N-slit interferometer

Abstract: Summary form only given. We show that a Young's N-slit interferometer can be used to factor the integer N. When the number of slits is a product of integer factors, then an analysis of the diffraction pattern can be used to determine these factors. This work provides a simple example of number theory's appearance in physics, and can be helpful in understanding the advantages of quantum-digital over classical-analog computers in handling integer factoring problems.

Abstract: The N-slit interferometer is demonstrated to function with an intra interferometric propagation path length of 527.33 m. Interferograms representing several interferometric characters, corresponding to N = 2, 3, 4, and 5, were recorded at the interferometric plane located at the end of an open air propagation range. Interferometric computations, based on the application of Dirac's notation, were successfully used to predict the structure and divergence of the propagating interferograms. These measurements were carried out during an unusual mild-temperature, low-humidity, summer night in northern Alabama. In the laboratory, at an intra interferometric propagation path length of 7.235 m, the N-slit interferometer was also used to successfully detect the intrusion of microscopic fibers into the intra interferometric propagation path. These experiments led to the detection of diffraction patterns superimposed over the interferograms.

Abstract: An N-slit interferometer is demonstrated with an intra-interferometric propagation path of up to 35 m. The configuration of the N-slit interferometer was extended to its maximum as allowed by the available grating, laser wavelength, and dimensions of the digital detector. Interferometric computations, based on the application of Dirac's notation, were successfully used to predict the structure and divergence of the propagating interferograms. The high sensitivity of the interferometric signal to intra-path perturbations renders this instrument particularly suitable for detecting and registering clear air turbulence, and variations in the refractive index, in the propagation path.

Abstract: We show that a Young's N slit interferometer can be used to factor the integer N. The device could factor four- or five-digit numbers in a practical fashion. This work shows how number theory may arise in physical problems, and may provide some insight as to how quantum computers can carry out factoring problems by interferometric means.