Lecture 19 Jeffrey H. Shapiro Optical and Quantum Communications - PDF document

November 17, 2016 6.453 Quantum Optical Communication Lecture 19 Jeffrey H. Shapiro Optical and Quantum Communications Group www.rle.mit.edu/qoptics 6.453 Quantum Optical Communication - Lecture 19 § Announcements § Pick up lecture notes, slides § Continuous-Time Photodetection § Noise spectral densities in direct detection § Semiclassical theory of coherent detection § Quantum theory of coherent detection § Coherent-detection signatures of non-classical light 2 www.rle.mit.edu/qoptics 1

Semiclassical versus Quantum Photodetection § Semiclassical Theory: Given § is an inhomogeneous Poisson Impulse Train § Rate function § Quantum Theory: 3 www.rle.mit.edu/qoptics Stationary Statistics for Continuous-Wave Sources § Stationary Mean and Covariance Functions: § Semiclassical Photodetection: § Quantum Photodetection: 4 www.rle.mit.edu/qoptics 2

Photocurrent Noise Spectral Density § Photocurrent Noise Spectral Density: § Propagation Through a Linear Time-Invariant Filter: § Physical Interpretation: = mean-squared fluctuation strength per unit bilateral bandwidth (in Hz) in frequency ω components of 5 www.rle.mit.edu/qoptics Direct-Detection Signatures of Non-Classical Light § Semiclassical Theory: § Quantum Theory: § Sub-Shot-Noise Non-Classical Signature: 6 www.rle.mit.edu/qoptics 3

Balanced Homodyne Detection LPF � § Signal = , LO = § Low-Pass Filter: 7 www.rle.mit.edu/qoptics Balanced Homodyne Detection (Within Passband) § Semiclassical Statistics in Strong Local Oscillator Limit: § Gaussian-process local oscillator shot noise: § Quantum Statistics in Strong Local Oscillator Limit: § Gaussian-process sub-unity quantum efficiency noise: 8 www.rle.mit.edu/qoptics 4

Balanced Heterodyne Detection BPF � § Signal = § LO = § Bandpass Filter: 9 www.rle.mit.edu/qoptics Balanced Heterodyne Detection (Within Passband) § Semiclassical Statistics in Strong Local Oscillator Limit: § Gaussian-process local oscillator shot noise: § Quantum Statistics in Strong Local Oscillator Limit: § Gaussian-process sub-unity quantum efficiency noise: 10 www.rle.mit.edu/qoptics 5

Coherent-Detection Non-Classical Light Signatures § Semiclassical Theory (within filter passband): § Quantum Theory (within filter passband): S i hom i hom ( ω ) ≥ S i η i η ( ω ) = q 2 η (1 − η ) P LO ~ ω 0 § Sub-Shot-Noise Spectra (in passband) are Non-Classical: 11 www.rle.mit.edu/qoptics Coming Attractions: Lecture 20 § Lecture 20: Nonlinear Optics of Interactions § Maxwell ’ s equations with a nonlinear polarization § Coupled-mode equations for parametric downconversion § Phase-matching for efficient interactions 12 www.rle.mit.edu/qoptics 6

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