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

We have mapped the 3P1−3P2 fine structure line emission at 63 microns from neutral oxygen in the vicinity of the galactic center. The emission is extended over more than 4′ and is centered on Sgr A West. We conclude that the bulk of the OI emission arises in a predominantly neutral region outside of the ionized central 3 pc of our galaxy. Assuming that the oxygen is collisionally excited by neutral hydrogen impact, we estimate that the gas temperatures in this region are ≳130K, that is, significantly higher than the dust temperature of 70K. The OI line center velocities change systematically along the galactic plane in a manner consistent with galactic rotation. However, the unusual velocity distribution and linewidths suggest that the motions have a large noncircular component and that there are large scale inhomogeneities in the OI‐emitting gas. We also have detected the 88 micron 3P1‐3P0 fine structure line of OIII in a 45▴ FWHM beam centered on Sgr A West. The ratio of this line intensity to that of 52 micron 3P2‐3P1 line indicates that most of the ionized gas in this region has electron density ≳104 cm−3.

OI and OIII in Sgr A: neutral and ionized gas at the Galactic center

.Dust surrounding the star V Hydrae has been measured at a 11.15 μm wavelength using the three-telescope Infrared Spatial Interferometer (ISI). The narrowband heterodyne detection system is tuned to a region free of spectral lines due to molecules surrounding the star, and only continuum radiation from the dust and star is measured. Closure-phase data show that the dust is symmetrically distributed around the star. Results obtained in 2006–2007 are well fitted by a model with a Gaussian intensity distribution with HWHM of 49 mas that contributes 0.52 of the total flux and by a uniform disk of radius 287 mas with a total flux fraction of 0.26; the remaining 0.22 of the total flux is due to the star, which is unresolved. Visibility measurements conducted in 1997 show a substantial difference from those of 2006–2007, indicating that the star was surrounded by more dust in 1997.

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The Dust Distribution Immediately Surrounding V Hydrae

Quantum effects and optimization of heterodyne detection

We have constructed an infrared imaging system that achieves diffraction-limited spatial resolution (about 0.8 arc seconds) at 10 um on 3 meter ground-based telescopes. The system uses a linear array of sensitive HgCdTe photodiodes, scanned in the direction perpendicular to the array axis, to form two-dimensional images. Scans are completed rapidly enough to freeze atmospheric fluctuations. Individual detectors are small compared to the diameter of the Airy disk, and images are oversampled heavily in the scan direction. This method has a number of advantages for studying small fields with very high spatial resolution, and has been applied successfully to the problem of directly imaging faint circumstellar dust shells.

Diffraction-Limited 10 µm Imaging With 3 Meter Telescopes

An overview of the development of molecular astronomy, together with future prospects, is given.

Charles H. Townes

Papers

OI and OIII in Sgr A: neutral and ionized gas at the Galactic center

The Dust Distribution Immediately Surrounding V Hydrae

Quantum effects and optimization of heterodyne detection

Diffraction-Limited 10 µm Imaging With 3 Meter Telescopes

Introduction: Radio and IR studies of molecular clouds