Higher order coherence

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In quantum optics, correlation functions are used to characterize the statistical and coherence properties – the ability of waves to interfere – of electromagnetic radiation, like optical light. Higher order coherence or n-th order coherence (for any positive integer n>1) extends the concept of coherence to quantum optics and coincidence experiments.^[1] It is used to differentiate between optics experiments that require a quantum mechanical description from those for which classical fields are sufficient.

Classical optical experiments like Young's double slit experiment and Mach-Zehnder interferometry are characterized only by the first order coherence. The 1956 Hanbury Brown and Twiss experiment brought to light a different kind of correlation between fields, namely the correlation of intensities, which correspond to second order coherences.^[2] Coherent waves have a well-defined constant phase relationship. Coherence functions, as introduced by Roy Glauber and others in the 1960s, capture the mathematics behind the intuition by defining correlation between the electric field components as coherence.^[3] These correlations between electric field components can be measured to arbitrary orders, hence leading to the concept of different orders or degrees of coherence.^[4]

Orders of coherence can be measured using classical correlation functions or by using the quantum analogue of those functions, which take quantum mechanical description of electric field operators as input. The underlying mechanism and description of the physical processes are fundamentally different because quantum interference deals with interference of possible histories while classical interference deals with interference of physical waves.^[3]

Analogous considerations apply to other wave-like systems. From example the case of Bose–Einstein correlations in condensed matter physics.