Four-Plate Interferometry in Phase-Space

Abstract

We now discuss the case where an additional interferometer loop is used to revive coherence properties, which appear to be hidden behind the first in-terferometer loop. Such systems engender some interest, because there exist coupled interferometer loops that are partly fed with coherent beams, instead of incoherent beams as in the case of standard interferometers. The wave functions and the intensities can be calculated by extending the methods applied to the triple-plate interferometer to a multi-plate system [50]. In certain cases, the total interfering intensity can be higher than in the standard triple-Laue case interferometer. Multi-plate interferometers have again demonstrated the linear superposition principle of quantum mechanics and have stimulated discussion about coherent beam mixing and non-sharp particle or wave property determination [24]. Here we concentrate on double-loop systems. The system is described and the coherence properties are expressed via Wigner and distribution functions. Squeezing effects are discussed and correlations, as well as visibility aspects, are investigated. 8.1 Double-Loop System In Fig. 8.1 a double-loop system is shown, which is an extension of a standard three-plate neutron interferometer (Fig. 6.1), and where a second loop is added and separate phase shifters ∆ (see (7.1)) can be inserted in each loop. Three path ways I, II and III can be distinguished and, therefore, three total phase shifts: ∆ I = ∆ 1A + ∆ 1B + ∆ 2B , ∆ II = ∆ 1A + ∆ 2AB + ∆ 3B , ∆ III = ∆ 2A + ∆ 3A + ∆ 3B. (8.1) χ A and χ B are total phase shifts in loops A and loop B, respectively, and we obtain: χ A = k 0 (∆ II − ∆ III), χ B = k 0 (∆ I − ∆ II), χ AB = k 0 (∆ I − ∆ III) = χ A + χ B. (8.2)