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14 pages, 583 KB

Open AccessArticle

Intrinsic Bi-Stability Due to Local Dipole–Dipole Interactions in Two-Level Systems and in Excited Crystalline Atomic Dimers

by Yacob Ben-Aryeh

Solids 2026, 7(1), 2; https://doi.org/10.3390/solids7010002 - 23 Dec 2025

Viewed by 739

Abstract

Intrinsic optical bi-stability in dense two-level systems is developed for the bad cavity limit where electromagnetic modes are adiabatically eliminated. Each atom interacts via dipole–dipole forces with its nearby spatial distribution of atoms. The theory is developed into two parts, corresponding to the [...] Read more.

Intrinsic optical bi-stability in dense two-level systems is developed for the bad cavity limit where electromagnetic modes are adiabatically eliminated. Each atom interacts via dipole–dipole forces with its nearby spatial distribution of atoms. The theory is developed into two parts, corresponding to the short sample, with dimensions shorter than the wavelength, and the long sample. In both cases, the local field corrections modify the Maxwell–Bloch equations, so that cubic or quartic equations are obtained for the inversion of population as a function of the external light intensity, thus leading to intrinsic bi-stability. The effects of noise sources on intrinsic bi-stability were treated, and I found that while the observability of bi-stability was not obtained experimentally for a simple two-level system, there were many observations of bi-stability obtained through the ‘up-conversion’ of rare earth excited crystals. I show the differences between these two systems. Full article

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22 pages, 690 KB

Open AccessArticle

Liouvillian Superoperator and Maxwell–Bloch Dynamics Under Optical Feedback via the Self-Mixing Effect in Terahertz Quantum Cascade Lasers

by Aleksandar Demić, Zoran Ikonić, Paul Dean, Xiaoqiong Qi, Thomas Taimre, Karl Bertling, Aleksandar D. Rakić and Dragan Indjin

Photonics 2025, 12(11), 1134; https://doi.org/10.3390/photonics12111134 - 17 Nov 2025

Cited by 1 | Viewed by 879

Abstract

We present a Maxwell–Bloch dynamics model for Terahertz Quantum Cascade Lasers (THz QCLs) that integrates a density matrix transport model, independent of the number of states per QCL period, with the Maxwell wave equation under the slow-varying envelope approximation. This model is extended [...] Read more.

We present a Maxwell–Bloch dynamics model for Terahertz Quantum Cascade Lasers (THz QCLs) that integrates a density matrix transport model, independent of the number of states per QCL period, with the Maxwell wave equation under the slow-varying envelope approximation. This model is extended to include external homodyne feedback, generalizing the Lang–Kobayashi model typically used for diode lasers. Unlike previous approaches, our model allows for the simulation of the self-mixing (SM) effect in THz QCLs without the need for effective parameters, commonly used in diode laser models. We demonstrate the model’s ability to capture laser dynamics and analyze the SM effect through numerical simulations. The model enables us to evaluate the quality of THz QCL designs for SM applications, which is not possible with effective two-level treatment via the Lang–Kobayashi approach. Full article

(This article belongs to the Special Issue Quantum Cascade Lasers: Recent Progress and Novel Applications)

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18 pages, 5635 KB

Open AccessArticle

Multi-Soliton Propagation and Interaction in Λ-Type EIT Media: An Integrable Approach

by Ramesh Kumar Vaduganathan, Prasanta K. Panigrahi and Boris A. Malomed

Photonics 2025, 12(10), 1034; https://doi.org/10.3390/photonics12101034 - 19 Oct 2025

Viewed by 811

Abstract

Electromagnetically induced transparency (EIT) is well known as a quantum optical phenomenon that permits a normally opaque medium to become transparent due to the quantum interference between transition pathways. This work addresses multi-soliton dynamics in an EIT system modeled by the integrable Maxwell–Bloch [...] Read more.

