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

Recent upgrades of the Infrared Spatial Interferometer are described. These provide improved sensitivity, precision and convenience of measurement. Analysis of phase fluctuations within the interferometer as well as in the atmosphere above indicates that popular simple atmospheric models need to be refined. Results of stellar observations are presented in another paper (cf. Danchi et al., in these Proceedings).

Latest technical developments at the infrared spatial interferometer

The dynamics of the surface and inner atmosphere of the red supergiant star Betelgeuse are the subject of numerous high angular resolution and spectroscopic studies. Here, we present three-telescope interferometric data obtained at 11.15 microns wavelength with the Berkeley Infrared Spatial Interferometer (ISI), that probe the stellar surface continuum. We find striking variability in the size, effective temperature, and degree of asymmetry of the star over the years 2006-2009. These results may indicate an evolving shell of optically thick material close to the stellar photosphere.

The many faces of Betelgeuse

The first observations of the [CII] line toward the nuclei of gas-rich external galaxies, showed that the far-infrared line emission contributes up to 1% of the total luminosity and most likely originates from dense photon-dominated regions (PDRs) associated with the surfaces of molecular clouds exposed to FUV from external or embedded OB stars (Crawford et al. 1985, Lugten et al. 1986, Stacey et al. 1991). We have mapped the [CII] emission toward NGC 6946 over an 8′x 6′ (23 x 17 kpc) (Madden et al. 1991) using the Max-Planck Instutute/U.C.Berkeley Far- Infrared Imaging Fabry-Perot Interferometer (FIFI) on the Kuiper Airborne Observatory (KAO).

A 158μm [CII] Map of NGC 6946: Detection in Extragalactic Atomic and Ionized Gas

The spatial distribution of dust around a sample of well-known late-type stars has been studied with the Infrared Spatial Interferometer (ISI) located at Mt. Wilson. Currently operating with a single baseline as a heterodyne interferometer at 11.15 µm, the ISI has obtained visibility curves of these stars. Radiative transfer modeling of the visibility curves has yielded estimates of the inner radii of the dust shells, the optical depth at 11 µm, and the temperature of the dust at the inner radii. For stars in which the dust is resolved, estimates of the stellar diameter and temperature can also be made. Broadly speaking two classes of stars have been found. One class has inner radii of their dust shells very close to the photospheres of the stars themselves (3-5 stellar radii) and at a higher temperature(~ 1200 K) than previously measured. This class includes VY CMa, NML Tau, IRC +10216, and o Ceti. For the latter two the visibility curves change with the luminosity phase of the star and new dust appears to form at still smaller radii during minimum luminosity. The second class of stars has dust shells with substantially larger inner radii and very little dust close to the stars, and includes α Ori, α Sco, α Her, R Leo, and χ Cyg. This indicates sporadic production of dust and no dust formation within the last several decades.

Charles H. Townes

Papers

Latest technical developments at the infrared spatial interferometer

The many faces of Betelgeuse

A 158μm [CII] Map of NGC 6946: Detection in Extragalactic Atomic and Ionized Gas

Long Baseline Interferometric Observations of Circumstellar Dust Shells at 11 Microns

The U.C. Berkeley infrared spatial interferometer: Instrumentation and first results