Illustrated Physics
physics, drawn
Concept

Standard quantum limit — where it appears

The best precision a measurement reaches with independent quanta or with a probe that disturbs what it reads, scaling as one over the square root of the number used. Correlated states such as squeezed light or entangled atoms can beat it; uncorrelated ones cannot.

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

Four states of light, each with the same area of noise. The field of a single mode of light drawn as a point in a plane whose two axes are its two quadratures — the parts of the wave in step with a reference and a quarter-cycle out of step. The distance from the centre is the amplitude and the angle is the phase. Each state is a cloud of 400 sampled measurements with its two-standard-deviation outline, in units where the vacuum's noise is one in every direction. The vacuum is a round cloud at the centre. Steady laser light is the same round cloud moved away from the centre. Light squeezed by 4 dB is an ellipse of the same area: narrower than the vacuum by a factor of 0.63 in one direction and wider by 1.58 in the other. Pointed along the direction from the centre it is quiet in amplitude; pointed across it, quiet in phase. The sampled spreads were checked against each state's widths.

The noise pushed below the floor

A perfectly steady laser beam still flickers, by an amount set by the vacuum itself, and for most of the twentieth century that flicker was treated as the floor of any optical measurement. It is a floor only for one shape of noise. Light can be made quieter than the vacuum in one property by being made louder in another — and the price, the fragility and the use of that trade are all visible in how the noise is shaped, which is why the world's gravitational-wave detectors now run on it.

quantum · Photon A round uncertainty sheared into a thin one. The uncertainty in the direction of 100 atoms' combined spin, seen along the spin, drawn out to one standard deviation in each direction. Left: the atoms each in an independent superposition — a disk of variance N/4 = 25 in every transverse direction, so a rotation shows only once it moves the spin by √N/2 = 5.0 units. Right: after one-axis twisting, which turns the spin about the vertical axis at a rate proportional to its height, so that the upper half of the disk is pushed one way and the lower half the other (arrows). The disk becomes an ellipse with variances 1.22 and 535, its long axis tilted 12.2° from the horizontal. Its narrow direction, turned to lie along the rotation to be measured, is 12.0 dB quieter than the disk, allowing for the 11.8% the twisting costs in the length of the spin.

The atoms that measure better together

A clock read with a hundred independent atoms locates its phase no better than the scatter of a hundred coin tosses allows, because each atom answers the final question by itself. Let the atoms interact for a moment before they are read and that scatter can be shaped: the round uncertainty of their combined spin is sheared into a thin ellipse, and a phase error invisible against the coin-toss noise becomes four standard deviations wide. The gain grows with the number of atoms, and it is real only if the detector can count atoms nearly one by one.

quantum · Measurement

Named alongside it

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

Uncertainty principleAtomic clockBinomial distributionBloch sphereEntanglementGravitational wavesOptical lossQuadratureQuantum projection noiseShot noiseSpin squeezingSqueezed light

All concepts