The aim of this introductory article is two-fold. First, we aim to offer a general introduction to
the theme of Bose-Einstein condensates, and briefly discuss the evolution of a number of …

We point out a link between orbital angular momentum (OAM) carrying light beams and
number theory. The established link makes it possible to formulate and implement a simple …

We discover a connection between a Gauss sum of number theory and the degree of
coherence (DOC) of the field in a transverse plane of structured speckled light beams. We …

We report on prime number decomposition by use of the Talbot effect, a well-known
phenomenon in classical near field optics whose description is closely related to Gauss …

We experimentally investigate the effects of phase noise on the resonant and non-resonant
dynamics of the atom-optics kicked rotor. Employing sinusoidal phase modulation at various …

Quantum walks have gained significant attention over the past decades, mainly because of
their variety of implementations and applications. Atomic quantum walks are typically subject …

We construct an analog computer based on light interference to encode the hyperbolic
function f (ζ)≡ 1/ζ into a sequence of skewed curlicue functions. The resulting interferogram …

We investigate the dynamics of the atom-optics δ-kicked rotor in the vicinity of quantum
resonance. Although small deviations from resonant conditions lead to a negligible change …

Factorization of numbers with Gauss sums: I. Mathematical background Page 1 OPEN ACCESS
Factorization of numbers with Gauss sums: I. Mathematical background To cite this article: S …

Abstract Truncated Fourier, Gauss, Kummer and exponential sums can be used to factorize
numbers: for a factor these sums equal unity in absolute value, whereas they nearly vanish …