Lecture Notes

SES # TOPICS NOTES SLIDES
1

Introduction

Optical eavesdropping tap, action at a distance, and long-distance quantum state transmission

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2

Dirac-notation quantum mechanics

Quantum systems, states as ket vectors, state evolution via Schrödinger's equation, and quantum measurements

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3

Dirac-notation quantum mechanics (cont.)

Quantum measurement statistics, Schrödinger picture versus Heisenberg picture, and Heisenberg Uncertainty Principle

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4

Quantum harmonic oscillator

Quantization of a classical LC circuit, annihilation and creation operators, and energy eigenstates

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5

Quantum harmonic oscillator (cont.)

Measurement statistics and transition to the classical limit of noiseless oscillation

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6

Quantum harmonic oscillator (cont.)

Quadrature-representation wave functions, minimum uncertainty-product states, squeezed states and their measurement statistics

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7

Quantum harmonic oscillator (cont.)

Quadrature measurement statistics and phase space, characteristic functions and Wigner distribution, and positive operator-valued measurement of â

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8

Quantum harmonic oscillator (cont.)

Positive operator-valued measurement

Single-mode photodetection

Contrasting semiclassical and quantum theories of direct detection and balanced homodyne detection in ideal photodetectors

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9

Single-mode photodetection (cont.)

Optical heterodyne detection and the â positive operator-valued measurement

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10

Single-mode photodetection (cont.)

Signatures of non-classical light and the squeezed-state waveguide tap

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11

Single-mode photodetection (cont.)

Single-mode photodetection with inefficient detectors

Single-mode linear systems

Classical and quantum theories of linear attenuation and linear amplification

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12

Single-mode and two-mode linear systems

Quantum mechanics of attenuators and amplifiers; phase-insensitive and phase-sensitive amplifiers

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13

Two mode linear systems (cont.)

Dual parametric amplifier, photon twins, and entanglement

Four-mode quantum systems

Polarization entanglement and qubit teleportation

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14

Teleportation

Polarization entanglement and qubit teleportation; and quadrature entanglement and continuous-variable teleportation

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15

Teleportation (cont.)

Continuous-variable teleportation

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16

Quantum cryptography

One-time pad classical cryptography, Bennett-Brassard 1984 quantum key distribution protocol, Clauser-Home-Shimony-Holt form of Bell's inequality, and Ekert protocol quantum key distribution

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17

Quantization of the electromagnetic field

Maxwell's equations, plane-wave mode expansions, and multi-mode number states and coherent states

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18

Continuous-time photodetection

Poisson shot-noise semiclassical model, photon-flux operator measurement quantum model, and direct-detection signatures of non-classical light

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19

Continuous-time photodetection (cont.)

Noise spectral densities in direct detection, semiclassical and quantum theories of coherent detection, and coherent-detection signatures of non-classical light

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20

Nonlinear optics

Maxwell's equations with a nonlinear polarization, coupled-mode equations for parametric downconversion, phase-matching for efficient interactions, and classical theory of optical parametric amplification in second-order nonlinear crystals

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21

Nonlinear optics (cont.)

Coupled-mode equations for parametric downconversion, continuous-time field operator theory of spontaneous parametric downconversion and Gaussian-state characterization

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22

Quantum signatures from parametric interactions

Quantum interference, photon indistinguishability, Hong-Ou-Mandel interferometry, the biphoton, generation of polarization entanglement, photon twins from an optical parametric amplifier

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23

More quantum optical applications

Binary optical communication with squeezed states, phase-sensing interferometry with squeezed states, super-dense coding with entangled states, and quantum lithography with "N00N" states

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