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

arXiv:1905.06897 · Scientific Reports

Light propagation in inhomogeneous media, coupled quantum harmonic oscillators and phase transitions

Alejandro R. Urzúa, I. Ramos-Prieto, Francisco Soto, Victor M. Arrizon, H. M. Moya-Cessa

Published Nov 14, 2019• 17 citations
arXivHTMLPDF

Abstract

This contribution has two main purposes. First, using classical optics we show how to model two coupled quantum harmonic oscillators and two interacting quantized fields. Second, we present classical analogs of coupled harmonic oscillators that correspond to anisotropic quadratic graded indexed media in a rotated reference frame, and we use operator techniques, common to quantum mechanics, to solve the propagation of light through a particular type of graded indexed medium. Additionally, we show that the system presents phase transitions.

DOI
10.1038/s41598-019-53024-5

Related papers

Optical realization of quantum-mechanical invariants

H. M. Moya-Cessa, M. Fernández‐Guasti, Victor M. Arrizon +1 more

We study the problem of paraxial propagation in two grade-index media by using invariant techniques that allow a continuous solution of the problem. By using the well-known fact that this problem is analogous to the time-dependent harmonic oscillator in quantum mechanics, known methods there may be imported producing on the one hand a solution to the propagation problem and on the other hand a realization of a quantum-mechanical invariant.

Optics Letters•Apr 28, 2009•9 citations

Coherent states and light propagation in inhomogeneous media

Sergei G. Krivoshlykov, I N Sisakyan

Methods of integrals of motion, coherent states, dynamical symmetry group, and density matrix formalism are used to describe the propagation of light in weakly inhomogeneous media, in particular, in a two-dimensional medium having a quadratic transverse distribution of the refractive index and an arbitrarily inhomogeneous longitudinal distribution. Expressions are obtained for the trajectories and widths of the modes and rays. The coefficients of coupling between the modes and rays due to the longitudinal inhomogeneity of the medium and distortion of the axis are discussed. It is shown that, for certain laws of longitudinal inhomogeneity, matching occurs when no energy redistribution takes place between the modes and mismatch is found when all the energy is coupled out of the medium. On the basis of these effects, methods of matched joining of two different graded-index optical waveguides and of coupling light out of a graded-index waveguide are proposed. It is shown that each initial mode of the medium is strongly coupled to three final modes. These results may be used in fiber-optic communication lines.

Soviet Journal of Quantum Electronics•Mar 31, 1980•12 citations

Quantum Electromagnetics: A New Look—Part II

Weng Cho Chew, Anna Yan Liu, C. Salazar-Lazaro +1 more

In this work, quantization of electromagnetic fields in a general anisotropic inhomogeneous media is considered. First, the classical Hamiltonian is derived. Once the Hamiltonian is derived, with it the classical equations of motion follow. Next, the fields are elevated to become quantum operators, for which conjugate pairs are endowed with commutators. Since as previously shown, such commutators induce functional derivatives, the quantum equations of motion can be easily derived. Next, the mode decomposition of the fields is demonstrated. Upon substitution into the classical Hamiltonian, each mode then behaves like a simple harmonic oscillator. These oscillators can then be elevated to become quantum harmonic oscillators. Both the traveling wave modes and the standing wave modes are discussed. Furthermore, the longitudinal modes are described. Finally, the case of impressed sources are considered, with the corresponding Hamiltonian and field quantization. The Green's functions for the linear system are presented. Finally, the quantum Maxwell's equations are derived. A short discussion on field-atom interaction is given.

IEEE journal on multiscale and multiphysics computational techniques•Jan 1, 2016•52 citations

Oscillating between classically entangled state and separable state: an analogy between classical and quantum optics

Shahram Dehdashti, Firat Yasar

In this paper, we study the possible realization of a classical system with quantum characteristics on the level of classical optics. Indeed, following Arrizon et al. [ J. Opt. Soc. Am. A 32 , 1140 ( 2015 ) JOAOD6 0740-3232 10.1364/JOSAA.32.001140 ], we first use quantum optics formalism to consider the propagation of two coherent states in a Kerr medium where the interaction between the two states is described by the cross-Kerr interaction. We then draw an analogy between the dynamical process of this structure and that of a Gaussian wave propagating in a quadratic gradient index medium. We demonstrate that by using this structure, we can generate a state that oscillates between a classically entangled state and a separable one.

Journal of the Optical Society of America B•May 26, 2020•0 citations

Propagation of quantized fields through negative-index media

Martin Ligare

Dielectric materials in which both the relative permittivity, ε, and the relative permeability, μ, are negative exhibit striking optical properties, which are a consequence of the fact that the effective index of refraction in such materials is negative. Most studies of the propagation of electromagnetic fields in these media have concentrated on classical fields with well-defined phases. In contrast, I use simple fully-quantized models to illustrate how some of the striking properties of negative-index media are manifested in the propagation of single, spontaneously emitted, photons. Single-photon quantum fields do not have an absolute phase, but the examples in this paper demonstrate a quantum analog of the negative phase accumulated by classical fields as photons propagate through negative-index media. The single photons also exhibit classical reflection and transmission coefficients, as well as the expected group velocity.

