Illustrated Physics
physics, drawn
Concept

Quantum limit — where it appears

The lowest noise a measurement or an amplifier can reach once only the discreteness of quanta and the uncertainty principle remain. An amplifier that treats both quadratures alike must add at least half a photon of noise per mode, and a laser's phase must diffuse at a rate set by spontaneous emission.

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

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 How narrow a laser's line can be, against its power. The Schawlow–Townes limit on linewidth, πhνΓ²n/P with Γ the cavity linewidth and n the inversion factor, against output power on logarithmic axes, for a helium–neon laser with a 30 cm cavity of finesse about 300 (Γ = 1.6 MHz) and for a semiconductor laser a third of a millimetre long (Γ about 30 GHz, n = 2), the latter also with Henry's linewidth enhancement 1 + α² for α = 4 (dashed). At a milliwatt the helium–neon laser's limit is 0.0025 Hz — millihertz, a coherence length of tens of millions of kilometres — and the semiconductor laser's 7.2·10⁵ Hz, 1.2·10⁷ Hz with the enhancement. Both fall in proportion to one over the power: more photons in the mode make each spontaneous kick a smaller fraction of the field. The square of the cavity linewidth is why a short, lossy diode cavity has a line ten billion times broader.

The width a perfect laser still has

A laser's light is the nearest thing to a single pure frequency that anything makes, and it is still not one. Every photon spontaneously emitted into the lasing mode adds a kick of random phase, and because nothing in a laser cares what its phase is, nothing pulls the phase back: it wanders, and a wandering phase is a line of finite width. Schawlow and Townes worked out how wide in 1958, before any laser had been built. For a milliwatt helium–neon laser the answer is a few thousandths of a hertz, a coherence length a quarter of the way to the Sun — and no real laser of that kind has ever come close, because mirrors move. For a semiconductor laser the answer is megahertz, and the measured lines were wider still, by a factor nobody expected.

optics · Coherence

Named alongside it

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

CoherenceHeterodyneCoherence lengthDoppler effectInterferenceLaserLinewidthLocal oscillatorQuadratureRandom phaseShot noiseSpontaneous emission

All concepts