# Two articles in OSA journals

Two of our articles have recently been accepted in OSA Journals. The first one, **Photon statistics as an interference phenomenon**, has been published in Optics Letters.

**Abstract:**

Interference of light fields, first postulated by Young, is one of the fundamental pillars of physics. Dirac extended this observation to the quantum world by stating that each photon interferes only with itself. A precondition for interference to occur is that no welcher-weg information labels the paths the photon takes; otherwise, the interference vanishes. This remains true, even if two-photon interference is considered, e.g., in the Hong–Ou–Mandel-experiment. Here, the two photons interfere only if they are indistinguishable, e.g., in frequency, momentum, polarization, and time. Less known is the fact that two-photon interference and photon indistinguishability also determine the photon statistics in the overlapping light fields of two independent sources. As a consequence, measuring the photon statistics in the far field of two independent sources reveals the degree of indistinguishability of the emitted photons. In this Letter, we prove this statement in theory using a quantum mechanical treatment. We also demonstrate the outcome experimentally with a simple setup consisting of two statistically independent thermal light sources with adjustable polarizations. We find that the photon statistics vary indeed as a function of the polarization settings, the latter determining the degree of welcher-weg information of the photons emanating from the two sources.

The second article, **Prime Number Decomposition using the Talbot Effect**, has been published in Optics Express.

**Abstract:**

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 sums. The latter are a mathematical tool from number theory used to analyze the properties of prime numbers as well as to decompose composite numbers into their prime factors. We employ the well-established connection between the Talbot effect and Gauss sums to implement prime number decompositions with a novel approach, making use of the longitudinal intensity profile of the Talbot carpet. The new algorithm is experimentally verified and the limits of the approach are discussed.