Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Nonlinear Optical Phenomena in Atomic Media: Gaussian Beam Propagation with Kerr Effect and Spatial Refractive Index Modulation

Muhammad T ariq, Abuzar Khan

Published Feb 8, 2024• 0 citations
Publisher

Abstract

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.

DOI
10.21203/rs.3.rs-3933720/v1

Related papers

Dynamics of Hermite-Gaussian Beam Propagation in a Five-Level Tripod-Type Atomic Medium with Spatially Dependent Refractive Index

Muhammad Tariq, Abuzar Khan

This research investigates the intricate interplay between a Hermite-Gaussian (HG) weak probe field and a five-level tripod atomic medium, modulated by three laser fields. The atomic medium's refractive index is made spatially dependent by a Hermite-Gaussian beam of light and influenced further by a Kerr field and a control field. The study focuses on exploring the impact of key parameters on the propagation dynamics of the HG probe field. The primary parameters under scrutiny include the probe field detuning ($\Delta_P/\gamma$), Kerr, coherent pump, and control field characteristics such as Rabi frequencies and detunings ($\Omega_{1,2,3}/\gamma$, $\Delta_{1,2,3}/\gamma$), as well as spatial coordinates $x/\omega_0$ and $y/\omega_0$, where $\omega_0$ denotes the Gaussian beam waist. Through systematic analysis, we elucidate the intricate effects of these parameters on the modulation of the HG probe field within the atomic medium. The study not only contributes to the fundamental understanding of light-matter interactions in complex atomic systems but also holds promise for potential applications in quantum information processing and communication. The results provide valuable insights into the control and manipulation of light beams in spatially varying media, paving the way for advancements in quantum optics and atomic physics.

•Jan 30, 2024•0 citations

Dynamics of Hermite-Gaussian Beam Propagation in a Five-Level Tripod-Type Atomic Medium with Spatially Dependent Refractive Index

Muhammad Tariq, Abuzar Khan

This research investigates the intricate interplay between a Hermite-Gaussian (HG) weak probe field and a five-level tripod atomic medium, modulated by three laser fields. The atomic medium's refractive index is made spatially dependent by a Hermite-Gaussian beam of light and influenced further by a Kerr field and a control field. The study focuses on exploring the impact of key parameters on the propagation dynamics of the HG probe field. The primary parameters under scrutiny include the probe field detuning ($\Delta_P/\gamma$), Kerr, coherent pump, and control field characteristics such as Rabi frequencies and detunings ($\Omega_{1,2,3}/\gamma$, $\Delta_{1,2,3}/\gamma$), as well as spatial coordinates $x/\omega_0$ and $y/\omega_0$, where $\omega_0$ denotes the Gaussian beam waist. Through systematic analysis, we elucidate the intricate effects of these parameters on the modulation of the HG probe field within the atomic medium. The study not only contributes to the fundamental understanding of light-matter interactions in complex atomic systems but also holds promise for potential applications in quantum information processing and communication. The results provide valuable insights into the control and manipulation of light beams in spatially varying media, paving the way for advancements in quantum optics and atomic physics.

•Jan 30, 2024•0 citations

Theoretical study of spatially controlled atomic localization using hybrid Gaussian & Laguerre–Gaussian beams

Himani Thakur, Zubair Iqbal Dar, Paramjit Kaur

Abstract We study high-resolution atomic localization in a multilevel atomic system driven simultaneously by a Gaussian and a Laguerre–Gaussian (LG) beam. The coexistence of the two fields creates a hybrid coupling landscape in which the Gaussian beam supplies radial confinement, while the LG beam contributes an orbital angular momentum (OAM)-dependent azimuthal modulation. By solving the steady-state density-matrix equations, we show that the resulting localization patterns contain mixed spatial harmonics whose structure is set by the topological charge, beam waist, and probe detuning. The OAM index determines the angular symmetry of the localized absorption features, whereas the beam waist controls their radial extent. Probe detuning provides an additional tuning mechanism that alters the contrast and geometry of the localization regions. These results highlight how structured light fields can be used to engineer controllable spatial localization in atomic media, with relevance to precision metrology, spatially resolved quantum control, and structured-light sensing.