Electromagnetically induced transparency (EIT) is well known as a quantum optical phenomenon that permits a normally opaque medium to become transparent due to the quantum interference between transition pathways. This work addresses multi-soliton dynamics in an EIT system modeled by the integrable Maxwell–Bloch (MB) equations for a three-level

Λ

-type atomic configuration. By employing a generalized gauge transformation, we systematically construct explicit N-soliton solutions from the corresponding Lax pair. Explicit forms of one-, two-, three-, and four-soliton solutions are derived and analyzed. The resulting pulse structures reveal various nonlinear phenomena, such as temporal asymmetry, energy trapping, and soliton interactions. They also highlight coherent propagation, elastic collisions, and partial storage of pulses, which have potential implications for the design of quantum memory, slow light, and photonic data transport in EIT media. In addition, the conservation of fundamental physical quantities, such as the excitation norm and Hamiltonian, is used to provide direct evidence of the integrability and stability of the constructed soliton solutions. Full article

(This article belongs to the Section Quantum Photonics and Technologies)

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26 pages, 2724 KB

Open AccessReview

From Different Systems to a Single Common Model: A Review of Dynamical Systems Leading to Lorenz Equations

by Juan Carlos Chimal-Eguía, Florencio Guzmán-Aguilar, Víctor Manuel Silva-García, Héctor Báez-Medina and Manuel Alejandro Cardona-López

Axioms 2025, 14(6), 465; https://doi.org/10.3390/axioms14060465 - 13 Jun 2025

Cited by 2 | Viewed by 2160

Abstract

This paper presents an analytical exploration of how diverse dynamical systems, arising from different scientific domains, can be reformulated (under specific approximations and assumptions) into a common set of equations formally equivalent to the Lorenz system originally derived to model atmospheric convection. Unlike [...] Read more.

This paper presents an analytical exploration of how diverse dynamical systems, arising from different scientific domains, can be reformulated (under specific approximations and assumptions) into a common set of equations formally equivalent to the Lorenz system originally derived to model atmospheric convection. Unlike previous studies that focus on analyzing or applying the Lorenz equations, our objective is to show how these equations emerge from distinct models, emphasizing the underlying structural and dynamical similarities. The mathematical steps involved in these reformulations are included. The systems examined include Lorenz’s original atmospheric convection model, the chaotic water wheel, the Maxwell–Bloch equations for lasers, mechanical gyrostat, solar dynamo model, mesoscale reaction dynamics, an interest rate economic model, and a socioeconomic control system. This work includes a discussion of the unifying features that lead to similar qualitative behaviors across seemingly unrelated systems. By highlighting the Lorenz system as a paradigmatic limit of a broad class of nonlinear models, we underscore its relevance as a unifying framework in the study of complex dynamics. Full article

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13 pages, 245 KB

Open AccessArticle

Exact Solution of the Nonlocal

PT

-Symmetric (2 + 1)-Dimensional Hirota–Maxwell–Bloch System

by Zhaidary Myrzakulova, Zaruyet Zakariyeva, Anar Zhumakhanova and Kuralay Yesmakhanova

Mathematics 2025, 13(7), 1101; https://doi.org/10.3390/math13071101 - 27 Mar 2025

Cited by 1 | Viewed by 994

Abstract

This paper investigates the (2 + 1)-dimensional nonlocal Hirota–Maxwell–Bloch (NH-MB) system under various types of nonlocality. The mathematical consistency of possible nonlocal structures is analyzed, and three types that lead to a well-posed system are identified. The integrability of the system is established [...] Read more.

