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

Electromagnetically induced transparency is a technique for eliminating the effect of a medium on a propagating beam of electromagnetic radiation EIT may also be used, but under more limited conditions, to eliminate optical self‐focusing and defocusing and to improve the transmission of laser beams through inhomogeneous refracting gases and metal vapors, as figure 1 illustrates The technique may be used to create large populations of coherently driven uniformly phased atoms, thereby making possible new types of optoelectronic devices

Electromagnetically Induced Transparency

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 analyze the electromagnetically induced transparency (EIT) in $V$-, $\ensuremath{\Lambda}$-, and cascade-type schemes in a time-dependent way via the Schr\"odinger-Maxwell formalism. We derive explicitly the analytical expressions of the space-time dependent probe field, the corresponding phase shift, absorption or amplification, group velocity, and group velocity dispersion for all the three schemes. These simple analytical expressions not only demonstrate explicitly the similarities and essential differences of the three schemes but also provide a convenient basis for investigating how the many-body effects in solids modify the magnitude, spectral shape, and space and time dependence of EIT and EIT-related quantum coherence phenomena.

Electromagnetically induced transparency in V -, Λ -, and cascade-type schemes beyond steady-state analysis

As stated in the text, Figs. 3 and 4 (transmission versus probe laser detuning) were taken at an energy of 10 nJ in a 0.5-mm-diam beam. We should have noted that when the probe energy is increased to 150 n3 (— 10" W/cm ) the absorption cross section at the transmission maximum increases by a factor of approximately 2. At this energy density, with or without the coupling laser present, transmitted probe energy is no longer linear with incident probe energy.

Observation of Electromagnetically Induced Transparency in Collisionally Broadened Lead Vapor

A theoretical and experimental investigation has been carried out into the viability of V-type, \ensuremath{\Lambda}-type, and cascade systems within rubidium for the observation of electromagnetically-induced transparency (EIT). A \ensuremath{\Lambda}-type system is also discussed where EIT is induced on a two-photon transition. Continuous-wave single-frequency titanium sapphire lasers have been employed to provide the applied optical fields. It is found that systems that have a strong coupling field resonant with the 5${\mathit{S}}_{1/2}$ ground state suffer from complicating optical pumping mechanisms that tend to mask EIT windows. It is also found that wavelength matching of the applied optical fields enhances the observation of EIT since this results in a reduced residual Doppler linewidth of the atomic system.

Continuous-wave electromagnetically induced transparency: A comparison of V, Λ, and cascade systems

Spatial Consequences of Electromagnetically Induced Transparency: Observation of Electromagnetically Induced Focusing.

The effect of changing the coupling laser transition, and hence the wavelength, on the coherently induced transparency seen by a probe beam in a Doppler-broadened cascade electromagnetically induced transparency (EIT) configuration is studied experimentally and theoretically. The transparency of the vapor is shown to be an effect not just of EIT, but of the varying Autler-Townes splitting for each velocity group within the vapor. Consequently, the best overall transparency for Rabi splittings less than the Doppler width is not at the position of matched coupling and probe wavelengths, but for coupling wavelengths less than that of the probe. \textcopyright{} 1996 The American Physical Society.

Wavelength dependence of coherently induced transparency in a Doppler-broadened cascade medium.

Electromagnetically-induced focusing.

We demonstrate the magnitude dependence of electromagnetically induced transparency, in a three-level cascade scheme in rubidium, on the probe and coupling field polarizations. We show that this dependence is due to the presence of the degenerate magnetic sublevels and the strengths of their relative dipole matrix elements. It is shown that this can lead to modified absorption profiles when electromagnetically induced transparency is used for spectroscopic purposes. We present theory that is in good agreement with our experiments.

David J. Fulton

Papers

Continuous-wave electromagnetically induced transparency: A comparison of V, Λ, and cascade systems

Spatial Consequences of Electromagnetically Induced Transparency: Observation of Electromagnetically Induced Focusing.

Wavelength dependence of coherently induced transparency in a Doppler-broadened cascade medium.

Electromagnetically-induced focusing.

Polarization effects in electromagnetically induced transparency