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.

/pdf/electromagnetically-induced-transparency-optics-in-coherent-2dhges92td.pdf

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.

/pdf/the-confrontation-between-general-relativity-and-experiment-5dqdube5p9.pdf

The Confrontation Between General Relativity and Experiment

Measurements by the U.C. Berkeley Infrared Spatial Interferometer at 11.15 micron have yielded strong evidence for multiple dust shells and/or significant asymmetric dust emission around NML Cyg. New observations reported also include multiple 8-13 micron spectra taken from 1994-1995 and N band (10.2 micron) photometry from 1980-1992. These and past measurements are analyzed and fitted to a model of the dust distribution around NML Cyg. No spherically symmetric single dust shell model is found consistent with both near- and mid-infrared observations. However, a circularly symmetric maximum entropy reconstruction of the 11 micron brightness distribution suggests a double shell model for the dust distribution. Such a model, consisting of a geometrically thin shell of intermediate optical depth ($\tau_{11 micron} \sim 1.9$) plus an outer shell ($\tau_{11 micron} \sim 0.33$), is consistent not only with the 11 micron visibility data, but also with near-infrared speckle measurements, the broadband spectrum, and the 9.7 micron silicate feature. The outer shell, or large scale structure, is revealed only by long-baseline interferometry at 11 micron, being too cold ($\sim$ 400 K) to contribute in the near-infrared and having no unambiguous spectral signature in the mid-infrared. The optical constants of Ossenkopf, Henning, & Mathis (1992) proved superior to the Draine & Lee (1984) constants in fitting the detailed shape of the silicate feature and broadband spectrum for this object. Recent observations of H$_2$O maser emission around NML Cyg by Richards, Yates, & Cohen (1996) are consistent with the location of the two dust shells and provide further evidence for the two-shell model.

https://arxiv.org/pdf/astro-ph/9702103.pdf

Non-Uniform Outflow Observed around Infrared Object NML Cygni

An imaging upconverter has been constructed which is suitable for use in the study of the thermal 10-micron radiation from astronomical sources. The infrared radiation is converted to visible radiation by mixing in a 1-cm-long proustite crystal. The phase-matched 2-kayser bandpass is tunable from 9 to 11 microns. The conversion efficiency is 2 by 10 to the -7th power and the field of view of 40 arc seconds on the sky contains several hundred picture elements, approximately diffraction-limited resolution in a large telescope. The instrument has been used in studies of the sun, moon, Mercury, and VY Canis Majoris.

An infrared upconverter for astronomical imaging

Water Spectrum Near One-Centimeter Wave-Length

The size and variability of the continuum photosphere of o Ceti have been measured with 11 μm heterodyne interferometry to an accuracy of about 1%. Narrow bandwidths (~0.17 cm-1) were used to avoid spectral lines and measure continuum only. The resulting 11 μm diameter of o Cet is larger than the previously measured visible and near-infrared sizes. In addition, variations in the diameter with phase and a possible elongation have been observed. Visibilities were also measured at wavelengths known to contain strong H2O spectral contamination, giving larger apparent stellar sizes and information on the distribution of hot H2O gas.

/pdf/interferometry-on-mira-in-the-mid-infrared-cyclic-54m2kx7ng1.pdf

Interferometry on Mira in the Mid-Infrared: Cyclic Variability of the Continuum Diameter and the Effect of Spectral Lines on Apparent Size

This paper presents a group of t ables t hat give the frequencies, assignment of qua nt um numbers, and intensities of over 700 microwave absorption lines. The best availabl e valu es of other per t inen t m olecul ar data, s uch a s moment s of in ert ia, dipole moments, quadrupole coupling constant s, a nd rotation-vibration constants are also in cluded. The freq uencies are listed once for' each molecule and again in consecut ive ascending order of frequency . References are given for all data included. Frequencies listed to t he neares t megacycle were generally measured with a cavi ty wave meter a nd may be in error by as much as 10 mega cycles, whereas t hose given to' a fraction of a megacycle are genera lly known to a n accuracy of about 0.1 megacycle. A short discuss ion of mi crowave spcctra an d impor tan t formulas is given. For easy calculation of hyperfine st ructure Cas imir's fun ction is tab ulated up to J = 10 a nd 1 = 9/2.

/pdf/molecular-microwave-spectra-tables-129kejf8lv.pdf

Charles H. Townes

Papers

Non-Uniform Outflow Observed around Infrared Object NML Cygni

An infrared upconverter for astronomical imaging

Water Spectrum Near One-Centimeter Wave-Length

Interferometry on Mira in the Mid-Infrared: Cyclic Variability of the Continuum Diameter and the Effect of Spectral Lines on Apparent Size

Molecular Microwave Spectra Tables