There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

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

This paper has two purposes: 1) to clarify the relationship between the quantum theory of radiation, where the electromagnetic field-expansion coefficients satisfy commutation relations, and the semiclassical theory, where the electromagnetic field is considered as a definite function of time rather than as an operator; and 2) to apply some of the results in a study of amplitude and frequency stability in a molecular beam maser. In 1), it is shown that the semiclassical theory, when extended te take into account both the effect of the field on the molecules and the effect of the molecules on the field, reproduces almost quantitatively the same laws of energy exchange and coherence properties as the quantized field theory, even in the limit of one or a few quanta in the field mode. In particular, the semiclassical theory is shown to lead to a prediction of spontaneous emission, with the same decay rate as given by quantum electrodynamics, described by the Einstein A coefficients. In 2), the semiclassical theory is applied to the molecular beam maser. Equilibrium amplitude and frequency of oscillation are obtained for an arbitrary velocity distribution of focused molecules, generalizing the results obtained previously by Gordon, Zeiger, and Townes for a singel-velocity beam, and by Lamb and Helmer for a Maxwellian beam. A somewhat surprising result is obtained; which is that the measurable properties of the maser, such as starting current, effective molecular Q, etc., depend mostly on the slowest 5 to 10 per cent of the molecules. Next we calculate the effect of amplitude and frequency of oscillation, of small systematic perturbations. We obtain a prediction that stability can be improved by adjusting the system so that the molecules emit all their energy h Ω to the field, then reabsorb part of it, before leaving the cavity. In general, the most stable operation is obtained when the molecules are in the process of absorbing energy from the radiation as they leave the cavity, most unstable when they are still emitting energy at that time. Finally, we consider the response of an oscillating maser to randomly time-varying perturbations. Graphs are given showing predicted response to a small superimposed signal of a frequency near the oscillation frequency. The existence of "noise enhancing" and "noise quieting" modes of operation found here is a general property of any oscillating system in which amplitude is limited by nonlinearity.

Comparison of quantum and semiclassical radiation theories with application to the beam maser

Recent advances in the field of nonlinear optical phenomena are reviewed with particular empphasis placed on such topics as parametric oscillation self-focusing and trapping of laser beams, and stimulated Raman, Rayleigh, and Brillouin scattering. The optical frequency radiation is treated classically in terms of the amplitudes and phases of the electromagnetic fields. The interactions of light waves in a mterial are then formulated in terms of Maxwell's equations and the electric dipole approximation. In this method, non-linear susceptibility tensors are introdueed which relate the induced dipole moment to a power series expansion in field strengths. The tensor nature and the frequency dependence of the nonlinearity coefficients are considered. The various experimental, observations are described and interpreted in terms of this formalism.

https://ieeexplore.ieee.org/iel5/5/31089/01447053.pdf

Nonlinear optics

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

Measured nuclear quadrupole effects in solids are discussed, compared with nuclear quadrupole coupling in gases, and correlated to some extent with molecular structure in the solid state. The iodine crystal affords a good example of intermolecular interactions in the solid state. In this crystal, nuclear quadrupole effects combined with crystallographic information show two intermolecular covalent bonds per atom, each of about 9 percent importance.

Nuclear Quadrupole Effects and Electronic Structure of Molecules in the Solid State

A fully sampled, 1000-point, 1-arcmin-resolution map of the inner 6.5 x 10 arcmin (alpha x delta) regions of the Orion Nebula in the 157.7409-micron forbidden fine-structure line is constructed. Large-scale strip maps in forbidden C II across the face of the Orion molecular cloud, and CO(17-16), (14-13), and (7-6) spectra are obtained at selected positions in the Orion H II region/molecular cloud interface. Strong forbidden C II line emission is observed across the face of the Orion molecular. The total forbidden C II luminosity from the Orion molecular cloud is about 1500 solar luminosities, or 0.3 percent of the FIR luminosity. The extended forbidden C II emission probably arises in either the UV-exposed surface of the molecular cloud or from the surfaces of UV-exposed clumps within the molecular cloud.

158 micron forbidden C II mapping of the Orion molecular cloud

We present first results of an experiment to combine data from Keck aperture masking and the Infrared-Optical Telescope Array (IOTA) to image the circumstellar environments of evolved stars with ~20 milliarcsecond resolution. The unique combination of excellent Fourier coverage at short baselines and high-quality long-baseline fringe data allows us to determine the location and clumpiness of the inner-most hot dust in the envelopes, and to measure the diameters of the underlying stars themselves. We find evidence for large-scale inhomogeneities in some dust shells and also significant deviations from uniform brightness for the photospheres of the most evolved M-stars. Deviations from spherically-symmetric mass loss in the red supergiant NML Cyg could be related to recent evidence for dynamically-important magnetic fields and/or stellar rotation. We point out that dust shell asymmetries, like those observed here, can qualitatively explain the difficulty recent workers have had in simultaneously fitting the broad-band spectral energy distributions and high-resolution spatial information, without invoking unusual dust properties or multiple distinct shells (from hypothetical ``superwinds''). This paper is the first to combine optical interferometry data from multiple facilities for imaging, and we discuss the challenges and potential for the future of this method, given current calibration and software limitations.

High-resolution imaging of dust shells using Keck aperture masking and the IOTA Interferometer

Test of isotropy of space for light propagation and effect of earth orbital velocity on velocity of light, using he-ne infrared masers

Charles H. Townes

Papers

Nuclear Quadrupole Effects and Electronic Structure of Molecules in the Solid State

158 micron forbidden C II mapping of the Orion molecular cloud

High-resolution imaging of dust shells using Keck aperture masking and the IOTA Interferometer

Test of special relativity or of the isotropy of space by use of infrared masers.

Frequency Stability of He-Ne Masers and Measurements of Length