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Journal of Optics

Combinations of orbital angular momentum in two degenerate four-wave mixing processes in Rb vapor

M. R. L. da Motta, A. A. C. de Almeida, S. S. Vianna

Published Jul 12, 2023• 2 citations
Publisher

Abstract

Abstract We present experimental measurements showing the combination of the orbital angular momentum (OAM) content of incident light beams in two distinct processes of degenerate four-wave mixing induced in hot rubidium vapor. These two processes, driven by the same fields, must satisfy distinct topological charge (TC) selection rules, which impose OAM conservation. These selection rules are readily obtained from the so-called overlap integral of the incident beams and allow us to control the relations between the two nonlinear signals, in particular, to characterize the conditions to obtain the two signals with symmetric or anti-symmetric TCs. The tilted lens method was employed to measure the OAM content of the output fields. We also discuss the transition from the near- to the far-field distributions of the generated signals.

DOI
10.1088/2040-8986/ace6bb

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Abstract We present experimental measurements showing the combination of the orbital angular momentum (OAM) content of incident light beams in two distinct processes of degenerate four-wave mixing induced in hot rubidium vapor. These two processes, driven by the same fields, must satisfy distinct topological charge (TC) selection rules, which impose OAM conservation. These selection rules are readily obtained from the so-called overlap integral of the incident beams and allow us to control the relations between the two nonlinear signals, in particular, to characterize the conditions to obtain the two signals with symmetric or anti-symmetric TCs. The tilted lens method was employed to measure the OAM content of the output fields. We also discuss the transition from the near- to the far-field distributions of the generated signals.
We explore the conservation of orbital angular momentum (OAM) in the four-wave mixing (FWM) process in hot rubidium vapor. Since most modern communication systems send data in pulses corresponding to bits, we can use OAM to encode more information in each pulse by assigning structure to each signal. Furthermore, because FWM can be used to generate entangled photon pairs, we can use this process to bring enhanced signal security. We experimentally studied FWM with a wide range of Laguerre-Gaussian modes and their superpositions and observed OAM transfer from the probe field to a generated Stokes field. By studying the output Stokes intensity and phase distributions, we confirm l mode (OAM) conservation for pure l and p modes, as well as for the superpositions of l and -l for the mode numbers up to l = 4, p = 4. We also found that p index is generally not conserved and its conservation is highly dependent on the relative sizes of the probe and pump beams in the Rb cell. We also identify parameters to improve FWM gain with OAM transfer and propose an analytical method for determining OAM p number.
We explore a degenerate four-wave mixing process induced by transversely structured light beams in a rubidium vapor cell. In particular, we consider the nonlinear interaction driven by optical modes contained in the orbital angular momentum Poincar\'e sphere, which can be parametrized in terms of a polar and an azimuthal angle. In this context we investigate the transfer of spatial structure to two distinct four-wave mixing (FWM) signals, possessing different propagation directions in space. We show that under usual assumptions, the output fields can also be described by modes belonging to Poincar\'e spheres, and that the angles describing the input and output modes are related according to well-defined rules. Our experimental results show good agreement with the calculations, which predict intricate field structures and a transition of the FWM transverse profile between the near- and far-field regions.
We report on experimentally observed addition, subtraction, and cancellation of orbital angular momentum (OAM) in the process of parametric four-wave mixing that results in frequency up- and down-converted emission in Rb vapor. Specific features of OAM transfer from resonant laser fields with different optical topological charges to the spatially and temporally coherent blue light (CBL) have been considered. We have observed the conservation of OAM in nonlinear wave mixing in a wide range of experimental conditions, including a noncollinear geometry of the applied laser beams, and furthermore, that the CBL accumulates the total OAM of the applied laser light. Spectral and power dependences of vortex and plane wavefront blue light beams have been compared.
We present a theoretical analysis of the spatial shape (transverse and longitudinal) of two degenerate four-wave mixing (FWM) signals induced by fields Ea and Eb, with nonuniform transverse profiles, and wave-vectors ka and kb. The two signals are generated in a cold sample of two-level atoms, in the forward directions 2ka − kb and 2kb − ka. In all cases, the transverse shapes of the generated signals (both near- and far-field) are dictated by the projection of the nonlinear coherence onto the Laguerre-Gaussian (LG) function space. Our calculations show that the longitudinal profile of each generated beam is affected by the spectral characteristics of the medium, described by the third order nonlinear susceptibility. For Gaussian incident fields with equal detunings from resonance, the FWM beam shapes are completely symmetric, with an asymmetry induced by different detunings of incident fields. By considering incident beams with LG distributions, the topological charge conservation determines the orbital angular momentum of each signal and the longitudinal profiles show similar behaviors to the case with Gaussian beams. The phase discontinuities of LG modes reveal a rotation and distortion of the phase distribution of the FWM beams caused by the detunings. We discuss for selected configurations, the relations between both generated beams and their propagation properties. We also present preliminary experimental results of the power spectra of the two FWM signals generated in our magneto-optical trap of rubidium atoms.
We present an experimental platform which can generate quantum-correlated beams with Orbital Angular Momentum (OAM) via degenerate Four-Wave Mixing (FWM) in Rubidium vapor. We further investigated the conservation of OAM before and after FWM by performing LG mode decomposition using interferometer. To compare our experimental result with theoretical prediction, we simulated a simplified version of our set up. Moreover, we used this toy model to study the conservation of radial and angular intensity profile through changing parameters limited by our set up. In general, we found that FWM preserves most information consisted in OAM, but has a rather loose control over the information stored in radial profile.
Detuning Tunable OAM Generation via Double-ΛΛΛ Four-Wave Mixing in Hot Rubidium Vapor
We demonstrate detuning-tunable generation of orbital-angular-momentum (OAM) light using a double Lambda four-wave-mixing (FWM) process in Doppler broadened rubidium vapor. Two near-resonant pumps on the D1 line drive non degenerate FWM that produces bright probe conjugate beams whose transverse modes evolve with pump detuning. A paraxial density-matrix model coupled to split-step propagation predicts detuning-dependent spatial gain shaping that sets the OAM content; experiments with a mode cleaned pump laser and a 12-mm AR-coated vapor cell validate these predictions. We quantify mode formation by imaging, spectroscopy, and power measurements, and verify OAM conservation between the generated beams. The results establish resonant atomic vapor as a compact, tunable platform for structured-light generation with applications to high-dimensional quantum communications and imaging.