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

Techniques that use quantum interference effects are being actively investigated to manipulate the optical properties of quantum systems1. One such example is electromagnetically induced transparency, a quantum effect that permits the propagation of light pulses through an otherwise opaque medium2,3,4,5. Here we report an experimental demonstration of electromagnetically induced transparency in an ultracold gas of sodium atoms, in which the optical pulses propagate at twenty million times slower than the speed of light in a vacuum. The gas is cooled to nanokelvin temperatures by laser and evaporative cooling6,7,8,9,10. The quantum interference controlling the optical properties of the medium is set up by a ‘coupling’ laser beam propagating at a right angle to the pulsed ‘probe’ beam. At nanokelvin temperatures, the variation of refractive index with probe frequency can be made very steep. In conjunction with the high atomic density, this results in the exceptionally low light speeds observed. By cooling the cloud below the transition temperature for Bose–Einstein condensation11,12,13 (causing a macroscopic population of alkali atoms in the quantum ground state of the confining potential), we observe even lower pulse propagation velocities (17?m?s−1) owing to the increased atom density. We report an inferred nonlinear refractive index of 0.18?cm2?W−1 and find that the system shows exceptionally large optical nonlinearities, which are of potential fundamental and technological interest for quantum optics.

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Light speed reduction to 17 metres per second in an ultracold atomic gas

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

Electromagnetically induced transparency1,2,3 is a quantum interference effect that permits the propagation of light through an otherwise opaque atomic medium; a ‘coupling’ laser is used to create the interference necessary to allow the transmission of resonant pulses from a ‘probe’ laser. This technique has been used4,5,6 to slow and spatially compress light pulses by seven orders of magnitude, resulting in their complete localization and containment within an atomic cloud4. Here we use electromagnetically induced transparency to bring laser pulses to a complete stop in a magnetically trapped, cold cloud of sodium atoms. Within the spatially localized pulse region, the atoms are in a superposition state determined by the amplitudes and phases of the coupling and probe laser fields. Upon sudden turn-off of the coupling laser, the compressed probe pulse is effectively stopped; coherent information initially contained in the laser fields is ‘frozen’ in the atomic medium for up to 1 ms. The coupling laser is turned back on at a later time and the probe pulse is regenerated: the stored coherence is read out and transferred back into the radiation field. We present a theoretical model that reveals that the system is self-adjusting to minimize dissipative loss during the ‘read’ and ‘write’ operations. We anticipate applications of this phenomenon for quantum information processing.

Observation of coherent optical information storage in an atomic medium using halted light pulses

Electron transport in conductors is usually well described by Fermi-liquid theory, which assumes that the energy states of the electrons near the Fermi level EF are not qualitatively altered by Coulomb interactions. In one-dimensional systems, however, even weak Coulomb interactions cause strong perturbations. The resulting system, known as a Luttinger liquid, is predicted to be distinctly different from its two- and three-dimensional counterparts1. For example, tunnelling into a Luttinger liquid at energies near the Fermi level is predicted to be strongly suppressed, unlike in two- and three-dimensional metals. Experiments on one-dimensional semiconductor wires2, 2,3 have been interpreted by using Luttinger-liquid theory, but an unequivocal verification of the theoretical predictions has not yet been obtained. Similarly, the edge excitations seen in fractional quantum Hall conductors are consistent with Luttinger-liquid behaviour4, 5, but recent experiments failed to confirm the predicted relationship between the electrical properties of the bulk state and those of the edge states6. Electrically conducting single-walled carbon nanotubes (SWNTs) represent quantum wires7,8,9,10 that may exhibit Luttinger-liquid behaviour11, 12. Here we present measurements of the conductance of bundles (‘ropes’) of SWNTs as a function of temperature and voltage that agree with predictions for tunnelling into a Luttinger liquid. In particular, we find that the conductance and differential conductance scale as power laws with respect to temperature and bias voltage, respectively, and that the functional forms and the exponents are in good agreement with theoretical predictions.

Luttinger-liquid behaviour in carbon nanotubes

We develop a theory of electromagnetically induced transparency in a three-level, ladder-type Doppler-broadened medium, paying special attention to the case where the coupling and probe beams are counterpropagating and have similar frequencies, so as to reduce the total Doppler width of the two-photon process. The theory is easily generalized to deal with the \ensuremath{\Lambda} configuration, where the ideal arrangement involves two copropagating beams. We discuss different possible regimes, depending on the relative importance of the various broadening mechanisms, and identify ways to optimize the absorption-reduction effect. The theory is compared to the results of a recent experiment (on a ladder-type system), using the Rb D2 line, with generally very good agreement. The maximum absorption reduction observed (64.4%) appears to be mostly limited by the relatively large (\ensuremath{\sim}5 MHz) linewidth of the diode lasers used in our experiment.

Electromagnetically induced transparency in ladder-type inhomogeneously broadened media: Theory and experiment

The dispersive properties of the atomic transition in the rubidium ${D}_{2}$ line ($5{S}_{\frac{1}{2}}\ensuremath{-}5{P}_{\frac{3}{2}}$) at 780.0 nm are measured with a Mach-Zehnder interferometer when an additional coupling field at 775.8 nm is applied to an upper transition ($5{P}_{\frac{3}{2}}\ensuremath{-}5{D}_{\frac{5}{2}}$). This ladder-type system is observed to exhibit electromagnetically induced transparency together with a rapidly varying refractive index. A reduction in group velocity for the probe beam (${v}_{g}=\frac{c}{13.2}$) is inferred from the measured dispersion curve with 52.5% suppressed absorption on resonance.

Measurement of Dispersive Properties of Electromagnetically Induced Transparency in Rubidium Atoms

A 64.4% reduction in absorption at the rubidium D2 line is observed when a pumping field at 775.8 nm is tuned on resonance to the transition between the excited states 5${\mathit{P}}_{3/2}$ and 5${\mathit{D}}_{5/2}$. As the pumping field is tuned off resonance, an absorption peak appears at the side of the Doppler-broadened D2 line. This modification in absorption is related to pumping-induced atomic coherence in this three-level ladder-type system. This experiment is done in a Rb vapor cell at room temperature and with cw diode lasers for both pumping and probe beams in a Doppler-free configuration.

Observation of an electromagnetically induced change of absorption in multilevel rubidium atoms

Hyperfine spectroscopy of highly-excited atomic states based on atomic coherence

Although an ideal degenerate optical parametric oscillator (DOPO) can generate perfect squeezing at the output of a one-sided optical cavity when operating just below threshold, its intracavity squeezing is limited to less than one-half (50%) of its perfect value. However, when two-level atoms are introduced into the DOPO cavity, the amount of intracavity squeezing can be enhanced, from its maximum value of 50%, to a maximum value of 75% in the good-cavity limit due to the strong interaction between the two-level atoms and the subharmonic field mode. This extra intracavity squeezing is significant in studying spectroscopy of atoms interacting with a squeezed field mode inside an optical cavity.

Shaozheng Jin

Papers

Electromagnetically induced transparency in ladder-type inhomogeneously broadened media: Theory and experiment

Measurement of Dispersive Properties of Electromagnetically Induced Transparency in Rubidium Atoms

Observation of an electromagnetically induced change of absorption in multilevel rubidium atoms

Hyperfine spectroscopy of highly-excited atomic states based on atomic coherence

Extra intracavity squeezing of a degenerate optical parametric oscillator coupling with n two-level atoms