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

We review the field of cavity optomechanics, which explores the interaction between electromagnetic radiation and nano- or micromechanical motion This review covers the basics of optical cavities and mechanical resonators, their mutual optomechanical interaction mediated by the radiation pressure force, the large variety of experimental systems which exhibit this interaction, optical measurements of mechanical motion, dynamical backaction amplification and cooling, nonlinear dynamics, multimode optomechanics, and proposals for future cavity quantum optomechanics experiments In addition, we describe the perspectives for fundamental quantum physics and for possible applications of optomechanical devices

Cavity Optomechanics

The status of experimental tests of general relativity and of theoretical frameworks for analyzing them is reviewed and updated. Einstein’s equivalence principle (EEP) is well supported by experiments such as the Eotvos experiment, tests of local Lorentz invariance and clock experiments. Ongoing tests of EEP and of the inverse square law are searching for new interactions arising from unification or quantum gravity. Tests of general relativity at the post-Newtonian level have reached high precision, including the light deflection, the Shapiro time delay, the perihelion advance of Mercury, the Nordtvedt effect in lunar motion, and frame-dragging. Gravitational wave damping has been detected in an amount that agrees with general relativity to better than half a percent using the Hulse-Taylor binary pulsar, and a growing family of other binary pulsar systems is yielding new tests, especially of strong-field effects. Current and future tests of relativity will center on strong gravity and gravitational waves.

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The Confrontation Between General Relativity and Experiment

A topical review of numerical and experimental studies of supercontinuum generation in photonic crystal fiber is presented over the full range of experimentally reported parameters, from the femtosecond to the continuous-wave regime. Results from numerical simulations are used to discuss the temporal and spectral characteristics of the supercontinuum, and to interpret the physics of the underlying spectral broadening processes. Particular attention is given to the case of supercontinuum generation seeded by femtosecond pulses in the anomalous group velocity dispersion regime of photonic crystal fiber, where the processes of soliton fission, stimulated Raman scattering, and dispersive wave generation are reviewed in detail. The corresponding intensity and phase stability properties of the supercontinuum spectra generated under different conditions are also discussed.

Supercontinuum generation in photonic crystal fiber

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

We present measurements of dark-line resonances excited in cesium atoms confined in submillimeter cells with a buffer gas. The width and contrast of the resonances were measured for cell lengths as low as 100 mm. The measured atomic Q factors are reduced in small cells because of frequent collisions of atoms with the cell walls. However, the contrast of coherent population trapping resonances measured in the small cells is similar in magnitude to that obtained in centimeter-sized cells, but substantially more laser intensity is needed to excite the resonance fully when increased buffer-gas pressure is used. The effect of the higher intensity on the linewidth is reduced because the intensity broadening rate decreases with buffer-gas pressure. OCIS codes: 020.1670, 300.6260. Compact frequency references have become increasingly important for military 1 and civilian 2 applications in recent years. For many applications in the f ield of navigation (e.g., global positioning systems) and communication systems, inexpensive miniature references with frequency stabilities in the 10 211 range at integration times approaching one day would be of great advantage. It has been predicted 3 that atomic clocks based on coherent population trapping (CPT) spectroscopy in millimeter-sized vapor cells might fulfill these requirements. It is well known that two phase-stable laser fields in resonance with a resonance line of the alkali atoms, and with a difference frequency equal to the hyperfine splitting, induce coherence between the two hyperfine ground

Dark-line atomic resonances in submillimeter structures

We demonstrate three-dimensional quenched narrow-line laser cooling and trapping of 40Ca. With 5 ms of cooling time we can transfer 28% of the atoms from a magneto-optic trap based on the strong 423-nm cooling line to a trap based on the narrow 657-nm clock transition (which is quenched by an intercombination line at 552 nm), thereby reducing the atoms’ temperature from 2 mK to 10 μK. This reduction in temperature should help to reduce the overall systematic frequency uncertainty for our Ca optical frequency standard to <1 Hz. Additional pulsed, quenched, narrow-line third-stage cooling in one dimension yields subrecoil temperatures as low as 300 nK and makes possible the observation of high-contrast two-pulse Ramsey spectroscopic line shapes.

Quenched narrow-line second- and third-stage laser cooling of 40 Ca

Surprising as it might seem, it is possible to phase-coherently track, synthesize, count and divide optical frequencies of visible laser sources. In essence, the technologies described here now allow direct connection of basically any frequency from DC to 1000 THz. Modern 'self-referenced' femtosecond mode-locked lasers have enormously simplified the required technology. These revolutionary new systems build on a long history of optical frequency metrology that spans from the early days of the laser. The latest systems rely heavily on technologies previously developed for laser frequency stabilization, optical phase-locked-loops, nonlinear mixing, ultra-fast optics and precision opto-electronic metrology. Using examples we summarize some of the heroic efforts that led to the successful development of harmonic optical frequency chains. Those systems played critical roles in defining the speed of light and in redefining the metre. We then describe the present state-of-the-art technology in femtosecond laser frequency combs, their extraordinary performance capabilities and some of the latest results.

The measurement of optical frequencies

We have designed and tested a set of five miniature nested magnetic shields constructed of high-permeability material, with external volumes for the individual shielding layers ranging from 0.01to2.5cm3. We present measurements of the longitudinal and transverse shielding factors (the ratio of external to internal magnetic field) of both individual shields and combinations of up to three layers. The largest shielding factor measured was 6×106 for a nested set of three shields, and from our results we predict a shielding factor of up to 1×1013 when all five shields are used. Two different techniques were used to measure the internal field: a chip-scale atomic magnetometer and a commercially available magnetoresistive sensor. Measurements with the two methods were in good agreement.

Demonstration of high-performance compact magnetic shields for chip-scale atomic devices

Extremely broadband femtosecond pulse sources with well defined carrier-envelope phase evolution have been a field of intense research over the past years [1–3]. The time-domain motivation for the push towards increased bandwidth is the generation of optical pulses that approach the single-cycle regime and can be used for phase-sensitive nonlinear experiments [4]. The frequency-domain motivation is the interest in extending the bandwidth over which optical frequencies can be precisely synthesized and subsequently used for absolute optical frequency measurements or comparisons [1, 5, 6]. Nonlinear frequency conversion is one route to overcome the bandwidth limitations of current systems based on one femtosecond laser. A second attractive route is linking two femtosecond lasers with overlapping emission spectra. Phase-locking the repetition rates of two femtosecond lasers with different gain media has recently been demonstrated. Here, we use a Ti:sapphire laser and a Cr:forsterite laser to extend this approach and additionally equalize the rate at which the carrier-waves move underneath their pulse envelopes. In other words, we link the absolute position of the two frequency combs, thereby establishing a true phase-coherence between all modes of their combined spectrum. The laser repetition rates are phase-locked by using a nonlinear cross-correlation technique.

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Leo W. Hollberg

Papers

Dark-line atomic resonances in submillimeter structures

Quenched narrow-line second- and third-stage laser cooling of 40 Ca

The measurement of optical frequencies

Demonstration of high-performance compact magnetic shields for chip-scale atomic devices

Broadband Phase-Coherent Optical Frequency Synthesis With Actively Linked Ti:Sapphire and Cr:Forsterite Femtosecond Lasers