Four-wave mixing driven by structured light in atomic media : optical mode transfer and spatial correlations

Abstract

In this work we present a series of results on four-wave mixing (FWM) processes induced by structured light in atomic media. We start with a theoretical study focusing on a cascade FWM process in rubidium vapor, generating a blue light field at 420 nm. In this setting, we show that in the extended-medium regime the Hermite-Gaussian basis presents a unique property of optical structure transfer. We then exploit this result to show that, by carefully tailoring the structure of the pump beams, one can obtain desired spatial modes with cylindrical and elliptical symmetries with high fidelity at the blue light output. Following that, we consider an experimental configuration where two degenerate FWM signals are generated in different directions of space by the same pump fields. In this setup, we present results in heated rubidium vapor evidencing the simultaneous conservation of orbital angular momentum (OAM) in the two FWM processes. We show that the two-channel setting allows to encode the OAM content of the input beams onto the OAM carried by the two FWM signals. Next, we explore the transverse mode dynamics in the context of optical modes contained in the so-called orbital angular momentum Poincaré sphere (PS). Defined in analogy with a general polarization state, this family of modes is parametrized in terms of polar and azimuthal angles. We show that the two FWM signals can also be described as belonging to Poincaré spheres, and that the angles on the output PS are related to those on the input PS by well-defined symmetries. The predicted FWM intensity profiles, as well as the consequences of the symmetry properties, are in good agreement with our experimental results. We also explore interesting scenarios, such as combinations of different PS modes and the fulfillment of one of the symmetry relations in each sphere independently, and restrictions that arise in the extended-medium regime. In the last part, we study the correlations between the light fields participating in the two-channel FWM configuration. Following our recent work on cold atoms, we investigate the correlations originating from the conversion of phase-noise to amplitude-noise as a result of the light-atom interaction, and discuss our attempts to discriminate transverse spatial dependencies on these correlations. Finally, we outline the quantum theory of FWM, exploring the multi-spatial-mode nature of the generated light state and the associated spatial correlations.