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Results in Physics

Propagation of generalized multi-Gaussian correlated Schell-model beams in electromagnetically induced transparency atomic vapor

Wenbo Li, Zhirong Liu

Published Nov 28, 2023• 2 citations
Publisher

Abstract

Propagation of generalized multi-Gaussian correlated Schell-model (GMGCSM) beams through four-level electromagnetically induced transparency (EIT) atomic vapor is investigated for the first time. Analytical expression for the GMGCSM beam passing through an ABCD optical system of EIT vapor is deduced and employed to analyze its propagation properties. It is demonstrated that intensity evolution of the targeted GMGCSM beam through EIT atomic vapor is dependent on the coupling Rabi frequency of the control light, the beam’s index and coherence length. Moreover, analysis shows that degree of coherence of the beam can also be regulated by the coupling Rabi frequency. Additionally, it is shown that, selecting appropriate coherence length, GMGCSM beams of the first kind would form a shift from a dark-centered distribution known as “optical cage”, to a peak-centered distribution; GMGCSM beams of the second kind would shift from a flat-topped distribution to a Gaussian distribution. Therefore, EIT atomic vapor provides a method to regulate the coherence of partially coherent beams. Results obtained here could be expected applications in free-space optical communications, material thermal processing, and optical trapping.

DOI
10.1016/j.rinp.2023.107212

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Propagation of generalized multi-Gaussian correlated Schell-model (GMGCSM) beams through four-level electromagnetically induced transparency (EIT) atomic vapor is investigated for the first time. Analytical expression for the GMGCSM beam passing through an ABCD optical system of EIT vapor is deduced and employed to analyze its propagation properties. It is demonstrated that intensity evolution of the targeted GMGCSM beam through EIT atomic vapor is dependent on the coupling Rabi frequency of the control light, the beam’s index and coherence length. Moreover, analysis shows that degree of coherence of the beam can also be regulated by the coupling Rabi frequency. Additionally, it is shown that, selecting appropriate coherence length, GMGCSM beams of the first kind would form a shift from a dark-centered distribution known as “optical cage”, to a peak-centered distribution; GMGCSM beams of the second kind would shift from a flat-topped distribution to a Gaussian distribution. Therefore, EIT atomic vapor provides a method to regulate the coherence of partially coherent beams. Results obtained here could be expected applications in free-space optical communications, material thermal processing, and optical trapping.
We study the propagation properties of an Airy beam through a four-level electromagnetic induced transparency (EIT) atomic vapor. The analytical expression for the Airy beam passing through the ABCD optical system of the EIT vapor is deduced and employed to analyze the propagation characteristics of the beam. It is shown that both the deflection position and the intensity of the Airy beam can be modulated by the Rabi frequency of the control light. Such a tunable optical behavior may have some potential applications in medicine science.
Analytical expression is obtained for the cross-spectral density function of a Gaussian Schell-model (GSM) beam passing through an electromagnetic induced transparency (EIT) atomic vapor. The formula can be used in the study of the changes in the spectral density and spectral degree of coherence of the beam through the EIT atomic vapor. Numerical examples show that both the spectral density and the spectral degree of coherence of the GSM beam can be modulated by the Rabi frequency of the control light.
Electromagnetically induced transparency (EIT) is an important phenomenon in quantum optics, and has a wide range of applications in the fields of quantum information processing and quantum precision metrology. Recently, with the rapid progress of the generation and detection of structured light, the EIT with structured light has attracted enormous interests and offers new and novel functionalities and applications. Here, we theoretically study the propagation and evolution of Gaussian vortex beams, a typical type of structured light, in an EIT medium with Λ-type three-level atoms. Based on the generalized Huygens-Fresnel principle, we derive the analytical expressions of fully and partially coherent Gaussian vortex beams propagating in the EIT medium, and study the evolution of the intensity and phase distributions of the beams and their dependencies on parameters such topological charge, coherence length, Rabi frequency, etc. It is shown that both the fully and partially coherent Gaussian vortex beams undergo focusing and diverging periodically during propagation. The phase singularity of the fully coherent beam keeps unchanged, while the phase singularity of the partially coherent beam experiences splitting and recombination periodically. In addition, new phase singularities with opposite topological charge are generated in the latter case. Our results not only advance the study of the interaction between structured light and coherent media, but also pave the avenue for manipulating structured light via EIT.
Abstract This study investigates the propagation properties of two-dimensional Airy vortex beams in an electromagnetically induced transparency (EIT) medium, based on a four-level rubidium atomic vapor system controlled by dual coupling Rabi frequencies. By establishing the ABCD transmission matrix of the EIT medium and employing the Collins integral formula, analytical expression for the propagation of the Airy vortex beam in the EIT medium is derived. Using the obtained analytical solution, this study further examines the beam’s intensity distribution, phase evolution characteristics, and their dependencies on several key parameters such as transverse scale, truncation factor, and vortex center position. Results demonstrate that the intensity of the Airy vortex beam can be modulated by the coupling Rabi frequency: with the change of the coupling Rabi frequency, the Airy vortex beam will be focused, and the main lobe will form a quasi-focus, accompanied by the reproduction of phase singularities. Moreover, the transverse deflection of the beam will be reduced when the coupled Rabi frequency is increased. At the same time, the vortex position, truncation factor and transverse scale also affect the field intensity distribution of the beam. These research results could have potential application value in the fields of optical bullets and optical micromanipulation.
Quantum coherence and interference in atomic systems can lead to interesting optical phenomena such as nonabsorbing resonances, lasing without inversion, generating an ultrahigh index of refraction without absorption, propagation of light pulses without losses. In the last-named is given the title transparency. Up to now it is known some types of transparency in multi-level resonant media. One of them is electromagnetically induced transparency (EIT). The phenomenon of EIT in the propagation of laser radiation through an absorbing medium has been recently investigated and explained in terms of quantum coherence and interference for multi-level atomic system. For instance in the (Lambda) -system, if the atomic medium is prepared in a quantum superposition of states, matched pulses, i.e., a pair of optical pulses whose amplitude and phase have a well defined relation, propagate without absorption. The mechanism of coherent population trapping is responsible for EIT in a (Lambda) -system. There is another, well known mechanism for creating transparency in a two-state atom: self-induced transparency, or SIT. Here, a single pulse whose area (the integral of its Rabi frequency over time) is 2(pi) is applied to the medium. Such a pulse causes the atoms to cycle smoothly from the ground to the excited state and then back again. In principle, such a pulse can propagate over long distances. SIT can be generalized to multi-level systems and multiple quasi-monochromatic fields. Generalization of SIT in a (Lambda) -system was obtained in reference 2. In this report we present a new type of transparency (combined transparency). This type describes propagation of laser pulse through a (Lambda) -type medium where the initial atomic state is prepared in the form of spatially varying coherent superposition of low-energetic states (initial coherency gradient). The common envelope behaves as usual 2(pi) hyperbolic secant pulse, but the ratio between the components of frequencies transitions 1> yields 3> and 2> yields 3> changes due to coherent Raman scattering so (phi) equals atan(E1/E2) equals (pi) /2-Gz, where z is the coordinate, G is the constant determined by both the incident pulse parameters and the initial coherence between the atomic states. Our solution demonstrates a direct connection of EIT in adiabatic regime to the SIT effects. This type of a transparency is given the title screw-type transparency, because for the given form of incident pulse (pitch of screw) medium is transparent, if medium's the initial coherence gradient is correspondingly prepared (thread on a engine nut). Besides a transparency, this phenomenon contains a transformation of the incident pulse frequency during the process of the propagation. This property of the phenomena can be result in a complete conversion of the frequency.