Position measurement-induced collapse states and boundary bound diffraction: an idealised experiment

Abstract

In an earlier work, it was shown that single-slit diffraction of matter waves can be considered as position measurement of particles and that the Fresnel and Fraunhofer diffraction patterns result from the time evolution of the same collapsed quantum wave function. This quantum mechanical treatment of diffraction of particles, based on the standard postulates of quantum mechanics and the postulate of existence of quantum trajectories, leads to the ‘position measurement-induced collapse’ (PMIC) states. In the present work, an idealised experimental set-up to test these PMIC states is proposed. The apparatus consists of a modified Lloyd’s mirror in optics, with two reflectors instead of one. The diffraction patterns for this case predicted by the PMIC formalism are presented. They exhibit quantum fractal structures in space-time called ‘quantum carpets’, first discovered by Berry. The PMIC formalism in this case closely follows the ‘boundary bound diffraction’ analysed in a previous work by Tounli, Alverado and Sanz. In addition to having obtained their results, we have identified that the Fresnel and Fraunhofer patterns are indeed present here. It is anticipated that the verification of fractal and nonfractal features of the wave function at various times and also the predicted revival distances to the screen by this experiment will help to better understand ‘quantum collapse’.