New Quantum Mechanical Results in Interferometry.

New interferometric results concerning particle pairs are obtained through the introduction of newly defined physical quantities. A quantum mechanical study is made of two-particle interferometry in an idealized four-beam apparatus. There are two transducers, each fed by two paths from a source of particle pairs and each having two exit paths. When observations are made in all four exit paths, exactly one particle from each pair is found exiting from each transducer. Single and joint detection rates in the various paths are studied as functions of controllable transducer parameters. The joint detection rates provide striking illustrations of the non-locality of entangled two-particle states. The visibility (or fringe contrast) v _{i}, i = 1,2, of one-particle interference fringes and the visibility of two-particle fringes v_{12} (the latter being properly defined for the first time) are first shown to obey the new complementarity relation v_sp {i}{2} + v_sp{12}{2 }<= 1 in a special case where each transducer is a beam-splitter with a single variable phase shifter, and the two-particle states are assumed to have real coefficients in the source-path basis. An unrestricted class of two -particle states is then studied in a fully general two -particle four-beam interferometer, wherein particle pairs enter arbitrary transducers, the influence of which is characterized by unitary unimodular transformations. It is shown that the visibilities of one-particle and two -particle interference fringes in the general arrangement, V_{i} (i = 1,2) and V _{12}, obey the stronger complementarity relation V_sp{12}{2} + V_sp{i}{2} = 1. Next, a complementarity is demonstrated between single-particle path distinguishability and single-particle interference in a two-beam apparatus, namely [ max{cal D}({cal P})]^2 + v_sp{1} {2} = 1,where the measure {cal D}({cal P}) of path distinguishability is defined on the basis of strategies for predicting the particle's path, given the preparation {cal P} of an ensemble of similar particles. This complementarity strengthens previously known results. Finally, the relationship between the two complementarity results is discussed.