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.
Medium Summary
In this lecture from MIT OpenCourseWare, Colin discusses how light can be treated as a quantum harmonic oscillator and how to describe its quantum states using phase space distributions. The instructor emphasizes several representations for phase-space densities: the Glauber-Sudarshan P representation, the Husimi Q distribution, and the Wigner distribution. He explains that the P representation is highly singular for many states, the Q distribution is always positive and smooth, and the Wigner distribution best mirrors classical phase-space intuition but can take negative values, signaling non-classicality. A central focus is the coherent state, defined as an eigenstate of the annihilation operator with complex eigenvalue α. Coherent states are minimum uncertainty states, their electric field expectation value is proportional to α, and their phase-space distribution is a blurred circle of area on the order of unity, illustrating why they are the closest quantum analogue to a classical electromagnetic wave. The discussion then moves to number states and the complementarity of photon number and phase, noting that number states have a fixed energy but a completely uncertain phase. Time evolution for a single mode shows a rotation in phase space, preserving the circle unless squeezing is introduced. The lecture introduces the second-order coherence function G2, explaining its classical interpretation as an intensity correlation and contrasting it with the quantum expectation value, where G2 can drop below 1, especially for non-classical states like number states. Attenuation of coherent states is discussed to illustrate that reducing a laser beam does not produce a true single-photon state, a point demonstrated by the photon-number distribution of attenuated coherent states versus the fixed N=1 number state. The session concludes with methods to generate true single photons, including heralded schemes with atoms and cavities, and introduces the Henbury Brown-Twiss experiment as a foundational tool for measuring quantum correlations.