This paper investigates the (2 + 1)-dimensional nonlocal Hirota–Maxwell–Bloch (NH-MB) system under various types of nonlocality. The mathematical consistency of possible nonlocal structures is analyzed, and three types that lead to a well-posed system are identified. The integrability of the system is established through its Lax pair representation, and a Darboux transformation is constructed. Exact soliton solutions are obtained for both the defocusing and focusing cases. The results obtained may find applications in nonlinear optics, quantum theory, and the theory of integrable systems. Full article

(This article belongs to the Section E4: Mathematical Physics)

7 pages, 1658 KB

Open AccessProceeding Paper

Multilevel Phase Switch Generation in Alkali Vapors

by Abu Mohamed Alhasan and Salah Abdulrhmann

Eng. Proc. 2023, 31(1), 69; https://doi.org/10.3390/ASEC2022-13849 - 12 Dec 2022

Cited by 2 | Viewed by 1514

Abstract

We attempt to demonstrate optical phase switches in a typical light storage experiment. We computed propagation dynamics of light pulses in sodium-23, rubidium-87, and potassium-39 vapors. These vapors have the same tensorial sets of the density matrix with a nuclear spin I = [...] Read more.

We attempt to demonstrate optical phase switches in a typical light storage experiment. We computed propagation dynamics of light pulses in sodium-23, rubidium-87, and potassium-39 vapors. These vapors have the same tensorial sets of the density matrix with a nuclear spin I = 3/2. The energy scheme is known as the double-Λ system. We considered an excitation mechanism in which one of two Λ systems was excited by two-color pulses, probe, and drive, following the standard electromagnetically induced transparency configuration. The probe channel contains delayed two pulses after the first probe pulse. Gain is generated through the drive channel and is exposed during propagation. We further investigated the spatiotemporal phase variations in the pulses and found discrete phase distribution for different vapors. The spatiotemporal evolution of the irreducible tensorial sets defines structural differential equations. Additionally, it is particularly suitable for parallel processing. We hope our study finds an application in comparison to alkali vapor magnetometry. Full article

(This article belongs to the Proceedings of The 3rd International Electronic Conference on Applied Sciences)

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13 pages, 472 KB

Open AccessArticle

Approximate Closed-Form Solutions for the Maxwell-Bloch Equations via the Optimal Homotopy Asymptotic Method

by Remus-Daniel Ene, Nicolina Pop, Marioara Lapadat and Luisa Dungan

Mathematics 2022, 10(21), 4118; https://doi.org/10.3390/math10214118 - 4 Nov 2022

Cited by 12 | Viewed by 2299

Abstract

This paper emphasizes some geometrical properties of the Maxwell–Bloch equations. Based on these properties, the closed-form solutions of their equations are established. Thus, the Maxwell–Bloch equations are reduced to a nonlinear differential equation depending on an auxiliary unknown function. The approximate analytical solutions [...] Read more.

This paper emphasizes some geometrical properties of the Maxwell–Bloch equations. Based on these properties, the closed-form solutions of their equations are established. Thus, the Maxwell–Bloch equations are reduced to a nonlinear differential equation depending on an auxiliary unknown function. The approximate analytical solutions were built using the optimal homotopy asymptotic method (OHAM). These represent the

ε

-approximate OHAM solutions. A good agreement between the analytical and corresponding numerical results was found. The accuracy of the obtained results is validated through the representative figures. This procedure is suitable to be applied for dynamical systems with certain geometrical properties. Full article

(This article belongs to the Special Issue Application of Mathematical Method and Models in Dynamic System)

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20 pages, 2366 KB

Open AccessArticle

Atomistic Band-Structure Computation for Investigating Coulomb Dephasing and Impurity Scattering Rates of Electrons in Graphene

by Thi-Nga Do, Danhong Huang, Po-Hsin Shih, Hsin Lin and Godfrey Gumbs

Nanomaterials 2021, 11(5), 1194; https://doi.org/10.3390/nano11051194 - 1 May 2021

Cited by 6 | Viewed by 3187

Abstract

In this paper, by introducing a generalized quantum-kinetic model which is coupled self-consistently with Maxwell and Boltzmann transport equations, we elucidate the significance of using input from first-principles band-structure computations for an accurate description of ultra-fast dephasing and scattering dynamics of electrons in [...] Read more.

