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Journal of Modern Optics

Slow light in a thin gas cell by means of a traveling monochromatic wave

Sohrab Ahmadi-Kandjani, Ghazal Rejali

Published Dec 17, 2008• 3 citations
Publisher

Abstract

In this paper we demonstrate that the interaction of a traveling monochromatic light wave with atoms of a dilute gas in a cell whose length is much less than the diameter of the light beam can slow down the velocity of light. This slowing down is achieved by the specific transit relaxation of particles between walls of the cell (along the wave vector). For a two-level atomic system the group index is in the order of 103. The results show that such a slow down could be achieved by a single traveling light wave in a gas medium.

DOI
10.1080/09500340802517678

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Journal of Optics B Quantum and Semiclassical Optics•Apr 18, 2002•3 citations
In this paper we demonstrate that the interaction of a traveling monochromatic light wave with atoms of a dilute gas in a cell whose length is much less than the diameter of the light beam can slow down the velocity of light. This slowing down is achieved by the specific transit relaxation of particles between walls of the cell (along the wave vector). For a two-level atomic system the group index is in the order of 103. The results show that such a slow down could be achieved by a single traveling light wave in a gas medium.
We theoretically propose a strategy to use a travelling monochromatic wave in a simple two level atomic system to tune the group velocity over a wide range. Both subliminal and superluminal group velocity are demonstrated from the interaction of a light wave with atoms in the case where the cell length is much less than the light beam diameter. The tunable control of the light group velocity for the negative (superluminal light) to positive (subluminal light) are achieved in different physical conditions. In fact, we control the group velocity by tuning the relaxation parameters such as, the collision between atoms, the incident intensity and the beam diameter. This allows us to switch from subluminality to superluminality and back in a sub-Doppler system.
This work continues a theoretical investigation of the capabilities of the well-known method based on using a monochromatic probe light beam in combination with optical pumping of atoms (molecules) of a rarefied-gas medium by a broadband radiation in a thin cell the diameter of which is much larger than its internal thickness. In contrast to calculations carried out in the previous publications on this method of spectroscopy, here, we consider the case of arbitrary values of pump intensity and thickness of a cylindrical gas cell. Thus, all the possible mechanisms and specificities of velocity selection of atoms in optically excited levels caused by transit-time relaxation of such atoms in gas cells of this kind are analyzed. Within the framework of this approach, sub-Doppler absorption resonances of the probe light beam corresponding to quantum transitions from the upper level excited by optical pumping are investigated. The obtained results can be used in high-resolution spectroscopy of atoms (molecules), as well as for laser-frequency stabilization to established narrow spectral resonances.
In early 1999, a news article in the prestigious journal Nature led off with the announcement, "€œAn experiment with atoms at nanokelvin temperatures has produced the remarkable observation of light pulses traveling at velocities of only 17 m/s."€ The review continued with the understatement, "Observation of light pulses propagating at a speed no faster than a swiftly moving bicycle...comes as a surprise."€ These findings (and their review) marked the beginning of the current wave of interest in the field that has come to be called "€œslow light.â€" When we refer to "the speed of light," we typically mean c, the phase velocity of light in a vacuum, or the speed of propagation of the phase fronts of monochromatic light. The phase fronts travel more slowly through a material, propagating at the speed c/n, where n is the index of refraction of the medium. However, this ordinary slowing of the phase velocity is not slow light. "€œSlow light"€ and "€œfast light"€ refer to changes in the group velocity of light in a medium. A pulse of light can be decomposed mathematically into a group of monochromatic waves at slightly different frequencies, as in Fig. 19.1. In a dispersive material, these monochromatic waves travel at different speeds. When one views the propagation of the pulse as a whole, its apparent velocity depends on the extent of the spread of individual monochromatic-wave velocities. Each monochromatic wave travels at its own phase velocity, while the pulse travels at the group velocity. Of course, the group velocity of a pulse of light is not a new concept. The field of slow and fast light has drawn on theory and developments from the work of Sommerfeld and Brillouin from 1907 to 1914, experiments with early laser amplifiers in 1966, and other work done through the end of the 20th century. (For more of the history behind slow and fast light, see Refs. 8 and 9.)
Single light beam transmission spectroscopy in an ultrathin dilute vapor cell (10--100 \ensuremath{\mu}m) reveals sub-Doppler features. Indeed, atoms with fast (normal) velocity undergo a short interaction between the cell walls, and are shown to be less absorbing because they have not reached their steady state of interaction with light. The effect is observed in the linear-response regime with a simple two-level system, as ensured from the ultralow level of light irradiation ($<~1\ensuremath{\mu}{\mathrm{W}/\mathrm{c}\mathrm{m}}^{2}$ for the Cs D2{D}_{2}D2​ line). The effect, known for a long time in the microwave domain, is demonstrated here in the optical domain, and is extended to cell thicknesses large relative to the optical wavelength.
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.
A theoretical investigation is carried out through the interaction of the plane running monochromatic light wave, having an arbitrary intensity, with atoms (molecules) of a rarefied gas in the plane cell (at the normal incidence of the wave). Cases of closed and open resonance transitions from the non-degenerate ground (or metastable) quantum level are considered. Possible sub-Doppler resonances are analysed in the wave absorption, caused by the transient establishment of the optical coherence on the transition, Rabi oscillations between its levels, and optical pumping during the free flights of particles between the walls of the cell. Results of the previous works on given problems are generalized, which were obtained at definite restrictions on the wave intensity and cell length. Moreover, non-trivial sub-Doppler spectral structures, resulting as a consequence of the dependence of the absorption saturation on the transit relaxation of particles, have been established and investigated. Such structures may consist of a number of peaks and dips caused by Rabi oscillations between the transition levels. The results obtained can be used in sub-Doppler spectroscopy and for the stabilization of laser frequencies in thin gas cells.