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Physical Review Research

Generalized angular momentum transfer to up-converted photons via four-wave mixing in atomic gases

L. A. Mendoza-López, J. G. Acosta-Montes, I. F. Ángeles-Aguillón, D. Sierra-Costa, Y. M. Torres, Rocío Jáuregui, Daniel Sahagún

Published Aug 20, 2021• 11 citations
Publisher

Abstract

Experimental results on the phase transfer from structured beams to parametric light, generated by inducing four-wave mixing in an atomic gas, are reported. Near-infrared, Mathieu, and Gaussian pump beams yield a blue coherent Mathieu electromagnetic field and an infrared beam. Two complementary techniques enable full characterization of the up-converted modes. The unambiguous and efficient phase heritage of these complex quasipropagation invariant modes to up-converted photons is demonstrated. The presented data enable a quantitative study of dynamical variables related to Mathieu beams. These include elliptic angular momentum, a generalization of the orbital angular momentum of light, which is also up-converted through the nonlinear process.

DOI
10.1103/physrevresearch.3.033170

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Experimental results on the phase transfer from structured beams to parametric light, generated by inducing four-wave mixing in an atomic gas, are reported. Near-infrared, Mathieu, and Gaussian pump beams yield a blue coherent Mathieu electromagnetic field and an infrared beam. Two complementary techniques enable full characterization of the up-converted modes. The unambiguous and efficient phase heritage of these complex quasipropagation invariant modes to up-converted photons is demonstrated. The presented data enable a quantitative study of dynamical variables related to Mathieu beams. These include elliptic angular momentum, a generalization of the orbital angular momentum of light, which is also up-converted through the nonlinear process.
Arrays of multiple vortices were transferred from infrared to the blue region of the optical spectrum. This demonstration was achieved by inducing four-wave mixing in an atomic gas with a Gaussian beam and a quasi-invariant propagation beam of the Mathieu type. The latter structure was analyzed in the Fourier space for the pump and the generated light. In both cases, the phase structure can be written with a compact mathematical expression by using the same parameters within experimental error bars. A Michelson–Morley interferometer was used to confirm that a phase singularity was present at each site as predicted by the theory. These studies add to the available control over orbital angular momentum in photons generated by atoms, which has a broad span of applications in quantum and classical information management.
We report the transfer of phase structure and, in particular, of orbital angular momentum from near-infrared pump light to blue light generated in a four-wave-mixing process in 85Rb vapor. The intensity and phase profile of the two pump lasers at 780 and 776 nm, shaped by a spatial light modulator, influences the phase and intensity profile of light at 420 nm, which is generated in a subsequent coherent cascade. In particular, we observe that the phase profile associated with orbital angular momentum is transferred entirely from the pump light to the blue. Pumping with more complicated light profiles results in the excitation of spatial modes in the blue that depend strongly on phase matching, thus demonstrating the parametric nature of the mode transfer. These results have implications on the inscription and storage of phase information in atomic gases.
We report the transfer of phase structure, and in particular of orbital angular momentum (OAM), from near-infrared pump light to blue light generated in a four-wave-mixing process in85Rb vapour. The intensity and phase profile of the two pump lasers at 780nm and 776nm, shaped by a spatial light modulator (SLM), influences the phase and intensity profile of light at 420nm which is generated in a subsequent coherent cascade. In particular we observe that the phase profile associated with orbital angular momentum is transferred entirely from the pump light to the blue. Pumping with more complicated light profiles results in the excitation of spatial modes in the blue that depend strongly on phase matching, thus demonstrating the parametric nature of the mode transfer. These results have implications on the inscription and storage of phase information in atomic gases.
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.
Abstract We study various coherent optical properties, e.g., two-photon electromagnetically induced transparency (EIT) and three-photon electromagnetically induced transparency and absorption (TPEIT/TPEIA), in a four-level ladder (Ξ)-type system of 87Rb atoms, where the probe and control fields are Gaussian-shaped laser beams and the pump field is structured laser beam. Additionally, the generated four-wave mixing (FWM) signal has been studied. Interestingly, it is found that the generated FWM signal is spatially structured along with the azimuthal phase, which carries the orbital angular momentum (OAM) of light. It is also observed that the coherent optical responses (EIT, TPEIT/TPEIA, and FWM signals) can be manipulated by utilizing the OAM number of the pump beam as a control knob.
We suggest a technique based on the transfer of topological charge from applied laser radiation to directional and coherent optical fields generated in ladder-type excited atomic media to identify the major processes responsible for their appearance. As an illustration, in Rb vapors, we analyze transverse intensity and phase profiles of the forward-directed collimated blue and near-IR light using self-interference and astigmatic transformation techniques when either or both of two resonant laser beams carry orbital angular momentum. Our observations unambiguously demonstrate that emission at 1.37 μm is the result of a parametric four-wave mixing process involving only one of the two applied laser fields.