In this paper, by introducing a generalized quantum-kinetic model which is coupled self-consistently with Maxwell and Boltzmann transport equations, we elucidate the significance of using input from first-principles band-structure computations for an accurate description of ultra-fast dephasing and scattering dynamics of electrons in graphene. In particular, we start with the tight-binding model (TBM) for calculating band structures of solid covalent crystals based on localized Wannier orbital functions, where the employed hopping integrals in TBM have been parameterized for various covalent bonds. After that, the general TBM formalism has been applied to graphene to obtain both band structures and wave functions of electrons beyond the regime of effective low-energy theory. As a specific example, these calculated eigenvalues and eigen vectors have been further utilized to compute the Bloch-function form factors and intrinsic Coulomb diagonal-dephasing rates for induced optical coherence of electron-hole pairs in spectral and polarization functions, as well as the energy-relaxation time from extrinsic impurity scattering of electrons for non-equilibrium occupation in band transport. Full article

(This article belongs to the Special Issue Graphene for Electronics)

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19 pages, 455 KB

Open AccessArticle

Some Classical and Quantum Aspects of Gravitoelectromagnetism

by Giorgio Papini

Entropy 2020, 22(10), 1089; https://doi.org/10.3390/e22101089 - 27 Sep 2020

Cited by 5 | Viewed by 2972

Abstract

It has been shown that, even in linear gravitation, the curvature of space-time can induce ground state degeneracy in quantum systems, break the continuum symmetry of the vacuum and give rise to condensation in a system of identical particles. Condensation takes the form [...] Read more.

It has been shown that, even in linear gravitation, the curvature of space-time can induce ground state degeneracy in quantum systems, break the continuum symmetry of the vacuum and give rise to condensation in a system of identical particles. Condensation takes the form of a temperature-dependent correlation over distances, of momenta oscillations about an average momentum, of vortical structures and of a positive gravitational susceptibility. In the interaction with quantum matter and below a certain range, gravity is carried by an antisymmetric, second order tensor that satisfies Maxwell-type equations. Some classical and quantum aspects of this type of “gravitoelectromagnetism” were investigated. Gravitational analogues of the laws of Curie and Bloch were found for a one-dimensional model. A critical temperature for a change in phase from unbound to isolated vortices can be calculated using an

X Y

-model. Full article

(This article belongs to the Special Issue Gravitomagnetism and Quantum Mechanics)

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9 pages, 723 KB

Open AccessArticle

Understanding of Collective Atom Phase Control in Modified Photon Echoes for a Near-Perfect Storage Time-Extended Quantum Memory

by Rahmat Ullah and Byoung S. Ham

Entropy 2020, 22(8), 900; https://doi.org/10.3390/e22080900 - 15 Aug 2020

Cited by 2 | Viewed by 3807

Abstract

A near-perfect storage time-extended photon echo-based quantum memory protocol has been analyzed by solving the Maxwell–Bloch equations for a backward scheme in a three-level system. The backward photon echo scheme is combined with a controlled coherence conversion process via controlled Rabi flopping to [...] Read more.

A near-perfect storage time-extended photon echo-based quantum memory protocol has been analyzed by solving the Maxwell–Bloch equations for a backward scheme in a three-level system. The backward photon echo scheme is combined with a controlled coherence conversion process via controlled Rabi flopping to a third state, where the control Rabi flopping collectively shifts the phase of the ensemble coherence. The propagation direction of photon echoes is coherently determined by the phase-matching condition between the data (quantum) and the control (classical) pulses. Herein, we discuss the classical controllability of a quantum state for both phase and propagation direction by manipulating the control pulses in both single and double rephasing photon echo schemes of a three-level system. Compared with the well-understood uses of two-level photon echoes, the Maxwell–Bloch equations for a three-level system have a critical limitation regarding the phase change when interacting with an arbitrary control pulse area. Full article

(This article belongs to the Special Issue Quantum Information Processing)

