Coherent preparation by laser light of quantum states of atoms and molecules can lead to quantum interference in the amplitudes of optical transitions. In this way the optical properties of a medium can be dramatically modified, leading to electromagnetically induced transparency and related effects, which have placed gas-phase systems at the center of recent advances in the development of media with radically new optical properties. This article reviews these advances and the new possibilities they offer for nonlinear optics and quantum information science. As a basis for the theory of electromagnetically induced transparency the authors consider the atomic dynamics and the optical response of the medium to a continuous-wave laser. They then discuss pulse propagation and the adiabatic evolution of field-coupled states and show how coherently prepared media can be used to improve frequency conversion in nonlinear optical mixing experiments. The extension of these concepts to very weak optical fields in the few-photon limit is then examined. The review concludes with a discussion of future prospects and potential new applications.

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Electromagnetically induced transparency : Optics in coherent media

The subject of electromagnetically induced transparency (EIT) is reviewed in this paper. Emphasis is placed on the experimental work reported in this field since 1990. Theoretical work is also covered, although it is not intended to review all the very numerous recent theoretical treatments on this topic. The basic physical ideas behind EIT are elucidated. The relation of EIT to other processes involving laser-induced atomic coherence, such as coherent population trapping, coherent adiabatic population transfer and lasing without inversion, is discussed. Experimental work is described covering the following topics: EIT with pulsed and continuous-wave sources, lasing without inversion, pulse propagation in a laser dressed medium and EIT in nonlinear optical processes. A full set of references and a bibliography are included.

Electromagnetically induced transparency

We perform a time-dependent analysis of four-wave mixing (FWM) in a double-$\ensuremath{\Lambda}$ system in an ultraslow-propagation regime and obtain the analytical expressions of pulsed probe laser, FWM-generated pulse, phase shifts and absorption coefficients, group velocities, and FWM efficiency. With these analytical expressions, we show that an efficiently generated FWM field can acquire the same ultraslow group velocity $({V}_{g}∕c\ensuremath{\sim}{10}^{\ensuremath{-}4}--{10}^{\ensuremath{-}5})$ and pulse shape of a probe pump and that the maximum FWM efficiency is greater than 25%, which is orders of magnitude larger than previous FWM schemes in the ultraslow-propagation regime.

Highly efficient four-wave mixing in double- Λ system in ultraslow propagation regime

The article illustrates recent experiments in which light is slowed, frozen, reversed, and stored in hot atomic vapors via electromagnetically induced transparency.

Slow, Ultraslow, Stored, and Frozen Light

We have experimentally studied the propagation of two optical fields in a dense rubidium (Rb) gas in the case when an additional microwave field is coupled to the hyperfine levels of Rb atoms. The Rb energy levels form a close-$\ensuremath{\Lambda}$ three-level system coupled to the optical fields and the microwave field. It has been found that the maximum transmission of the probe field depends on the relative phase between the optical and the microwave fields. We have observed both constructive and destructive interferences in electromagnetically induced transparency. A simple theoretical model and a numerical simulation have been developed to explain the observed experimental results.

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Electromagnetically induced transparency controlled by a microwave field

We demonstrate efficient, pulsed, gas-phase, nonlinear frequency conversion in a quadruply resonant, double- $\ensuremath{\Lambda}$ system and, simultaneously, verify theoretical predictions of Rabi-frequency matching unique to absorbing nonlinear media. This system is used to up-convert ultraviolet light at 233 nm to the vacuum ultraviolet at 186 nm in atomic Pb vapor with small-signal conversion efficiencies exceeding $30%$ and with modest atomic density-length (NL) products (scale ${10}^{14}{\mathrm{cm}}^{\ensuremath{-}2}$) and optical power densities $(10--100\mathrm{kW}/{\mathrm{cm}}^{2})$.

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Efficient Nonlinear Frequency Conversion in an All-Resonant Double- Λ System

We report the demonstration of a pulsed atomic lead (Pb) vapor-based vacuum ultraviolet frequency converter from 233 to 186??nm with unity photon-conversion efficiency. This conversion is attained without phase matching.

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Efficient gas-phase generation of coherent vacuum ultraviolet radiation.

We describe a pulsed, atomic lead (Pb) vapor-based vacuum ultraviolet (VUV) frequency converter from 233 to 186 nm with near-unity photon conversion efficiency. This conversion is attained without phasematching and is accomplished by using electromagnetically induced transparency to drive a Raman transition to near-maximal coherence without loss or beam blow-up. Under these conditions, the linear and nonlinear polarizations of the generated 186-nm field are of the same order and complete conversion from the 233-nm field occurs within a single (nonphasematched) coherence length.

Efficient gas-phase VUV frequency up-conversion

Summary form only given. The techniques of electromagnetically induced transparency (EIT) may be employed in order to create an effective nonlinear response at a given wavelength which is equal in magnitude to the linear response at that wavelength. Physically, this allows frequency converters wherein 100% photon-to-photon conversion occurs in a single coherence length, i.e., in that distance which causes a /spl pi/ phase slip between the driving polarization and the generated electromagnetic wave. These ideas were first implemented by Jain et al. (1996), to convert 425 nm to 293 nm, in a medium consisting of a single isotope of Pb. This paper reports the demonstration of a vapor-phase VUV frequency converter from 233 nm to 186 nm with an energy conversion efficiency exceeding 35%; the maximum generated signal energy and power were 250 /spl mu/J and 25 kW. The net conversion efficiency to 186 nm, including all beams, is roughly 2%. These wavelengths were chosen to demonstrate the utility of this type of frequency converter to generate wavelengths outside the transparency window of most crystalline media. Our technique involves the application of two strong laser fields which are almost two-photon resonant with a Raman transition of the Pb atoms.

Efficient vapor-phase vacuum ultraviolet (VUV) frequency conversion

The techniques of electromagnetically induced transparency (EIT) can be employed to create a nonlinear response at a given wavelength that is equal in magnitude to the linear response at that wavelength. Physically, this allows frequency converters wherein unity photon-to-photon conversion occurs within a single coherence length, i.e., in that distance that causes a n phase slip between the driving polarization and the generated field. These ideas were first implemented by Jain and coworkers' to convert 425-nm radiation to 293-nm radiation with an energy conversion efficiency of 40%. We have extended that work to the generation of coherent radiation below 200nm, outside the transparency window of most nonlinear crystals. This was possible with moderate pump intensities without the need for phase matching.

D. Manuszak

Papers

Efficient Nonlinear Frequency Conversion in an All-Resonant Double- Λ System

Efficient gas-phase generation of coherent vacuum ultraviolet radiation.

Efficient gas-phase VUV frequency up-conversion

Efficient vapor-phase vacuum ultraviolet (VUV) frequency conversion

Efficient vacuum ultraviolet generation using electomagnetically induced transparency