New Quantum Mechanical Results in Interferometry.
Abstract
New interferometric results concerning particle pairs are obtained through the introduction of newly defined physical quantities. A quantum mechanical study is made of twoparticle interferometry in an idealized fourbeam 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 nonlocality of entangled twoparticle states. The visibility (or fringe contrast) v _{i}, i = 1,2, of oneparticle interference fringes and the visibility of twoparticle 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 beamsplitter with a single variable phase shifter, and the twoparticle states are assumed to have real coefficients in the sourcepath basis. An unrestricted class of two particle states is then studied in a fully general two particle fourbeam interferometer, wherein particle pairs enter arbitrary transducers, the influence of which is characterized by unitary unimodular transformations. It is shown that the visibilities of oneparticle 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 singleparticle path distinguishability and singleparticle interference in a twobeam 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.
 Publication:

Ph.D. Thesis
 Pub Date:
 January 1995
 Bibcode:
 1995PhDT........12J
 Keywords:

 Physics: Optics