Physica Scripta•Apr 9, 2026•0 citations

Complement 7B: Nonlinear optics in optical Kerr media

G. Grynberg, Alain Aspect, Claude Fabre +1 more

In this complement we discuss several examples of optical phenomena in media where the refractive index depends nonlinearly on the intensity , known as optical Kerr media. This nonlinear effect exists in all materials, even isotropic ones, like glass or fused silica, but it is particularly marked in certain physical systems to be exemplified in Section 7B.1. After investigating the propagation of light through such media in Section 7B.2, we shall discuss three applications of the optical Kerr effect (which can be studied in any order). We begin by describing a bistable optical system , when this nonlinear medium is inserted in a Fabry–Perot cavity (Section 7B.3). We then study phase conjugate mirrors and examine their potential applications in adaptive optics (Section 7B.4). Finally, we discuss certain effects occurring during the propagation of an isolated wave, bounded either transversely or temporally, in a Kerr medium, and describe self-focusing effects (Section 7B.5) and self-phase-modulation effects (Section 7B.6). In particular, we shall show that nonlinear effects and dispersion effects can compensate to produce stable structures known as solitons , which maintain their shape during propagation. Examples of third-order nonlinearities Nonlinear response of two-level atoms We begin by studying a simple case of a nonlinear interaction, namely a two-level quantum system under the effects of a plane wave.

Cambridge University Press eBooks•Sep 2, 2010•0 citations

Modeling the nonlinear refractive index in atomic gases

Christian Kohler, Roland Guichard, Emmanuel Lorin +4 more

Accurate modeling of optical nonlinearities is crucial to describe macroscopic laser propagation in a medium, including sum frequency generation, spectral broadening due to self-phase modulation, various ionization processes and soliton formation. For incident laser light the response of the medium is given by the induced polarization of the microscopic system. The polarization is usually expanded in a Taylor series for the electric field amplitude, which is truncated after the first non-linear term being of third order for isotropic media. A third-order nonlinearity leads to the well-known optical Kerr effect, where the refractive index of the medium becomes intensity dependent via n = n0+ n2I. This leads to an inherent problem when modeling laser propagation in two or more spatial dimensions, linked to the formal divergence (n2> 0) of the refractive index for increasing intensity.

Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)•May 1, 2013•0 citations

Manipulating Spin-Torque Dynamics in Atomic Media Using Kerr Field with Two-Wave Interference

Muhammad Tariq, Abuzar Khan

Abstract In this article, Spin density and Torque of two interfering waves are controlled and manipulated by applying two interacting control fields in which one is the Kerr field with Rabi frequency Ω2 and a probe field using a four-level N-type atomic configuration of Rubidium-87 isotope. The spin density of light can be controlled coherently in the atomic medium by electromagnetically induced transparency (EIT). When the strong interacting control fields and the weak probe field are applied to the atomic medium, the Rubidium atoms become transparent to the probe field. It is due to the control fields that ”dress” the atoms, creating a new energy state that the weak probe field can interact with. As a result, the weak probe field can pass through the Rubidium atomic medium without being absorbed. Substantial variations can be seen in the electric SAM and Torque of two interfering waves with variations in the angle β between the two interfering waves, the Rabi frequencies of the control fields, the detuning of the probe field, and the phase difference δϕ between waves. By introducing these changes of parameters in the atomic medium, the spin density of two interfering waves can be made to rotate in a specific direction or at a specific rate. The parameters of control fields and probe field detuning play an essential role in the modification of electric SAM and electric spin vector field distribution of the probe field. The modified work of this manuscript is useful for Quantum computing, Optical communication, Quantum information processing.

