Keywords: Topology, optical vortex, nonlinear Schrödinger equation, photon fluid
The optical vortex carries an angular orbital moment (OAM), which is ħℓ per photon, where ℓ is a relative integer. The
OAM, which is a quantum variable of ℤ, can be used for quantum technologies, especially for coding and storing
information. One of the current challenges is to understand its exchange with matter. The internship proposes to study
the exchange of the OAM with the atom and to understand the rules of the exchange according to the experimental
conditions.

An experiment is in progress in which the atom is submitted to one or more optical vortices. It allows to realize a 4-
wave mixing based on a Raman transition of rubidium and to observe the conversion of the exciting vortices (red ones )
into vortices of another color (IR and blue). One wonders if it is possible to control the conversion by parameters such
as the geometry of the 4 wave mixing, the size of the vortex or the polarization. This could lead to OAM entanglement
of the pair of emitted photon..

The proposed internship has two aspects: experimental with the realization of OAM conversion and the learning of the
associated techniques; theoretical with the modeling of the exchange process. According to the sanitary conditions the
part theory/experiment will be adjusted. This work may be continued to a phD.

[1] High Helicity Vortex Conversion in a Rubidium Vapor, A. Chopinaud, M. Jacquey, B. Viaris de Lesegno and L. Pruvost, Phys. Rev.
A. 97, 063806 (2018)