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arXiv:1804.10132 · Physical Review A

Subvacuum effects on light propagation

V. A. De Lorenci, Lawrence H. Ford

Published Feb 26, 2019• 10 citations
arXivHTMLPDF

Abstract

Subvacuum effects arise in quantum field theory when a classically positive quantity, such as the local energy density, acquires a negative renormalized expectation value. Here we investigate the case of states of the quantized electromagnetic field with negative mean-squared electric field and their effects on the propagation of light pulses in a nonlinear dielectric material with a nonzero third-order susceptibility. We identify two distinct signatures of the subvacuum effect in this situation. The first is an increase in the speed of the pulse, which is analogous to the superluminal light propagation in gravity which can arise from negative energy density. This increase in speed leads to a phase shift which might be large enough to observe. The second effect is a change in the frequency and power spectra of the pulse. We identify a specific measure of the modified spectra which can signal the presence of a negative mean-squared electric field. These ideas are implemented in the particular example of a wave guide filled with a nonlinear dielectric material.

DOI
10.1103/physreva.99.023852

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Subvacuum effects arise in quantum field theory when a classically positive quantity, such as the local energy density, acquires a negative renormalized expectation value. Here we investigate the case of states of the quantized electromagnetic field with negative mean-squared electric field and their effects on the propagation of light pulses in a nonlinear dielectric material with a nonzero third-order susceptibility. We identify two distinct signatures of the subvacuum effect in this situation. The first is an increase in the speed of the pulse, which is analogous to the superluminal light propagation in gravity which can arise from negative energy density. This increase in speed leads to a phase shift which might be large enough to observe. The second effect is a change in the frequency and power spectra of the pulse. We identify a specific measure of the modified spectra which can signal the presence of a negative mean-squared electric field. These ideas are implemented in the particular example of a wave guide filled with a nonlinear dielectric material.
The influence of quantum fluctuations of the electromagnetic field on the propagation of a polarized light wave in a nonlinear dielectric is investigated. It is shown that in some cases the fluctuations couple to the optical nonlinearities of the medium and make its refractive index dependent on the polarization of the propagating wave. As a consequence, two light waves propagating in the same direction but with different polarizations will have different speeds, so there will be a Kerr-effect birefringence induced by quantum fluctuations. We consider the case of the electromagnetic field in a squeezed vacuum state, where there are regions where the mean squared electric field can be negative and the birefringence effect has the opposite sign to the Kerr effect in classical physics. We give some estimates for the magnitude of these effects, and discuss their possible observability.
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.
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.
Recently,there has been interest in modifying the group velocity of optical pulses,resulting in stopped,slow,and fast(superluminal)light.According to the physical theory,fast appears in the anomalous medium,and then it so called light medium.There are many experimeuts to produce fast light,this situation opens up new perspectives for the so called dispersion engineering.For example,signal propagating with a group velocity that exceeds the speed of light in vacuum(c) is intriguing for scientists.And then,the traveling of short wave pulses,microwave pulses and light pulses with group velocity vg,whose values exceed infinity,so called negative group velocity(NGV) propagation.Such circumstance occurs when the peak of a pulse traveling through DUT,exits before the peak of the input pulse has reached the beginning of DUT.This effect is counterintuitive,but it is a discover under the experimental basis.When the group velocity of light in a material is negative,it is the NGV medium. Although NGV are possible particularly in gain systems,there have been some experimental demonstrations of that phenomenon in passive systems,such as the coaxial cables,waveguides,micro-strip lines,and optical fibers,etc.If the experimental configuration used with a higher impedance mismatch,then it permits larger group delays,and a corresponding NGV.If n is the effective refraction index of the medium,we wantfn |f/ndn/df|1 to obtain the NGV. Many experiments showed the group velocity can surpass the light speed c,but scientists still lack the further understanding of the results.In 2001,Scientists obtained the formula v-e=|T|2vg,where v-e is average energy velocity,T is transmission coeficient of the system.If we want v-ec,the condition is vgc|T|-2.Hence it can be concluded that only vg/c is very large,the energy velocity can surpass c.This demonstration opens the door to interesting possibilities. The definition of signal velocity by Brillouin,mathemalical meaning exceeds physical meaning.We argue that undistorted wave group(wave packet) propagation are the first consideration.According to this viewpoint,the theoretical analysis show that superluminal propagation(i.e.superluminal communication) was observed by authors of many NGV researchers.……The superluminal group velocity wave propagation,the negative group velocity wave propagation——each of the two cases has its own use.Now,scientists do research works in these fields: such as optical communication,squeezed light and quantum entanglement.The condusion tell us that,a hight efficiency and low-loss fast light scheme may explore potential applications.
The problem of quantizing the radiation field inside a nonlinear dielectric is studied. Based on the quantization of radiation in a linear dielectric which includes absorption and dispersion, we extend the theory in order to treat also nonlinear optical processes. We derive propagation equations in space and time for the quantized radiation field including the effects of linear absorption and dispersion as well as nonlinear optical effects. As a special case we derive the propagation equation of a narrow-frequency band light pulse in a Kerr medium.