•Feb 13, 2024•0 citations
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.
This research investigates the intricate interplay between a Hermite-Gaussian (HG) weak probe field and a five-level tripod atomic medium, modulated by three laser fields. The atomic medium's refractive index is made spatially dependent by a Hermite-Gaussian beam of light and influenced further by a Kerr field and a control field. The study focuses on exploring the impact of key parameters on the propagation dynamics of the HG probe field. The primary parameters under scrutiny include the probe field detuning (ΔP/γ\Delta_P/\gammaΔP​/γ), Kerr, coherent pump, and control field characteristics such as Rabi frequencies and detunings (Ω1,2,3/γ\Omega_{1,2,3}/\gammaΩ1,2,3​/γ, Δ1,2,3/γ\Delta_{1,2,3}/\gammaΔ1,2,3​/γ), as well as spatial coordinates x/ω0x/\omega_0x/ω0​ and y/ω0y/\omega_0y/ω0​, where ω0\omega_0ω0​ denotes the Gaussian beam waist. Through systematic analysis, we elucidate the intricate effects of these parameters on the modulation of the HG probe field within the atomic medium. The study not only contributes to the fundamental understanding of light-matter interactions in complex atomic systems but also holds promise for potential applications in quantum information processing and communication. The results provide valuable insights into the control and manipulation of light beams in spatially varying media, paving the way for advancements in quantum optics and atomic physics.
This research investigates the intricate interplay between a Hermite-Gaussian (HG) weak probe field and a five-level tripod atomic medium, modulated by three laser fields. The atomic medium's refractive index is made spatially dependent by a Hermite-Gaussian beam of light and influenced further by a Kerr field and a control field. The study focuses on exploring the impact of key parameters on the propagation dynamics of the HG probe field. The primary parameters under scrutiny include the probe field detuning (ΔP/γ\Delta_P/\gammaΔP​/γ), Kerr, coherent pump, and control field characteristics such as Rabi frequencies and detunings (Ω1,2,3/γ\Omega_{1,2,3}/\gammaΩ1,2,3​/γ, Δ1,2,3/γ\Delta_{1,2,3}/\gammaΔ1,2,3​/γ), as well as spatial coordinates x/ω0x/\omega_0x/ω0​ and y/ω0y/\omega_0y/ω0​, where ω0\omega_0ω0​ denotes the Gaussian beam waist. Through systematic analysis, we elucidate the intricate effects of these parameters on the modulation of the HG probe field within the atomic medium. The study not only contributes to the fundamental understanding of light-matter interactions in complex atomic systems but also holds promise for potential applications in quantum information processing and communication. The results provide valuable insights into the control and manipulation of light beams in spatially varying media, paving the way for advancements in quantum optics and atomic physics.
Abstract We study high-resolution atomic localization in a multilevel atomic system driven simultaneously by a Gaussian and a Laguerre–Gaussian (LG) beam. The coexistence of the two fields creates a hybrid coupling landscape in which the Gaussian beam supplies radial confinement, while the LG beam contributes an orbital angular momentum (OAM)-dependent azimuthal modulation. By solving the steady-state density-matrix equations, we show that the resulting localization patterns contain mixed spatial harmonics whose structure is set by the topological charge, beam waist, and probe detuning. The OAM index determines the angular symmetry of the localized absorption features, whereas the beam waist controls their radial extent. Probe detuning provides an additional tuning mechanism that alters the contrast and geometry of the localization regions. These results highlight how structured light fields can be used to engineer controllable spatial localization in atomic media, with relevance to precision metrology, spatially resolved quantum control, and structured-light sensing.
In this complement we discuss several examples of optical phenomena in media where the refractive index depends nonlinearly on the intensity , known as optical Kerr media. This nonlinear effect exists in all materials, even isotropic ones, like glass or fused silica, but it is particularly marked in certain physical systems to be exemplified in Section 7B.1. After investigating the propagation of light through such media in Section 7B.2, we shall discuss three applications of the optical Kerr effect (which can be studied in any order). We begin by describing a bistable optical system , when this nonlinear medium is inserted in a Fabry–Perot cavity (Section 7B.3). We then study phase conjugate mirrors and examine their potential applications in adaptive optics (Section 7B.4). Finally, we discuss certain effects occurring during the propagation of an isolated wave, bounded either transversely or temporally, in a Kerr medium, and describe self-focusing effects (Section 7B.5) and self-phase-modulation effects (Section 7B.6). In particular, we shall show that nonlinear effects and dispersion effects can compensate to produce stable structures known as solitons , which maintain their shape during propagation. Examples of third-order nonlinearities Nonlinear response of two-level atoms We begin by studying a simple case of a nonlinear interaction, namely a two-level quantum system under the effects of a plane wave.
Accurate modeling of optical nonlinearities is crucial to describe macroscopic laser propagation in a medium, including sum frequency generation, spectral broadening due to self-phase modulation, various ionization processes and soliton formation. For incident laser light the response of the medium is given by the induced polarization of the microscopic system. The polarization is usually expanded in a Taylor series for the electric field amplitude, which is truncated after the first non-linear term being of third order for isotropic media. A third-order nonlinearity leads to the well-known optical Kerr effect, where the refractive index of the medium becomes intensity dependent via n = n0+ n2I. This leads to an inherent problem when modeling laser propagation in two or more spatial dimensions, linked to the formal divergence (n2> 0) of the refractive index for increasing intensity.
Abstract In this article, Spin density and Torque of two interfering waves are controlled and manipulated by applying two interacting control fields in which one is the Kerr field with Rabi frequency Ω2 and a probe field using a four-level N-type atomic configuration of Rubidium-87 isotope. The spin density of light can be controlled coherently in the atomic medium by electromagnetically induced transparency (EIT). When the strong interacting control fields and the weak probe field are applied to the atomic medium, the Rubidium atoms become transparent to the probe field. It is due to the control fields that ”dress” the atoms, creating a new energy state that the weak probe field can interact with. As a result, the weak probe field can pass through the Rubidium atomic medium without being absorbed. Substantial variations can be seen in the electric SAM and Torque of two interfering waves with variations in the angle β between the two interfering waves, the Rabi frequencies of the control fields, the detuning of the probe field, and the phase difference δϕ between waves. By introducing these changes of parameters in the atomic medium, the spin density of two interfering waves can be made to rotate in a specific direction or at a specific rate. The parameters of control fields and probe field detuning play an essential role in the modification of electric SAM and electric spin vector field distribution of the probe field. The modified work of this manuscript is useful for Quantum computing, Optical communication, Quantum information processing.