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

The subject of this review is the central 100 parsecs of our Galaxy, with a strong focus on the central few parsecs. Observations of the electromagnetic spectrum over 13 orders of magnitude in wavelength show a broad range of phenomena involving a number of physical processes. We discuss the stellar and interstellar components, the importance of magnetic and gravitational forces, the evidence for stellar formation and a central massive black hole, and the origin and nature of ionization, outflows and interstellar gas dynamics.

https://iopscience.iop.org/article/10.1088/0034-4885/57/5/001/pdf

The nucleus of our Galaxy

Precision measurements of the $J=1\ensuremath{\leftarrow}0$ rotational frequencies and the molecular magnetic moments for various isotopic species of carbon monoxide have been made in order to determine isotopic mass ratios. A correction amounting to several hundred micromass units and evaluated from the magnetic moment has been applied for the fact that the electrons are not spherically distributed about their respective nuclei. It is also shown that the rapidly precessing electronic angular momentum causes a "wobbling" motion of the nuclei which in turn produces a stretching of the molecule ("wobble stretching") inversely proportional to the reduced mass of the molecule, but independent of $J$. This stretching cannot be accurately evaluated from theory and therefore appears to be the ultimate limitation on microwave determinations of mass ratios. This correction amounts to about 20 micro-mass units and is evaluated by the use of the nuclear reaction value for the ${\mathrm{C}}^{14}$-${\mathrm{C}}^{12}$ mass ratio. The final mass ratios agree very closely with the nuclear reaction values.The sign of the electric dipole moment was determined from the relative magnetic moments of the several isotopic species and corresponds to the charge distribution, ${\mathrm{C}}^{\ensuremath{-}}$${\mathrm{O}}^{+}$. This appears to be the first measurement of the sign of the electric dipole moment in any molecule.

Isotopic Mass Ratios, Magnetic Moments and the Sign of the Electric Dipole Moment in Carbon Monoxide

Coherently Driven Molecular Vibrations and Light Modulation

Observations of infrared fine-structure line emission from compact clouds of ionized gas within Sgr A West are presented. These clouds have diameters of 0.1-0.5 pc, internal velocity dispersions of 100 km/s (FWHM), and line center velocities up to + or - 260 km/s. Their masses are not accurately determined but are probably between 0.1 and 10 solar masses. They are ionized by radiation like that of stars of effective temperature not greater than 35,000 K. The clouds are shown to have lifetimes of 10,000 yr and so must be generated and dissipated at a rate of a few per 1000 yr. From analysis of the distribution of the velocities of the clouds, a most probable mass distribution is derived which includes a central pointlike mass of several x 10 to the 6th solar masses in addition to several x 10 to the 6th solar masses of stars within 1 pc of the center.

Observations of the motion and distribution of the ionized gas in the central parsec of the galaxy. II

Beam trapping in cadmium sulfide noting threshold, trapping length, refractive index change and Stokes radiation

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Charles H. Townes

Papers

The nucleus of our Galaxy

Isotopic Mass Ratios, Magnetic Moments and the Sign of the Electric Dipole Moment in Carbon Monoxide

Coherently Driven Molecular Vibrations and Light Modulation

Observations of the motion and distribution of the ionized gas in the central parsec of the galaxy. II

Dynamics and Characteristics of the Self-Trapping of Intense Light Beams