This is an archived course. A more recent version may be available at ocw.mit.edu.

Calendar

SES # TOPICS KEY DATES
1

Introduction

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

 Problem set 1 out
2

Dirac-notation quantum mechanics

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

  
3

Dirac-notation quantum mechanics (cont.)

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

Problem set 1 due

Problem set 2 out
4

Quantum harmonic oscillator

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

  
5

Quantum harmonic oscillator (cont.)

Measurement statistics and transition to the classical limit of noiseless oscillation

Problem set 2 due

Problem set 3 out
6

Quantum harmonic oscillator (cont.)

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

  
7

Quantum harmonic oscillator (cont.)

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

Problem set 3 due

Problem set 4 out
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

  
9

Single-mode photodetection (cont.)

Optical heterodyne detection and the â positive operator-valued measurement

Problem set 4 due

Problem set 5 out
10

Single-mode photodetection (cont.)

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

Problem set 5 due

Problem set 6 out
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

 Term paper guidelines out
12

Single-mode and two-mode linear systems

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

Problem set 6 due

Problem set 7 out
13

Two mode linear systems (cont.)

Dual parametric amplifier, photon twins, and entanglement

Four-mode quantum systems

Polarization entanglement and qubit teleportation

  
14

Teleportation

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

Problem set 7 due

Problem set 8 out
15

Teleportation (cont.)

Continuous-variable teleportation

  
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

 Problem set 8 due
  Mid-term quiz Term paper proposal due
17

Quantization of the electromagnetic field

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

  
18

Continuous-time photodetection

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

  
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

  
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

  
21

Nonlinear optics (cont.)

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

  
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

  
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

 Term paper due