coherent state

A coherent state is the quantum state of an oscillator that behaves most like a classical swinging mass. Unlike a Fock state, which sits frozen on a single energy rung, a coherent state is a particular blend of many rungs, arranged so that its wave packet keeps a fixed shape and slides back and forth exactly as a classical oscillator would. It is the closest a quantum oscillator gets to looking ordinary.

Its defining trick is that it is an eigenstate of the annihilation operator: removing one quantum leaves the state essentially unchanged, just rescaled. This is why a coherent state has no sharp number of quanta — the count follows a Poisson distribution — yet it has a well-defined amplitude and phase. It also holds the minimum uncertainty allowed by Heisenberg's principle, evenly split between position and momentum, and keeps that minimum as it evolves without spreading out.

Coherent states are the natural description of laser light, where photons pour out in a stable, classical-looking wave with definite phase. Roy Glauber won a Nobel Prize for developing their theory in quantum optics. They are the bridge between the discrete, quantum world of photons and the smooth, classical world of radio waves and electromagnetic fields you can treat as ordinary oscillating quantities.