mit.edu/qopticsReal Photodetection Systems9www.rle.mit.edu/qopticsIdeal Photodetection System10www.rle.mit.edu/qopticsSingle-Mode Quantized Electromagnetic Field! Photon-Units Field Operator on Constant- Plane:for! Photon Annihilation and Creation Operators:with canonical commutation relation11www.rle.mit.edu/qopticsDirect Detection: Semiclassical versus Quantum! Single-Mode Photon Counter: Semiclassical Description! Single-Mode Photon Counter: Quantum Description12www.rle.mit.edu/qopticsSingle-Mode Balanced Homodyne Receiver! Semiclassical Description:! Quantum Description:13www.rle.mit.edu/qopticsComing Attractions: Lectures 9 and 10! Lecture 9:Single-Mode Photodetection! Heterodyne Detection — semiclassical versus quantum! Realizing the measurement! Lecture 10:Single-Mode Photodetection! Signatures of non-classical light! Squeezed-state waveguide
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