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arXiv:1112.0095 · Physics-Uspekhi

Photons traveling at the speed of light in a two-level atomic medium as a source of Cherenkov radiation cones

V. E. Ogluzdin

Published Aug 31, 2004• 6 citations
arXivHTMLPDF

Abstract

On speed of a photon in a dispersing medium Ogluzdin Valeriy E. Abstract Based on the author of the experimental results and their treatment, a model that demonstrates that the real dispersive medium in spectral regions where the refractive index greater than unity, the velocity of propagation of photons in this environment corresponds to the phase velocity of light. These portions of the spectrum (for example, atomic potassium vapor or other alkali metal) are from low-frequency side of the main lines of the doublet and are available for research using tunable lasers. In the calculations took into account the fact that the atomic vapor of alkali metal used as a dispersing medium, in accordance with the theory of dispersion in the above sections of the spectrum, on the periphery of the cross section of laser beam with Gaussian intensity distribution across the beam - in the shadows refractive index n (ν) is greater than unity, and the axis of the beam, where the radiation intensity is maximum - for radiation following the leading edge of the light pulse, the refractive index is unity, which ensures smooth on the beam axis, without any delay "superluminal "propagation of light with velocity c. This fact causes the appearance of the shadow cone of Vavilov - Cherenkov radiation, indicating a slow propagation of photons from the source of the cone with phase velocity c / n (ν).

DOI
10.1070/pu2004v047n08abeh001690

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On speed of a photon in a dispersing medium Ogluzdin Valeriy E. Abstract Based on the author of the experimental results and their treatment, a model that demonstrates that the real dispersive medium in spectral regions where the refractive index greater than unity, the velocity of propagation of photons in this environment corresponds to the phase velocity of light. These portions of the spectrum (for example, atomic potassium vapor or other alkali metal) are from low-frequency side of the main lines of the doublet and are available for research using tunable lasers. In the calculations took into account the fact that the atomic vapor of alkali metal used as a dispersing medium, in accordance with the theory of dispersion in the above sections of the spectrum, on the periphery of the cross section of laser beam with Gaussian intensity distribution across the beam - in the shadows refractive index n (ν) is greater than unity, and the axis of the beam, where the radiation intensity is maximum - for radiation following the leading edge of the light pulse, the refractive index is unity, which ensures smooth on the beam axis, without any delay "superluminal "propagation of light with velocity c. This fact causes the appearance of the shadow cone of Vavilov - Cherenkov radiation, indicating a slow propagation of photons from the source of the cone with phase velocity c / n (ν).
Summary form only given. The propagation of light in a dispersive medium is characterized by the group velocity /spl nu//sub g/=c(n+/spl nu//sup dn//d/spl nu/)/sup .1/ where n is the refractive index and /spl nu/ the optical frequency. Depending on the sign and magnitude of /sup dn//d/spl nu/ in the medium, the group velocity can be positive, infinite or negative. The group velocity corresponds to the speed of the propagation of the maximum of an optical pulse travelling into the medium. This remains true whether the dispersion in the medium is normal (/sup dn//d/spl nu/>0) or anomalous (/sup dn//d/spl nu/<0). It has been demonstrated that coherently prepared atomic systems can exhibit steep dispersion leading to small absolute values of the group velocity (slow light). In recent work, we have demonstrated that narrow resonances arising from the coherent interaction of two optical fields with a closed atomic transition between two degenerate levels may correspond to a steep anomalous dispersion and thus to slow and negative group velocity. We report on the experimental study of the propagation of an amplitude modulated wave in a medium presenting negative group velocity.
There is an interest in consideration of the propagation of the Gaussian monochromatic light beams through a cell filled with the medium of two-level atoms (in our case, the atomic potassium vapor), which has (at small detuning from resonant transition to low or high frequencies) the refractive index other than unity (n > 1 for v < v01 and n < 1 for v > v01, where v is the light frequency and v01 is the resonant-transition frequency). In this case, the properties of the radiation passed through the cell are changed. In the very close proximity of the resonance, the nonlinear processes (the three-photon electronic stimulated Raman scattering (SRS) and the six-photon parametric scattering (SPS)) play a crucial role. It is precisely these processes in the two-level medium that determine the irreversibly transformed spectral and angular structure of the light beams at the output of the cell.
The propagation of narrow packets of electromagnetic waves(EMWs) in frequency dispersive medium with the consideration of the complex refractive index is studied. It is shown that counting in the dispersion of the complex refractive index within the context of the conventional expression of the group velocity of narrow wave packets of EMWs propagating in a dispersive medium results in the appearance of additional constraints on the group velocity, which dictates that the physically acceptable group velocity can only be realized in the case of a negligible imaginary part of the group index. In this paper, the conditions that allow one to realize the physically acceptable group velocity are formulated and analyzed numerically for the relevant model of the refractive index of a system of two-level atoms in the optical frequency range. It is shown that in the frequency band where superluminal light propagation is expected, there is a strong dispersion of the refractive index that is accompanied with strong absorption, resulting in a strongly attenuated superluminal light.
The propagation of narrow packets of electromagnetic waves (EMWs) in frequency dispersive medium with the consideration of the complex refractive index is studied. It is shown that counting in the dispersion of the complex refractive index within the context of the conventional expression of the group velocity of narrow wave packets of EMWs propagating in a dispersive medium results in the appearance of additional constraints on the group velocity, which dictates that the physically acceptable group velocity can only be realized in the case of a negligible imaginary part of the group index. In this paper, the conditions that allow one to realize the physically acceptable group velocity are formulated and analyzed numerically for the relevant model of the refractive index of a system of two-level atoms in the optical frequency range. It is shown that in the frequency band where superluminal light propagation is expected, there is a strong dispersion of the refractive index that is accompanied with strong absorption, resulting in a strongly attenuated superluminal light.
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.
A. Existence of two types of effects in atom-photon interactionsConsider first a light beam with frequency L propagating through a medium consisting of atoms with resonance frequency A .The index of refraction describing this propagation has an imaginary part and a real part which are associated with two types of physical processes.The incident photons can be absorbed, more precisely scattered in all directions.The corresponding attenuation of the light beam is maximum at resonance.It is described by the imaginary part of the index of refraction which varies with L Ϫ A as a Lorentz absorption curve.We will call such an effect a dissipative (or absorptive) effect.The speed of propagation of light is also modified.The corresponding dispersion is described by the real part n of the index of refraction whose difference from 1, nϪ1, varies with L Ϫ A as a Lorentz dispersion curve.We will call such an effect a reactive (or dispersive) effect.