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Physica Scripta

Interaction of four level closed loop atomic systems in the presence of two vector beams

Rohit Kumar, Dixith Manchaiah, Raghavan K. Easwaran

Published May 26, 2023• 3 citations
Publisher

Abstract

Abstract In this manuscript, we have theoretically studied the four level closed loop atomic systems in the presence of two vector beams. A spatially dependent transparency for the probe vector beam is obtained based on the semiclassical model. We have explicitly shown that the number of petals formed for probe absorption depends on the value of orbital angular momentum (OAM) of the constituting beams. A detailed study for absorption and dispersion of right circularly polarized (RCP) and left circularly polarized (LCP) components of the probe beam is carried out and the importance of the polarization state of the beams on Higher Order Poincare Sphere (HOPS) is highlighted. An explicit effect of the interferometer phase of the vector beam which is geometric in nature, is shown for probe beam response. Three types of four level closed loop atomic system is studied with particular emphasis given for double Λ and Diamond atomic system. A dark state analysis of the atomic system is carried out which facilitate a physical understanding of the obtained results. Our study has explored the effects of inhomogeneity in both polarization and intensity for probe and coupling beam in a closed loop atomic system which is phase dependent.

DOI
10.1088/1402-4896/acd968

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Abstract In this manuscript, we have theoretically studied the four level closed loop atomic systems in the presence of two vector beams. A spatially dependent transparency for the probe vector beam is obtained based on the semiclassical model. We have explicitly shown that the number of petals formed for probe absorption depends on the value of orbital angular momentum (OAM) of the constituting beams. A detailed study for absorption and dispersion of right circularly polarized (RCP) and left circularly polarized (LCP) components of the probe beam is carried out and the importance of the polarization state of the beams on Higher Order Poincare Sphere (HOPS) is highlighted. An explicit effect of the interferometer phase of the vector beam which is geometric in nature, is shown for probe beam response. Three types of four level closed loop atomic system is studied with particular emphasis given for double Λ and Diamond atomic system. A dark state analysis of the atomic system is carried out which facilitate a physical understanding of the obtained results. Our study has explored the effects of inhomogeneity in both polarization and intensity for probe and coupling beam in a closed loop atomic system which is phase dependent.
Abstract The light–matter interaction for a four‐level double‐V‐type quantum system interacting with a pair of weak probe fields while located near a 2D array of metal‐coated dielectric nanospheres is studied. A situation is considered in which one of the probe field carries an optical vortex, that is, an electromagnetic field with optical angular momentum, and the other probe field has no vortex. It is demonstrated that due to the phase sensitivity of the closed‐loop double V‐type quantum system, the linear and nonlinear susceptibility of the non‐vortex probe beam depends on the azimuthal angle and orbital angular momentum (OAM) of the vortex probe beam. This feature is missing in an open four‐level double V‐type quantum system interacting with free‐space vacuum, as no quantum interference occurs in this case. The azimuthal dependence of optical susceptibility of the quantum system is used to determine the regions of spatially structured transparency.
Abstract We present an azimuthal phase-dependent scheme to study the spatially dependent electromagnetically induced transparency (EIT) and the generation of spatial light in a closed-loop four-level Y-type system. A structured control beam and a microwave (MW) field are adopted in the closed-loop structure. Interestingly, the weak non-vortex probe beam responses explicitly depend on the orbital angular momentum (OAM) of the control beam along with the MW-assisted quantum interference. The regions of spatially dependent EIT are demonstrated at different azimuthal angles. It is found that the intensity of the structured control beam and the relative phase arising out of the beams participating in the closed-loop can be used as the controlling knobs to tailor the shape and the angular location of the spatially dependent EIT.
In this paper, a theoretical investigation of electromagnetically induced transparency (EIT) using Laguerre–Gaussian (LG) beams has been carried out for the three canonical atom-laser coupled systems (e.g. [Formula: see text]-, V-, and [Formula: see text]-type) in [Formula: see text]Rb atom. The required optical Bloch equations (OBEs) are derived for each system. The OBEs are analytically solved in steady-state condition under the weak probe field approximation. We have used the iterative perturbative technique to obtain the probe coherence term. The probe response w.r.t. probe detuning for different orders of the orbital angular momentum (OAM) number of both the pump and probe LG beams has been studied. We have also studied the effect of the OAM number on probe response in both Doppler-free and Doppler-broadened mediums. It has been observed that the EIT signal is squeezed for nonzero OAM number of the pump beam with arbitrary OAM number of the probe beam. It is found that for higher-order OAM number, the EIT signal is further squeezed. The modification of the EIT signal is attributed because of the spatial-dependent Rabi frequency. Our study demonstrates that the dynamic of the probe field inside an atomic medium may be controlled by tuning the OAM number of the LG beam.
We conduct theoretical investigations into a fundamental closed-loop Λ-type atomic system using 87 Rb atoms, aiming to efficiently generate and manipulate structured light beams. A phase-singular microwave (MW) beam with a topological charge l μ and a phase-singular optical probe beam with a topological charge l p collectively induce phase-dependent atomic coherence, resulting in periodic oscillations of probe absorption in the transverse plane. The number of absorption or transparency windows in the transverse plane is determined by the resultant topological charge of the system, denoted as l = l μ − l p . We investigate the propagation of a paraxial doughnut-shaped probe beam through the phase-dependent atomic medium and showcase the generation of petal-like structured beams for various combinations of l μ and l p . We provide a detailed theoretical explanation of these results using the analytical expression of probe susceptibility. We outline how this scheme effectively serves as a sensor adept at discerning particular OAM modes. This selective detection capability is valuable in scenarios where only certain OAM states carry relevant information. The relative phase between the interacting fields can be used to rotate the structured probe beam by 360 deg in the clockwise or counterclockwise direction. This manipulation of spatial position of different OAM modes can be employed in implementing OAM-based logical operations.
Recently a scheme has been proposed for detection of the structured light by measuring the transmission of a vortex beam through a cloud of cold rubidium atoms with energy levels of the Λ-type configuration [N. Radwell et al., Phys. Rev. Lett.114, 123603 (2015) ]. This enables observation of regions of spatially dependent electromagnetically induced transparency (EIT). Here we suggest another scenario for detection of the structured light by measuring the absorption profile of a weak nonvortex probe beam in a highly resonant five-level combined tripod and Λ (CTL) atom-light coupling setup. We demonstrate that due to the closed-loop structure of CTL scheme, the absorption of the probe beam depends on the azimuthal angle and orbital angular momentum (OAM) of the control vortex beams. This feature is missing in simple Λ or tripod schemes, as there is no loop in such atom-light couplings. One can identify different regions of spatially structured transparency through measuring the absorption of probe field under different configurations of structured control light.
We investigate the propagation of an optical vector vortex beam in an atomic medium featuring four-level tripod transitions, where ground-state coherence is mediated by a transverse magnetic field. The vector beam consists of left- and right-circularly polarized components, each carrying an optical vortex with opposite orbital angular momentum (OAM). We study the linear response of the medium to the vector beam in order to determine the evolution of the beam's intensity and polarization profile. We find that the beam structure undergoes significant transformations as it propagates: the transverse intensity evolves from a ring-shaped profile to a petal-like structure, while the polarization transitions between left-circular, linear, and right-circular polarizations. Furthermore, when only the right-circular polarization component (a scalar vortex) enters the medium, it parametrically generates a left-circular polarization component, transferring its OAM to the generated field. This process converts the initial vortex beam into a superposition of left- and right-circular components, forming a scalar vortex beam where both polarization components carry the same OAM.