Bose–Einstein correlations

In physics, Bose–Einstein correlations are correlations between identical bosons. They have important applications in astronomy, optics, particle and nuclear physics.

The interference between two (or more) waves establishes a correlation between these waves. In particle physics, in particular, where to each particle there is associated a wave, we encounter thus interference and correlations between two (or more) particles, described mathematically by second or higher order correlation functions. These correlations have quite specific properties for identical particles. We then distinguish Bose–Einstein correlations for bosons and Fermi–Dirac correlations for fermions. While in Fermi–Dirac second order correlations the particles are antibunched, in Bose–Einstein correlations (BEC) they are bunched. Another distinction between Bose–Einstein and Fermi–Dirac correlation is that only BEC can present quantum coherence (cf. below).

In optics two beams of light are said to interfere coherently, when the phase difference between their waves is constant; if this phase difference is random or changing the beams are incoherent.

The coherent superposition of wave amplitudes is called first order interference. In analogy to that we have intensity or second order Hanbury Brown and Twiss (HBT) interference, which generalizes the interference between amplitudes to that between squares of amplitudes, i.e. between intensities.

In optics amplitude interferometry is used for the determination of lengths, surface irregularities and indexes of refraction; intensity interferometry, besides presenting in certain cases technical advantages (like stability) as compared with amplitude interferometry, allows also the determination of quantum coherence of sources.

The concept of higher order or quantum coherence of sources was introduced in quantum optics by Glauber. While initially it was used mainly to explain the functioning of masers and lasers, it was soon realized that it had important applications in other fields of physics, as well: under appropriate conditions quantum coherence leads to Bose–Einstein condensation. As the names suggest Bose–Einstein correlations and Bose–Einstein condensation are both consequences of Bose–Einstein statistics and thus applicable not only to photons but to any kind of bosons. Thus Bose–Einstein condensation is at the origin of such important condensed matter phenomena as superconductivity and superfluidity, and Bose–Einstein correlations manifest themselves also in hadron interferometry.

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