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.

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

The Confrontation Between General Relativity and Experiment

From the time when man first saw the sunlight until very recently, the light which he has used has come dominantly from spontaneous emission, like the random emission of incandescent sources. So have most other types of electromagnetic radiation-infrared, ultraviolet, or gamma rays. The maximum radiation intensities, or specifically the power radiated per unit area per unit solid angle per unit frequency bandwidth, have been controlled by Planck's black-body law for radiation from hot objects. This sets an upper limit on radiation intensity-a limit which increases with increasing temperature, but we have had available temperatures of only a few tens of thousands or possibly a few millions of degrees. Radio waves have been different. And, perhaps without our realizing it, even much of our thinking about radio waves has been different, in spite of Maxwell's demonstration before their discovery that the equations governing radio waves are identical with those for light. The black-body law made radio waves so weak that emission from hot objects could not, for a long time, have been even detected. Hence their discovery by Hertz and the great use of radio waves depended on the availability of quite different types of sources-oscilla-tors and amplifiers for which the idea of temperature and black-body radiation even seems rather out of place. For example, if we express the radiation intensity of a modern electronic oscillator in terms of temperature, it will typically be in the range 10 10 to 10 30 degrees Kelvin. These two regimes, radio electronics and optics, have now come much closer together in the field known as quantum electronics, and have lent each other interesting insights and powerful techniques. The development of radar stimulated many important applications of electronics to scientific problems, and what occupied me in particular during the late 1940's was microwave spectroscopy, the study of interactions between microwaves and molecules. From this research, considerable information could be obtained about molecular, atomic, and nuclear structure. For its success, coherent microwave oscillators were crucial in allowing a powerful

http://science.sciencemag.org/content/sci/149/3686/831.full.pdf

Production of Coherent Radiation by Atoms and Molecules.

Based on data obtained with the NASA Kuiper Airborne Observatory 91.4 cm telescope, the 158-micron fine structure line emission of C(+) is mapped near the galactic center. The strongest emission comes from a 10-pc FWHM diameter disk centered on Sgr A West whose dominant motion is rotation. Extended C(+) emission is also found from the +50 km/s galactic center molecular cloud, and a second cloud at v(LSR) of about -35 km/s. The rotation curve and mass distribution within 10 pc of the galactic center are derived, and the C(+) profiles show a drop-off of rotation velocity between 2 and 10 pc. A mass model is suggested with 2-4 million solar masses in a central point mass, and a M/L ratio of the central stellar cluster of 0.5 solar masses/solar luminosities, suggesting a large abundance of giants and relatively recent star formation in the center.

C II forbidden-line 158 micron mapping in Sagittarius A Rotation curve and mass distribution in the galactic center

Frequencies and intensities of a number of lines of the $J=3\ensuremath{\rightarrow}4$ rotational transition of ICl were measured and the spectrum analyzed. Constants obtained for IC${\mathrm{l}}^{35}$ are (in megacycles) ${\mathrm{B}}_{e}=3422.300$, ${\ensuremath{\alpha}}_{e}=16.060$, $e{q}_{\mathrm{I}}{Q}_{\mathrm{I}}=\ensuremath{-}2930.0$, $e{q}_{\mathrm{Cl}}{Q}_{\mathrm{Cl}}=\ensuremath{-}82.5$. The mass ratio $\frac{{\mathrm{Cl}}^{35}}{{\mathrm{Cl}}^{37}}$ obtained from this spectrum is 0.9459801, which appears inconsistent with the most recent mass spectroscopic determination. The molecular dipole moment is approximately 0.65 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}18}$ e.s.u. from intensity measurements.

The Pure Rotational Spectrum of ICl

A New Experimental Test of Special Relativity

NASA's Kuiper Airborne Observatory has been used to conduct an extensive, velocity-resolved survey at 1-arcsec resolution of the 158-micron forbidden C II fine-structure line emission in the central 50 pc of the Galaxy. The emission is found to be strongest toward the rotating circumnuclear disk surrounding Sgr A West; a continuous bridge of the emission connects the Sgr A complex to the thermal radio filaments in the radio arc 10 arcmin north of the center. This suggests a direct physical connection. The brightest emission occurs preferentially near the edges of the massive Galactic center molecular clouds. It is concluded that these clouds are predominantly ionized by external UV photons.

Charles H. Townes

Papers

Production of Coherent Radiation by Atoms and Molecules.

C II forbidden-line 158 micron mapping in Sagittarius A Rotation curve and mass distribution in the galactic center

The Pure Rotational Spectrum of ICl

A New Experimental Test of Special Relativity

A survey of the 158 micron forbidden C II fine-structure line in the central 50 parsecs of the Galaxy