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Physical Review A

Effect of photon propagation on a near-zero-refractive-index medium

Robert A. McCutcheon, Stefan Ostermann, Susanne F. Yelin

Published Sep 5, 2024• 3 citations
Publisher

Abstract

We present a model describing the transmission of light through atomic media with a vanishing index of refraction. Zero-index materials are of particular interest as the infinite phase velocity of light within the material offers the potential to manipulate electromagnetic waves to mediate dipole-dipole interactions over extended distances. We focus on the preparation of near-zero-index (NZI) conditions based on atomic coherence using two distinct atomic media as exemplary of generic NZI materials. We establish a model based on the Maxwell-Bloch equations to describe the propagation of a light pulse through these media. To investigate the sustainability of NZI under minimal light conditions, we assume single-photon intensity of the propagating pulse. Specifically, we examine whether the spatial phase change of the photon remains near zero as it traverses the medium. We employ a finite-element numerical approach to solve the coupled Maxwell-Bloch equations describing the photon propagation. Our results indicate that the presence of a photon within the medium will disrupt the NZI state, thus disallowing the establishment of enhanced dipole-dipole interactions over large distances.

DOI
10.1103/physreva.110.033705

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Journal of Modern Optics•Sep 6, 2011•1 citation
We present a model describing the transmission of light through atomic media with a vanishing index of refraction. Zero-index materials are of particular interest as the infinite phase velocity of light within the material offers the potential to manipulate electromagnetic waves to mediate dipole-dipole interactions over extended distances. We focus on the preparation of near-zero-index (NZI) conditions based on atomic coherence using two distinct atomic media as exemplary of generic NZI materials. We establish a model based on the Maxwell-Bloch equations to describe the propagation of a light pulse through these media. To investigate the sustainability of NZI under minimal light conditions, we assume single-photon intensity of the propagating pulse. Specifically, we examine whether the spatial phase change of the photon remains near zero as it traverses the medium. We employ a finite-element numerical approach to solve the coupled Maxwell-Bloch equations describing the photon propagation. Our results indicate that the presence of a photon within the medium will disrupt the NZI state, thus disallowing the establishment of enhanced dipole-dipole interactions over large distances.
We present a model describing the transmission of light through atomic media with a vanishing index of refraction. Zero index materials are of particular interest as the infinite phase velocity of light within the material offers the potential to manipulate electromagnetic waves to mediate dipole-dipole interactions over extended distances. We focus on the preparation of zero-index conditions based on atomic coherence using two distinct atomic media as exemplary of generic zero-index materials. We establish a model based on the Maxwell-Bloch equations to describe the propagation of a light pulse through these media. To investigate the sustainability of the zero index under minimal light conditions, we assume single-photon intensity of the propagating pulse. Specifically, we examine whether the spatial phase change of the photon remains zero as it traverses the medium. We employ a finite-element numerical approach to solve the coupled Maxwell-Bloch equations describing the photon propagation. Our results indicate that the presence of a photon within the medium will disrupt the zero-index state, thus disallowing the establishment of enhanced dipole-dipole interactions over large distances.
The refractive index of a system is often viewed as the collective response of a medium to an electromagnetic field. Nevertheless, even if targeted at a single atom, the incoming light undergoes the dispersion. By studying the propagation of a single photon interacting with a two-level atom, we examine the dispersion behavior, calculate the phase and group velocity of the photon wave packet, and further analyze the dispersion experienced by the photon. These findings are critical for advancing long-distance quantum communications.
The propagation of an off-resonant, single-photon pulse in and into a medium of two-level atoms is considered. When the pulse is launched from within the medium, there are two propagation speeds, neither of which is the normal group velocity. For densities as small as 1011{}^{11}11 atoms/cm3{}^{3}3 and detunings of order 1011{}^{11}11 s${}^{\ensuremath{-}1}$, both propagation speeds approach one half the speed of light in vacuum. Moreover, rather remarkably, there are Rabi oscillations between the field and atomic excitation, even for this single-photon pulse. In contrast, for a pulse sent into the medium, the atom-field system remains adiabatically in a dressed state that propagates with the normal group velocity. In the limit that the index of refraction is approximately equal to unity, we obtain the Fresnel equations for the reflection and transmission coefficients based on this microscopic model. The transmission coefficient differs from the conventional result owing to the fact that we quantize the field in free space.
We consider the interaction of atoms with the quantized electromagnetic field in the presence of materials with negative index of refraction. Spontaneous emission of an atom embedded in a negative index material is discussed. It is shown furthermore that the possibility of a vanishing optical path length between two spatially separated points provided by these materials can lead to complete suppression of spontaneous emission of an atom in front of a perfect mirror even if the distance between atom and mirror is large compared to the transition wavelength. Two atoms put in the focal points of a lens formed by a parallel slab of ideal negative index material are shown to exhibit perfect sub- and superradiance. The maximum length scale in both cases is limited only by the propagation distance within the free-space radiative decay time. Limitations of the predicted effects arising from absorption, finite transversal extension and dispersion of the material are analyzed.
For pt.I see ibid., vol.10, p.425 (1977). The effect of spatial dispersion or exciton formation on the steady propagation of a coherent light pulse in a dielectric medium is studied. The optical Bloch equation for a lattice of atomic dipoles coupled to one another by an exchange-type interaction is solved simultaneously with the Maxwell equation by the method of power-series expansion developed in the preceding paper. Two kinds of pulse solutions are obtained in general: one propagating by the medium of the radiation field and the other by excitation transfer between atomic dipoles. The former solution is SIT-like in the short pulse limit, but a polariton-soliton or a standing wave of non-linear polariton if the pulse width is long. The latter is an exciton-soliton containing little photon component. When the pulse width is extremely long, there appears a polariton-soliton of a new type in which the two propagation mechanisms are mixed. It is found that the spatial dispersion prevents the polariton-soliton solutions from existing in a certain frequency range. This effect is explained on the basis of the functional behavior of the dispersion relation of the non-linear polariton.
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.