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Scientific Reports

A novel method for analyzing complicated quantum behaviors of light waves in oscillating turbulent plasma

Jeong Ryeol Choi

Published Nov 3, 2014• 4 citations
Publisher

Abstract

Quantum dynamics of light waves traveling through a time-varying turbulent plasma is investigated via the SU(1,1) Lie algebraic approach. Plasma oscillations that accompany time-dependence of electromagnetic parameters of the plasma are considered. In particular, we assume that the conductivity of plasma involves a sinusoidally varying term in addition to a constant one. Regarding the time behavior of electromagnetic parameters in media, the light fields are modeled as a modified CK (Caldirola-Kanai) oscillator that is more complex than the standard CK oscillator. Diverse quantum properties of the system are analyzed under the consideration of time-dependent characteristics of electromagnetic parameters. Quantum energy of the light waves is derived and compared with the counterpart classical energy. Gaussian wave packet of the field whose probability density oscillates with time like that of classical states is constructed through a choice of suitable initial condition and its quantum behavior is investigated in detail. Our development presented here provides a useful way for analyzing time behavior of quantized light in complex plasma.

DOI
10.1038/srep06880

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Quantum dynamics of light waves traveling through a time-varying turbulent plasma is investigated via the SU(1,1) Lie algebraic approach. Plasma oscillations that accompany time-dependence of electromagnetic parameters of the plasma are considered. In particular, we assume that the conductivity of plasma involves a sinusoidally varying term in addition to a constant one. Regarding the time behavior of electromagnetic parameters in media, the light fields are modeled as a modified CK (Caldirola-Kanai) oscillator that is more complex than the standard CK oscillator. Diverse quantum properties of the system are analyzed under the consideration of time-dependent characteristics of electromagnetic parameters. Quantum energy of the light waves is derived and compared with the counterpart classical energy. Gaussian wave packet of the field whose probability density oscillates with time like that of classical states is constructed through a choice of suitable initial condition and its quantum behavior is investigated in detail. Our development presented here provides a useful way for analyzing time behavior of quantized light in complex plasma.
We present a simple description of classical and quantum light propagating through homogeneous conducting linear media. With the choice of Coulomb gauge, we demonstrate that this description can be performed in terms of a damped harmonic oscillator which is governed by the Caldirola-Kanai Hamiltonian. By using the dynamical invariant method and the Fock states representation we solve the time-dependent Schrödinger equation associated with this Hamiltonian and write its solutions in terms of a special solution of the Milne-Pinney equation. We also construct coherent states for the quantized light and show that they are equivalent to the well-known squeezed states. Finally, we evaluate some important properties of the quantized light such as expectation values of the amplitude and momentum of each mode, their variances and the respective uncertainty principle.
A simple elegant expression of nonadiabatic light wave evolution is necessary in order to have a deeper insight for complicated optical phenomena in light science as well as in everyday life. Light wave propagation in linear media which have time-dependent electromagnetic parameters is investigated by utilizing a quadratic invariant of the system. The time behavior of the nonadiabatic geometric phase of the waves that yield a cyclic nonadiabatic evolution is analyzed in detail. Various quantum properties of light waves in this situation, such as variances of electric and magnetic fields, uncertainty product, coherent and squeezed states, and their classical limits, are developed. For better understanding of our research, we applied our analysis in a particular case. The variances of the fields D and B are illustrated and their time behaviors are addressed. Equivalent results for the corresponding classical systems are deduced from the study of the time evolution of the appropriate coherent and squeezed states.
In this paper, we consider the quantum optical electromagnetic wave in time-varying media, where the electric permittivity ϵ(t) and the magnetic permeability μ(t) depend on time explicitly as ϵ(t) = ϵ 0(1+qt) and μ(t) = μ 0(1+qt). For these time-varying parameters, we solve Maxwell’s equations. To construct time-dependent coherent states for this light, we adopt the invariant method proposed by Lewis and Riesenfeld and express the fields in terms of the time-dependent step operators for the invariant. We also discuss the deformed Rabi oscillation for both on-resonance and off-resonance.
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In this paper, we use the Coulomb gauge, linear invariants and the dynamical invariant method in the framework of the Schrödinger equation to obtain a quantum description of light propagation through homogeneous conducting linear media with no charge density. We obtain exact wavefunctions for this problem in terms of solutions of a second-order ordinary differential equation which describes the amplitude of the classical damped harmonic oscillator. In addition, we construct Gaussian wave packet solutions and calculate the fluctuations in coordinate and momentum as well as the quantum correlations for each mode of the quantized electromagnetic field.
In this work we investigate the quantization of electromagnetic waves propagating through homogeneous conducting linear media with no charge density. We use Coulomb's gauge to reduce the problem to that of a time-dependent harmonic oscillator, which is described by the Caldirola–Kanai Hamiltonian. Furthermore, we obtain the corresponding exact wave functions with the help of quadratic invariants and of the dynamic invariant method. These wave functions are written in terms of a particular solution of the Milne–Pinney equation. We also construct coherent and squeezed states for the quantized electromagnetic waves and evaluate the quantum fluctuations in coordinates and momentum as well as the uncertainty product for each mode of the electromagnetic field.