Coherence (physics) - Quantum Coherence

Quantum Coherence

In quantum mechanics, all objects have wave-like properties (see de Broglie waves). For instance, in Young's Double-slit experiment electrons can be used in the place of light waves. Each electron's wave-function goes through both slits, and hence has two separate split-beams that contribute to the intensity pattern on a screen. According to standard wave theory these two contributions give rise to an intensity pattern of bright bands due to constructive interference, interlaced with dark bands due to destructive interference, on a downstream screen. (Each split-beam, by itself, generates a diffraction pattern with less noticeable, more widely spaced dark and light bands.) This ability to interfere and diffract is related to coherence (classical or quantum) of the wave. The association of an electron with a wave is unique to quantum theory.

When the incident beam is represented by a quantum pure state, the split beams downstream of the two slits are represented as a superposition of the pure states representing each split beam. (This has nothing to do with two particles or Bell's inequalities relevant to an entangled state: a 2-body state, a kind of coherence between two 1-body states.) The quantum description of imperfectly coherent paths is called a mixed state. A perfectly coherent state has a density matrix (also called the "statistical operator") that is a projection onto the pure coherent state, while a mixed state is described by a classical probability distribution for the pure states that make up the mixture.

Large-scale (macroscopic) quantum coherence leads to novel phenomena, the so-called macroscopic quantum phenomena. For instance, the laser, superconductivity, and superfluidity are examples of highly coherent quantum systems, whose effects are evident at the macroscopic scale. The macroscopic quantum coherence (Off-Diagonal Long-Range Order, ODLRO) for laser light, and superfluidity, is related to first-order (1-body) coherence/ODLRO, while superconductivity is related to second-order coherence/ODLRO. (For fermions, such as electrons, only even orders of coherence/ODLRO are possible.) Superfluidity in liquid He4 is related to a partial Bose–Einstein condensate. Here, the condensate portion is described by a multiply occupied single-particle state.

On the other hand, the Schrödinger's cat thought experiment highlights the fact that quantum coherence cannot be arbitrarily applied to macroscopic situations. In order to have a quantum superposition of dead and alive cat, one needs to have pure states associated with aliveness and pure states associated with death, which are then superposed. Given the problem of defining death (absence of EEG, heart beat, ...) it is hard to imagine a set of quantum parameters that could be used in constructing such superposition. In any case, this is not a good topic for a description of quantum coherence.

Regarding the occurrence of quantum coherence at a macroscopic level, it is interesting to note that the classical electromagnetic field exhibits macroscopic quantum coherence. The most obvious example is carrier signals for radio and TV. They satisfy Glauber's quantum description of coherence.