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

Water in interstellar regions detected by microwave emission from 6 sub 16 to 5 sub 23 rotational transition

Detection of Water in Interstellar Regions by its Microwave Radiation

We have mapped the [C II] 158 μm line over 85 × 65 in the Magellanic irregular galaxy IC 10, thus presenting the first complete [C II] map of an entire low-metallicity galaxy. The total luminosity in the [C II] line in IC 10 is 1.5 × 106 L☉. We discuss the origin of the [C II] emission toward different regions in the galaxy. Overall, about 10% of the [C II] emission can originate in standard H I clouds (n ~ 80, T ~ 100 K), while up to about 10% of the emission can originate in ionized gas, either the low-density warm gas or the denser H II regions. For the two brightest regions, most of the [C II] emission is associated with dense photodissociation regions (PDRs). For several regions, however, the [C II] emission may not be explained by standard PDR models. For these regions, emission solely from the atomic medium can also be precluded because the cooling rate per hydrogen atom would be much greater than the heating rate provided by photoelectric UV heating. We speculate that in these regions the presence of an additional column density of H2, 5 times that observed in H I, is required to explain the [C II] emission. The ambient UV fields present in these regions, combined with the low metallicity, create a situation where small CO cores exist surrounded by a relatively large [C II]-emitting envelope where molecular hydrogen is self-shielded. This additional molecular mass is equivalent to at least 100 times the mass in the CO core that one would derive from the CO integrated intensity alone using the standard CO-to-H2 conversion factor. These [C II] observations may, therefore, make a more reliable inventory of the gas reservoir in dwarf irregular galaxies where use of CO alone may significantly underestimate the molecular mass.

https://iopscience.iop.org/article/10.1086/304247/pdf

[C II] 158 Micron Observations of IC 10: Evidence for Hidden Molecular Hydrogen in Irregular Galaxies

Observations of infrared fine-structure line emission from compact clouds of ionized gas in the galactic center have been reported by Lacy et al (1979, 1980). These observations suggest the existence of a central black hole of nearly 3,000,000 solar masses and require mechanisms to generate, ionize, and dispose of the gas clouds. It is found that the best model to fulfill these requirements involves cloud generation through disruption of red giants by stellar collisions, ionization by a population of stars which is affected either by enhanced metal abundances or the death of the most massive stars, and gas disposal by star formation. Although the existence of a massive black hole cannot be ruled out, it would play no necessary role in this model and may cause the tidal disruption of stars at a rate such that their accretion into the black hole would produce more radiation than is observed.

The nature of the central parsec of the Galaxy

A relation between the electronegativity difference of two bonded atoms and the ionic character of the bond is obtained for singly bonded diatomic molecules in the gaseous state. The relation is based primarily on the wide variety of nuclear quadrupole coupling constants recently measured by microwave techniques. However, dipole moments of diatomic molecules are also used and discussed. Both quadrupole coupling constants and dipole moments indicate strongly that bonds involving electronegativity differences greater than 2 are almost completely ionic. Certain effects of hybridization, overlap, and polarization on considerations of ionicity are discussed.

The Ionic Character of Diatomic Molecules

Light pulses self steepening resulting from propagation in medium with intensity dependent refractive index

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Charles H. Townes

Papers

Detection of Water in Interstellar Regions by its Microwave Radiation

[C II] 158 Micron Observations of IC 10: Evidence for Hidden Molecular Hydrogen in Irregular Galaxies

The nature of the central parsec of the Galaxy

The Ionic Character of Diatomic Molecules

Self-steepening of light pulses.