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8 pages, 2081 KB

Open AccessArticle

Single and Multi-Soliton Solutions for a Spectrally Deformed Set of Maxwell-Bloch Equations

by Mehmet K. Baran

Symmetry 2019, 11(3), 435; https://doi.org/10.3390/sym11030435 - 25 Mar 2019

Viewed by 3054

Abstract

A specific spectral deformation of the Maxwell-Bloch equations of nonlinear optics is investigated. The Darboux transformation formalism is adapted to this spectrally deformed system to construct its single and multi-soliton solutions. The Effects of spectral deformation on soliton behaviour is studied. Full article

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24 pages, 234 KB

Open AccessArticle

Integrable (2 + 1)-Dimensional Spin Models with Self-Consistent Potentials

by Ratbay Myrzakulov, Galya Mamyrbekova, Gulgassyl Nugmanova and Muthusamy Lakshmanan

Symmetry 2015, 7(3), 1352-1375; https://doi.org/10.3390/sym7031352 - 3 Aug 2015

Cited by 73 | Viewed by 6554

Abstract

Integrable spin systems possess interesting geometrical and gauge invariance properties and have important applications in applied magnetism and nanophysics. They are also intimately connected to the nonlinear Schrödinger family of equations. In this paper, we identify three different integrable spin systems in (2 [...] Read more.

Integrable spin systems possess interesting geometrical and gauge invariance properties and have important applications in applied magnetism and nanophysics. They are also intimately connected to the nonlinear Schrödinger family of equations. In this paper, we identify three different integrable spin systems in (2 + 1) dimensions by introducing the interaction of the spin field with more than one scalar potential, or vector potential, or both. We also obtain the associated Lax pairs. We discuss various interesting reductions in (2 + 1) and (1 + 1) dimensions. We also deduce the equivalent nonlinear Schrödinger family of equations, including the (2 + 1)-dimensional version of nonlinear Schrödinger–Hirota–Maxwell–Bloch equations, along with their Lax pairs. Full article

(This article belongs to the Special Issue Symmetry Breaking)

31 pages, 6548 KB

Open AccessArticle

Bloch Modes and Evanescent Modes of Photonic Crystals: Weak Form Solutions Based on Accurate Interface Triangulation

by Matthias Saba and Gerd E. Schröder-Turk

Crystals 2015, 5(1), 14-44; https://doi.org/10.3390/cryst5010014 - 5 Jan 2015

Cited by 22 | Viewed by 12851

Abstract

We propose a new approach to calculate the complex photonic band structure, both purely dispersive and evanescent Bloch modes of a finite range, of arbitrary three-dimensional photonic crystals. Our method, based on a well-established plane wave expansion and the weak form solution of [...] Read more.

We propose a new approach to calculate the complex photonic band structure, both purely dispersive and evanescent Bloch modes of a finite range, of arbitrary three-dimensional photonic crystals. Our method, based on a well-established plane wave expansion and the weak form solution of Maxwell’s equations, computes the Fourier components of periodic structures composed of distinct homogeneous material domains from a triangulated mesh representation of the inter-material interfaces; this allows substantially more accurate representations of the geometry of complex photonic crystals than the conventional representation by a cubic voxel grid. Our method works for general two-phase composite materials, consisting of bi-anisotropic materials with tensor-valued dielectric and magnetic permittivities ε and μ and coupling matrices ς. We demonstrate for the Bragg mirror and a simple cubic crystal closely related to the Kelvin foam that relatively small numbers of Fourier components are sufficient to yield good convergence of the eigenvalues, making this method viable, despite its computational complexity. As an application, we use the single gyroid crystal to demonstrate that the consideration of both conventional and evanescent Bloch modes is necessary to predict the key features of the reflectance spectrum by analysis of the band structure, in particular for light incident along the cubic [111] direction. Full article

(This article belongs to the Special Issue Photonic Crystals)

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