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arXiv:2401.05793 · Physical Review A

Spatial characterization of Fraunhofer diffraction in a four-level light-matter-coupling system

Seyyed Hossein Asadpour, Teodora Kirova, Hamid Reza Hamedi, Reza Asgari

Published Feb 6, 2024• 18 citations
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Abstract

We explore the spatial features of various orders of Fraunhofer diffraction patterns in a four-level $N$-type atomic system. The system interacts with a weak probe light, a standing wave (SW) coupling field in the $x$ direction, and a cylindrical beam of composite optical vortex type. We derive the first-order linear and third-order cross-Kerr nonlinear parts of the probe susceptibility by expanding the probe susceptibility of the system into the second order of the SW beam. This allows us to solve the integral equation of Fraunhofer diffraction, decoding its varying degrees to specific degrees of Bessel functions containing the nonlinear susceptibility. Notably, the nonlinear susceptibility exhibits dependence on the orbital angular momentum (OAM) of the light beam, leading to spatial variations in the Bessel functions, and consequently, in the different orders of Fraunhofer diffraction. Leveraging the manipulation of OAM, we achieve precise control over the spatial mapping of diverse diffraction orders at various locations. Our research sheds light on the spatial behavior of Fraunhofer diffraction in complex atomic systems. It presents exciting prospects for harnessing the OAM characteristics of light in future optical technologies.

DOI
10.1103/physreva.109.023702

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Abstract In this paper, we study the Fraunhofer diffraction pattern in a four-level quantum dot nanostructure. The quantum dot interacts with two weak probe and signal laser fields and two strong coupling lights where one of them is a two-dimensional standing wave field. We study the Fraunhofer diffraction pattern of the transmitted probe light when the coherent driving light becomes plan wave or Laguerre Gaussian (LG) vortex light. We found that by controlling the relative phase of the applied lights and orbital angular momentum (OAM) of LG light, the Fraunhofer diffraction pattern can be controlled and the probe energy transfer from zero order to the higher orders, respectively. Moreover, we realized that by controlling the OAM number of the vortex light the asymmetric diffraction pattern is possible.
Abstract The experimental realization of two-dimensional (2D) electromagnetically induced grating is explored by monitoring the Fraunhofer diffraction pattern in a microwave-driven four-level Y-type atomic medium under the action of two orthogonal standing-wave (SW) fields. Due to the position-dependent atom–field interaction, the information about the high diffraction order of the probe light can be obtained via the Fraunhofer diffraction pattern of the probe light. It is found that the diffraction behavior is significantly improved due to the joint quantum interference induced by the SW and microwave-driven cycling fields. Most importantly, the amplitude and phase diagram of the transmission function of the probe light can be modulated at a particular position and the probe energy may transfer to the high orders of the diffraction by properly adjusting the system parameters. The proposed scheme may provide a promising way to achieve highly sensitive diffraction patterns with applications in quantum information processing.
Abstract In this paper, we investigated electromagnetically induced grating in a three-level atomic system via relative phase between applied lights. The three-level atomic system interacts with a weak probe light, a signal light and a strong standing wave coupling light in two-dimensional directions. We realized that Fraunhofer diffraction pattern can be obtained by tuning the intensity and detuning’s of the coupling light. We also use of optical vortex light instead of optical plane wave and found that the asymmetric diffraction pattern can be obtained via orbital angular momentum (OAM), respectively. We also studied the different orders of the diffraction pattern versus relative phase of applied lights for different number of OAM.
We demonstrate coherence-controlled azimuthal modulation of electromagnetically induced transparency (EIT) and all-optical switching in a four-level atomic ensemble coupled to a Laguerre-Gaussian beam, a control field, and a microwave field. The spatial EIT patterns exhibit doublet, quartet, and sextuplet structures, evolving into more complex structures with increasing orbital angular momentum (OAM). These structures can be dynamically switched between EIT and absorption patterns, preserving mirror image symmetry (with even OAM) and rotation symmetry (with odd OAM) by adjusting the relative phase of the coupling fields. By creating two-dimensional electromagnetically induced gratings (EIGs), we find that the diffractive patterns are influenced by probe field detuning, OAM, and relative phase. Specifically, the diffraction patterns of a probe field exhibit complex behavior across first to fourth orders, with intensities influenced by topological charge and azimuthal angle. The diffraction patterns are further modulated by the relative phase, with patterns at 0 and π being mirror images of each other, while the pattern at π /2 exhibits distinct behavior. These findings highlight the potential for precise control over structural EIT, all optical switching and diffraction patterns in coherent atomic media.
We investigate theoretically the spatially dependent linear and nonlinear optical properties of a four-level germanium-vacancy center system in diamond, driven by coherent laser fields under electromagnetically induced transparency conditions. In our model, one of the strong coupling fields carries orbital angular momentum (OAM) and is treated as a composite vortex beam. By numerically solving the steady-state equations of the motion, we demonstrate that both linear and third-order nonlinear optical susceptibilities are highly sensitive to the OAM value of the coupling field. Our results reveal that increasing the OAM induces spectral splitting, enhances Kerr nonlinearity, and enables the emergence of structured absorption and dispersion profiles with characteristic 2l-fold azimuthal symmetry. Notably, we identify the formation of nonlinear islands—localized spatial regions where strong Kerr nonlinearity coincides with minimal absorption. These islands are tunable via the OAM number and detuning parameters, providing a powerful mechanism for spatial control of light–matter interactions. This work offers new insights into OAM-mediated coherence effects in solid-state quantum systems and points toward promising applications in nonlinear photonics, optical information processing, and spatially structured quantum devices.
We study the propagation of probe pulses carrying orbital angular momentum (OAM) in a crystal of molecular magnets characterized by a double-$\mathrm{\ensuremath{\Lambda}}$ light-matter coupling scheme. The model is based on the four-wave mixing (FWM) of applied fields interacting with the magnetic dipole moment of the molecular magnets. We consider the light-matter interaction under the situation where a weak probe field carries an optical vortex and investigate the exchange of optical vortices between different frequencies via the FWM in the microwave region. The propagation of OAM beams with nonzero radial indices is then explored. It is found that the conservation of both azimuthal and radial indices is satisfied over the swapping of OAM states of light. Superimposing two initially weak OAM modes with different topological charges creates specific vortex beams with a very characteristic form. The resulting beam contains a central vortex as well as several singly charged peripheral vortices distributed at the same radial distance from the center of the light beam. This complex pattern of vortices arises because the intensity radius of two interfering OAM modes is different. It is shown that the boundary region of intensity dominance of two OAM modes can be controlled by the molecular magnets parameters and strong cw electromagnetic fields. Our proposed scheme may provide a route to study the solid systems suitable for quantum technologies as well as for OAM exchange devices for quantum information processing.