Photon interferences and correlations

Abstract

Interference is one of the most important phenomena in optical fields representing their wave properties. Such two optical fields can in principle be in constructive or destructive interference according to their mutual phase (value of difference of their simultaneous phases) giving rise to an increase in the intensity (white interference fringes) or to a decrease in the intensity (dark interference fringes). Such correlations of two wave amplitudes are quite natural to be understood in a wave picture whereas it is more difficult to understand them in terms of particles-photons. Nevertheless making use of principles of quantum theory, which assumes probability waves, also particlelike theory of interference can be constructed. It is a basis for explanation of photon interferences given by Dirac (1958) stating that “each photon interferes only with itself” (for a discussion, see Mandel (1976)). Such point of view is related to the use of standard two beam interferometers detecting single photons. Moreover Dirac assumed an ideal case of maximum visibility interference fringes. The observation of interference pattern is related, from the point of view of quantum theory, to uncertainties in observables determined by commutation relations for the corresponding operators (energy-time, coordinate-momentum, photon number-phase, etc.). The wave-particle duality and complementarity principle play the principal role here. If a particle cannot be distinguished with respect to these uncertainties, the interference pattern may be observed because the number of particles is uncertain in the measurement and the phase can be certain.