Illustrated Physics
physics, drawn
Concept

Quadrature — where it appears

Two components of an oscillation a quarter of a cycle apart, such as the cosine and sine parts of a wave. Together they fix its amplitude and phase; a phase-sensitive detector measures one quadrature at a time, and in quantum optics the two obey an uncertainty relation.

Named by 3 essays across 2 fields — 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 strong oscillator lifts a picowatt to the quantum limit. The signal-to-noise ratio for detecting a 1 pW signal at 1.55 µm in a 1 MHz bandwidth, with a detector of 80 per cent quantum efficiency whose amplifier adds 2 pA/√Hz of noise, against the power of the local oscillator. Detected directly, the signal is 66 dB below the amplifier's noise. Heterodyned, it rises with the oscillator's power — −3.3 dB with a microwatt, 7.4 dB with a hundred — until the oscillator's own shot noise swamps the amplifier's, above about 12 µW, and then it stops rising at 8.0 dB: ηPₛ/(hνB), the number of detected signal photons per resolution time, which no receiver can beat. A stronger oscillator raises the signal and its own noise together.

The faint light a bright one makes measurable

A photodetector does not respond to a light wave's field; it responds to the square of it. Shine a strong beam onto the detector together with a weak one at a slightly different frequency, and the square contains a term that is the weak field multiplied by the strong one — oscillating at the difference frequency, carrying the weak light's phase, and as large as the strong beam cares to make it. That product lifts a picowatt out of an amplifier's noise to the limit set by counting photons, turns an optical frequency shift into a radio one, and carries with it a quantum price that decides why radio telescopes and optical telescopes are built so differently.

optics · Coherence What an amplifier does to a signal's uncertainty. A signal drawn in the plane of its two quadratures — the in-phase and out-of-phase parts of a wave — as a disc one standard deviation across: a coherent input (black), with the vacuum's own uncertainty; and three outputs at a gain of 4: what a noiseless amplifier would give, the input disc scaled up by √G (dashed), which quantum mechanics forbids; what the least noisy phase-insensitive amplifier gives (blue), the same centre with a disc 1.323 times wider again; and what a phase-sensitive amplifier gives (red), the in-phase quadrature stretched by √G and the other squeezed by 1/√G, with no noise added. Referred back to the input, the phase-insensitive amplifier has added 0.375 of a quantum of noise; the signal's distance from the origin, measured in its own spread, has fallen by 0.756.

The noise every amplifier must add

An amplifier that magnifies a signal without caring about its phase must also add noise, and not because of hot transistors or bad design. However perfect it is, it adds at least half a quantum of noise referred to its input — exactly as much as the vacuum fluctuations the signal already carried — so a faint coherent signal always leaves with half its signal-to-noise ratio. The reason is the same rule that makes position and momentum uncertain, applied to the two halves of a wave, and an amplifier that broke it would be a machine for copying quantum states.

quantum · Uncertainty

Named alongside it

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

Shot noiseUncertainty principleAmplifierCoherenceCoherent stateCommutatorDoppler effectGravitational wavesHeterodyneInterferenceLocal oscillatorNo-cloning

All concepts