Journal of Modern Optics•Sep 6, 2011•1 citation

Propagation of quantized fields in negative-index media

Martin Ligare, J. Mod

Dielectric materials in which both the relative permittivity, , and the relative permeability, µ, are negative exhibit striking optical properties, which are the consequence of the fact that the effective index of refraction in such materials is negative.Most studies of the propagation of electromagnetic fields in these media have concentrated on classical fields with well-defined phases.In contrast, I use simple fully-quantized models to illustrate how some of the striking properties of negative-index media are manifested in the propagation of single, spontaneously emitted, photons.Single-photon quantum fields do not have an absolute phase, but the examples in this paper demonstrate a quantum analog of the negative phase accumulated by classical fields as photons propagate through negative-index media.The single photons also exhibit classical reflection and transmission coefficients, as well as the expected group velocity.

International Conference on Optical Communication Systems•Jan 1, 2011•0 citations
This contribution has two main purposes. First, using classical optics we show how to model two coupled quantum harmonic oscillators and two interacting quantized fields. Second, we present classical analogs of coupled harmonic oscillators that correspond to anisotropic quadratic graded indexed media in a rotated reference frame, and we use operator techniques, common to quantum mechanics, to solve the propagation of light through a particular type of graded indexed medium. Additionally, we show that the system presents phase transitions.
Methods of integrals of motion, coherent states, dynamical symmetry group, and density matrix formalism are used to describe the propagation of light in weakly inhomogeneous media, in particular, in a two-dimensional medium having a quadratic transverse distribution of the refractive index and an arbitrarily inhomogeneous longitudinal distribution. Expressions are obtained for the trajectories and widths of the modes and rays. The coefficients of coupling between the modes and rays due to the longitudinal inhomogeneity of the medium and distortion of the axis are discussed. It is shown that, for certain laws of longitudinal inhomogeneity, matching occurs when no energy redistribution takes place between the modes and mismatch is found when all the energy is coupled out of the medium. On the basis of these effects, methods of matched joining of two different graded-index optical waveguides and of coupling light out of a graded-index waveguide are proposed. It is shown that each initial mode of the medium is strongly coupled to three final modes. These results may be used in fiber-optic communication lines.
In this work, quantization of electromagnetic fields in a general anisotropic inhomogeneous media is considered. First, the classical Hamiltonian is derived. Once the Hamiltonian is derived, with it the classical equations of motion follow. Next, the fields are elevated to become quantum operators, for which conjugate pairs are endowed with commutators. Since as previously shown, such commutators induce functional derivatives, the quantum equations of motion can be easily derived. Next, the mode decomposition of the fields is demonstrated. Upon substitution into the classical Hamiltonian, each mode then behaves like a simple harmonic oscillator. These oscillators can then be elevated to become quantum harmonic oscillators. Both the traveling wave modes and the standing wave modes are discussed. Furthermore, the longitudinal modes are described. Finally, the case of impressed sources are considered, with the corresponding Hamiltonian and field quantization. The Green's functions for the linear system are presented. Finally, the quantum Maxwell's equations are derived. A short discussion on field-atom interaction is given.
In this paper, we study the possible realization of a classical system with quantum characteristics on the level of classical optics. Indeed, following Arrizon et al. [ J. Opt. Soc. Am. A 32 , 1140 ( 2015 ) JOAOD6 0740-3232 10.1364/JOSAA.32.001140 ], we first use quantum optics formalism to consider the propagation of two coherent states in a Kerr medium where the interaction between the two states is described by the cross-Kerr interaction. We then draw an analogy between the dynamical process of this structure and that of a Gaussian wave propagating in a quadratic gradient index medium. We demonstrate that by using this structure, we can generate a state that oscillates between a classically entangled state and a separable one.
Dielectric materials in which both the relative permittivity, ε, and the relative permeability, μ, are negative exhibit striking optical properties, which are a consequence of the fact that the effective index of refraction in such materials is negative. Most studies of the propagation of electromagnetic fields in these media have concentrated on classical fields with well-defined phases. In contrast, I use simple fully-quantized models to illustrate how some of the striking properties of negative-index media are manifested in the propagation of single, spontaneously emitted, photons. Single-photon quantum fields do not have an absolute phase, but the examples in this paper demonstrate a quantum analog of the negative phase accumulated by classical fields as photons propagate through negative-index media. The single photons also exhibit classical reflection and transmission coefficients, as well as the expected group velocity.
Dielectric materials in which both the relative permittivity, , and the relative permeability, µ, are negative exhibit striking optical properties, which are the consequence of the fact that the effective index of refraction in such materials is negative.Most studies of the propagation of electromagnetic fields in these media have concentrated on classical fields with well-defined phases.In contrast, I use simple fully-quantized models to illustrate how some of the striking properties of negative-index media are manifested in the propagation of single, spontaneously emitted, photons.Single-photon quantum fields do not have an absolute phase, but the examples in this paper demonstrate a quantum analog of the negative phase accumulated by classical fields as photons propagate through negative-index media.The single photons also exhibit classical reflection and transmission coefficients, as well as the expected group velocity.