Below is a short summary and detailed review of this video written by FutureFactual:
Quantum States of Light: Coherent States, Quasi-Probabilities, and Photon Statistics in Quantum Optics
Short Summary
This MIT OpenCourseWare lecture surveys quantum states of light with a focus on coherent states, quasi-probability distributions, and photon statistics. The talk explains how coherent states are defined as eigenstates of the annihilation operator, their time evolution in phase space, and why their associated quasi-probabilities are represented by P, Q, and Wigner functions. It contrasts coherent states with number states and thermal states, discusses minimum uncertainty and the circle versus ellipse in phase space, and introduces the second-order coherence function G2 as a probe of classical versus non-classical light. The session also covers how to describe photon fluctuations in a single mode, the Fano factor, and the distinction between single photons and attenuated coherent states, culminating in an outline of the Hanbury Brown–Twiss experiment and the path toward squeezed states.
Long Summary
The lecture begins by situating light within quantum mechanics, treating a single mode of the electromagnetic field as a harmonic oscillator. The speaker introduces three phase-space representations for quantum states of light: the Glauber-Sudarshan P distribution, the Husimi Q distribution, and the Wigner distribution. He explains that the P distribution is defined as a diagonal matrix element in the coherent-state basis and is a true probability distribution only for certain classical-like states, while for many quantum states it becomes highly singular or even non-existent as a bona fide probability. The Q distribution is always positive and smooth but is not a true probability distribution in the same sense because it corresponds to anti-normal ordering and contains an intrinsic smearing of the state in phase space. The Wigner distribution, although it can take negative values, provides the closest representation to a classical phase-space picture because the projections onto X and P reproduce the probability densities for quadrature components. The lecturer emphasizes that in single-mode quantum optics, the Wigner distribution is particularly informative for connecting quantum descriptions to classical phase space while acknowledging the trade-offs with its negativity in certain quantum states.
