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Physical Review A

Electromagnetically induced transparency line shapes for large probe fields and optically thick media

Michael Vern Pack, Ryan M. Camacho, John C. Howell

Published Jul 2, 2007• 24 citations
Publisher

Abstract

We calculate the line shape and linewidths for electromagnetically induced transparency (EIT) in optically thick, Doppler broadened media (buffer gasses are also considered). In generalizing the definition of the EIT linewidth to optically thick media, we find two different linewidth definitions apply depending on whether the experiment is pulsed or continuous wave (cw). Using the cw definition for the EIT line shape we derive analytic expressions describing the linewidth as a function of optical depth. We also review the EIT line shapes in optically thin media and provide physical arguments for how the line shapes change as a function of various parameters.

DOI
10.1103/physreva.76.013801

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We calculate the line shape and linewidths for electromagnetically induced transparency (EIT) in optically thick, Doppler broadened media (buffer gasses are also considered). In generalizing the definition of the EIT linewidth to optically thick media, we find two different linewidth definitions apply depending on whether the experiment is pulsed or continuous wave (cw). Using the cw definition for the EIT line shape we derive analytic expressions describing the linewidth as a function of optical depth. We also review the EIT line shapes in optically thin media and provide physical arguments for how the line shapes change as a function of various parameters.
Laser induced line narrowing effect in Doppler broadened systems was discovered thirty years ago. This effect can also be applied to recent experimental studies in high resolution spectroscopy or high precision measurements based on Electromagnetically Induced Transparency (EIT). In this report we derive an analytic expression for the linewidth of EIT resonance in a Doppler broadened system. It is shown here that the EIT linewidth is proportional to the Rabi frequency of the driving field and is independent of the Doppler width in a limiting case. This recovers the result found in the laser induced line narrowing effect by Feld and Javan. In the other limit, we recovers the usual power broadening case where the EIT linewidth is proportional to the intensity of the driving field and inversely proportional to the Doppler width.
We derive an analytic expression for the linewidth of electromagnetically induced transparency (EIT) resonance in a Doppler-broadened system. It is shown here that for relatively low intensity of the driving field the EIT linewidth is proportional to the square root of intensity and is independent of the Doppler width, similar to the laser-induced line narrowing effect described by Feld and Javan. In the limit of high intensity we recover the usual power-broadening case where the EIT linewidth is proportional to the intensity and inversely proportional to the Doppler width.
Abstract In this work, we have presented the variation of the amplitude of electromagnetically induced transparency (EIT) resonances with the density of the atom in a V-type system using 87 Rb D 1 and D 2 lines both theoretically and experimentally. Up to the value of atomic density 18.1 × 10 10 cm −3 , the amplitude of the EIT resonance gradually increases with the increase of atomic density and then it decreases with the increase of the density of the atom. We have also found the radiation trapping effect in this experiment. We observe the effect of the atomic density on the electromagnetically induced transparency when the systems act as a thin optical media as well as thick optical media. We have found that the amplitude of EIT also depends on pump laser Rabi frequency. Numerical simulations are agreed well with the experimental observations.
We present a theory describing the transients and rise times of the refractive Kerr nonlinearity which is enhanced using electromagnetically induced transparency (EIT). We restrict our analysis to the case of a pulsed signal field with continuous-wave EIT fields, and all fields are well below saturation. These restrictions enable the reduction of an EIT Kerr, four-level, density-matrix equation to a two-level Bloch-vector equation which has a simple and physically intuitive algebraic solution. The physically intuitive picture of a two-level Bloch vector provides insights that are easily generalized to more complex and experimentally realistic models. We consider generalization to the cases of Doppler broadening, many-level EIT systems (we consider the D1D1D1 line of 87Rb^{87}\mathrm{Rb}87Rb), and optically thick media. For the case of optically thick media we find that the rise time of the refractive EIT Kerr effect is proportional to the optical thickness. The rise time of the refractive EIT Kerr effect sets important limitations for potential few-photon applications.
We have investigated the spectra of the electromagnetically induced transparency (EIT) when a cell is filled with a buffer gas. Our theoretical results show that the buffer gas can induce a narrower spectra line and steeper dispersion than those of the usual EIT case in a homogeneous and Doppler broadened system. The linewidth decreases with the increase of the buffer gas pressure. This narrow spectra may be applied to quantum information processing, nonlinear optics and atomic frequency standard.
This thesis presents theoretical derivations and experimental demonstrations of Kerr optical nonlinearities and their dynamics. The Kerr nonlinearity studied is based on electromagnetically induced transparency (EIT), and is known for having an unusually large cross-phase modulation (XPM) [1]. Also, quantum nondemolition (QND) measurements of photon number using the EIT Kerr nonlinearity are discussed. We first discuss the EIT line shapes in hot atomic vapors both with and without buffer gasses, and for the specific case of EIT line shapes on the D1 line of rubidium. Using a Bloch-vector formalism to describe EIT, we derive new expressions describing the dynamical evolution of the EIT Kerr nonlinearity and the rise-time of the EIT Kerr effect. The theory of the EIT Kerr dynamics is confirmed by experiments using hot rubidium vapor in a buffer gas. These experimental observations confirm that the rise-time of the EIT Kerr effect is linearly proportional to the optical thickness of the EIT medium and inversely proportional to the width of the EIT transparency resonance.