Illustrated Physics
physics, drawn
Concept

Coincidence — where it appears

The simultaneous detection of particles at two or more detectors within a short time window. Counting coincidences rather than single clicks is how correlations between photons are measured, and a dip in coincidences is the signature of two-photon interference.

Named by 3 essays across 2 fields — each of them below, with the objects they name alongside it.

Three sources, and the number that separates them. The chance of detecting a second photon a delay τ after a first, divided by the chance if the two were independent, for three kinds of light. At long delay every curve is one, which is what independence means. At zero delay they are 2, 1 and 0, and those three numbers are three different physical situations. Thermal light is bunched: its intensity fluctuates, and a photon is more likely to be found where the intensity happened to be high, so it arrives with company for as long as the fluctuation lasts — 4 nanoseconds here. A laser is flat, because a coherent state has no intensity fluctuation to correlate with. And a single emitter is antibunched: it gives zero, exactly, because after emitting it is in its ground state and cannot emit again until it has been re-excited, which takes 12 nanoseconds. The zero is the important one. Every classical field, of every possible intensity distribution, has g²(0) at least one — the inequality follows from the fact that the mean square of a real positive quantity is at least the square of its mean. A measurement below one is not merely evidence for photons; it is a result no wave theory can produce.

The experiment a wave cannot pass

The photoelectric effect is offered everywhere as the proof that light is quantised, and it is not one — a classical wave falling on quantised matter reproduces every feature of it. The measurement that no wave can pass is a different one: send single photons at a beam splitter and count how often both detectors fire.

quantum · Photon Three identical photons in a three-way splitter: some outcomes are forbidden. One photon enters each input of a symmetric three-way splitter, which sends each photon to each output with equal probability. Across: the ten ways three photons can leave, written as how many leave by each output. Bars, for each outcome: photons that can be told apart, identical photons, and identical fermions. Distinguishable photons spread over all ten, as independent coins would. Identical photons never produce 210, 201, 120, 102, 021, 012 — the 6 outcomes whose output labels do not add to a multiple of three — and pile into the rest: 300 with 0.222, 111 with 0.333, 030 with 0.222, 003 with 0.222. Identical fermions leave one per output every time (probability 1.000). Each probability is a sum of amplitudes over the distinct ways to reach the outcome, and each set sums to one.

The outcomes identical photons refuse

Two identical photons meeting at a beam splitter always leave together, and that one fact carries three more. No classical light can empty the coincidence dip more than halfway, so the depth is a test of what light is; the depth measures how identical two photons are, however they differ; and with three photons in a three-way splitter whole classes of outcome become impossible — the first case of a sum over paths that no known algorithm can evaluate quickly as the photons multiply.

quantum · Photon The mass law: how much sound a limp wall stops. The transmission loss of a wall that only has mass — no stiffness — for sound arriving square-on, against frequency on a logarithmic axis, for surface masses of 10 kg/m², 20 kg/m², 40 kg/m². It is 10 log(1 + (ωm/2ρc)²) decibels. At 500 Hz, 10 kg/m² stops 31.6 dB, 20 kg/m² stops 37.6 dB, 40 kg/m² stops 43.6 dB. Doubling the mass or the frequency adds six decibels, and nothing else about the wall matters: it is the wall's inertia, set against air's characteristic impedance ρc = 413 rayl, that turns the sound back.

The wall that stops sound by its weight

A wall between two rooms keeps out sound not by absorbing it but by being hard to shake. The sound's pressure pushes the wall back and forth, the moving wall becomes a loudspeaker on the far side, and how much gets through depends almost entirely on the wall's mass per square metre against the frequency: six decibels more for every doubling of either. Read as impedance, a wall is a mass placed in series with the air, and the same reading explains the frequency at which a stiff pane of glass nearly vanishes and why two thin walls with a gap beat one thick one.

waves · Impedance

Named alongside it

The objects these essays reach for when they reach for this one.

Beam splitterPhotonAcoustic impedanceAntibunchingBending waveBosonBoson samplingCauchy schwarzDecibelIndistinguishabilityPermanentPhotoelectric effect

All concepts