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Scientific Reports

Coherent control of optical lattices and optical unit cells in atomic medium by counter propagation of Laguerre Gaussian beams

Latif Ur Rahman, U. Zakir, Bakht Amin Bacha, Kamal Shah, Thabet Abdeljawad, Khaled Naseralla

Published Oct 16, 2025• 1 citation
Publisher

Abstract

This manuscript explores the coherent control of optical lattices and optical unit cells. Optical lattices are formed by the counter-propagation of Laguerre Gaussian beams within an atomic medium. Variations in absorption and the refractive index along the x and y axes provide insight into the confined modes of the optical lattice and its unit cells, from which we can extract information about mode confinement. Density plots of the absorption spectrum and refractive index reveal the presence of unit cells in both the valley and peak regions of the counter-propagating Laguerre Gaussian standing wave fields. In this manuscript, we control the Wigner and cubic-type unit cells of optical lattices with lattice parameters [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text].

DOI
10.1038/s41598-025-19765-2

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This manuscript explores the coherent control of optical lattices and optical unit cells. Optical lattices are formed by the counter-propagation of Laguerre Gaussian beams within an atomic medium. Variations in absorption and the refractive index along the x and y axes provide insight into the confined modes of the optical lattice and its unit cells, from which we can extract information about mode confinement. Density plots of the absorption spectrum and refractive index reveal the presence of unit cells in both the valley and peak regions of the counter-propagating Laguerre Gaussian standing wave fields. In this manuscript, we control the Wigner and cubic-type unit cells of optical lattices with lattice parameters [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text].
Covalent and photonic interactions between atoms in lattice are controlled by probe absorption and dispersion spectrums. Similarly, information of covalent interaction among atoms within a crystal is extracted by absorption and dispersion spectrums in the range of [Formula: see text]. Localization of atoms and pairs of electron density are controlled by the gradients ([Formula: see text] and [Formula: see text]) variation of absorption and dispersion spectrums of the four-level atomic medium. Additionally, the covalent interaction between atoms are modified using structured light beams in the range of [Formula: see text]. The sharing of electrons between atoms are controlled and modified by the parameters of probe, control fields and the gradients variation of absorption and dispersion. This work will play an important role in the field of quantum enhanced metrology, trapping of atoms, nanolithography and Bose-Einstein condensate.
We propose a scheme to investigate the spatial modulation of the refractive index in a dense atomic ensemble under the action of the Laguerre–Gaussian (LG) beams. Theoretical derivations based on a density-matrix approach associated with numerical simulations are utilized to study the behaviors of the index of refraction, showing that the azimuthal and radial mode indices (i.e., l 2 and p 2) of the LG beams significantly affect the real and imaginary parts of the refractive index. To be specific, the number of the dispersive peaks is determined by ( p 2 + 1 ) | l 2 |, and there are 2 | l 2 | lossless petals in conjunction with p 2 concentric absorption rings centered on the vortex center. Furthermore, by tuning the phase values of the electric and magnetic components of the electromagnetic field, the index of refraction can be drastically tuned from negative to zero to positive and accompanied by periodic absorption and amplification. This investigation provides a powerful tool for manipulating the index of refraction through a nonlinear interaction between atoms and the vortex beams and suggests potential applications in optical switching, logic gates, and optical storage with spatially varying refractive indices.
The resonant absorption, emission, and scattering of light are the fundamental optical processes that have been used both to probe matter and to manipulate light itself. In the last decade there has been essential progress in coherent control of both linear and nonlinear optical responses based on resonant excitation of atomic coherence in multilevel quantum systems. Some interesting and useful phenomena, resulting from coherent control of absorption and the group index, such as electromagnetically induced transparency, lasing without inversion, and ultra-slow group velocity of light have been widely studied. This work is focused on coherent control of refractive index and resonant fluorescence in multilevel medium. \n \nWe suggest two promising schemes for resonant enhancement of the refractive index with eliminated absorption and propose their implementation in transition element doped crystals with excited state absorption and in a cell of Rb atoms at natural abundance. We show how to use one of these schemes for spatial variation of the refractive index via its periodic resonant increase/decrease, remarkably keeping at the same time zero absorption/gain. It opens the way to production of transparent photonic structures (such as distributed Bragg reflectors, holey fibers, or photonic crystals) in a homogeneous resonant atomic media such as dielectrics with homogeneously distributed impurities, atomic, or molecular gases. These optically produced photonic structures could easily be controlled (including switching on/off, changing amplitude and period of modulation) and would be highly selective in frequency, naturally limited by the width of the optical resonance. \n \nWe also derive the optical fluorescence spectra of a three-level medium driven by two coherent fields at the adjacent transitions in a general case when all three transitions are allowed. We show that coherent driving can efficiently control the distribution of intensities between the fluorescent channels. In particular, the total intensity of fluorescence at the transition which is not driven by the optical fields may essentially exceed the fluorescence intensity at the driven transitions under the condition of two-photon resonance. This counter-intuitive effect is due to depletion of the intermediate state via atomic interference.
Abstract This research investigates the intricate interplay between Gaussian beams and atomic media, introducing a novel approach by incorporating a Kerr field and spatially dependent refractive index. The study employs a Gaussian probe field as the primary interaction medium with the atomic ensemble, while simultaneously introducing two control fields. One of these control fields acts as a Kerr field, imparting a unique modulation on the propagation characteristics of the Gaussian beam. The key parameters under scrutiny encompass the probe field detuning (∆P /γ), as well as the Rabi frequencies and detunings of the control fields (Ω1,2/γ, ∆1,2/γ). Further exploration involves transforming one of the control fields into a Gaussian beam, resulting in the creation of a spatially dependent refractive index within the atomic medium. The investigation focuses on the spatial coordinates x/ω0 and y/ω0, where ω0 represents the Gaussian beam waist. This intricate configuration provides a unique platform for studying the manipulation and control of light propagation in atomic media. The research not only sheds light on fundamental interactions in quantum optics but also opens avenues for potential applications in quantum information processing and precision measurement. The outcomes of this study contribute valuable insights into the dynamics of Gaussian beams in complex atomic environments, with potential implications for quantum technology and communication.
Abstract Motivated by the need for controllable fast-light platforms in compact photonic systems, this work investigates surface plasmon polariton (SPP)-assisted superluminal group propagation in a four-level cesium atomic medium driven by Laguerre-Gaussian control fields. The aim is to examine how the beam waist and intensity of the structured control fields, together with plasmonic field confinement, modify absorption, dispersion, group index, and group velocity. Using a density-matrix formulation, the probe-field coherence is obtained, the optical susceptibility is calculated, and the group velocity is evaluated from the dispersion slope while the SPP contribution is included through the effective dielectric response. The results show that increasing the Laguerre-Gaussian beam waist broadens the spatial region of anomalous dispersion and negative group index, while SPP confinement strengthens the local atom-field interaction and enhances susceptibility modulation. The study demonstrates a tunable route for controlling localized superluminal group propagation without implying superluminal information transfer, with potential applications in optical switching, photonic signal processing, plasmonic sensing, and quantum optical devices.