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Optical methods for the study of radio-frequency resonances

Alfred Kastler

Published Sep 1, 1967• 12 citations

Abstract

D URING MY FIRST YEAR as a student at the Ecole Normale Supérieure in Paris, our professor, Eugene Bloch, introduced us to quantum physics, which was seldom taught in France at that time. Like him, I was from Alsace and spoke German. He strongly advised me to read Arnold Sommerfeld's excellent book Atombau und Spektrallinien. When reading this book, I was particularly interested in the application of the principle of conservation of angular momentum in interactions between electromagnetic radiation and matter—an application that guided A. Rubinowicz to the interpretation of the selection rules for the angular momentum quantum number and for polarization in the Zeeman effect. On the assumption of light quanta, this principle led to attributing an angular momentum to the photons +h/2π or −h/2π, according to whether the light was circularly polarized to the right (σ+) or to the left (σ−), natural light being a mixture of the two types of photon.

DOI: 10.1063/1.3034481

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D URING MY FIRST YEAR as a student at the Ecole Normale Supérieure in Paris, our professor, Eugene Bloch, introduced us to quantum physics, which was seldom taught in France at that time. Like him, I was from Alsace and spoke German. He strongly advised me to read Arnold Sommerfeld's excellent book Atombau und Spektrallinien. When reading this book, I was particularly interested in the application of the principle of conservation of angular momentum in interactions between electromagnetic radiation and matter—an application that guided A. Rubinowicz to the interpretation of the selection rules for the angular momentum quantum number and for polarization in the Zeeman effect. On the assumption of light quanta, this principle led to attributing an angular momentum to the photons +h/2π or −h/2π, according to whether the light was circularly polarized to the right (σ+) or to the left (σ−), natural light being a mixture of the two types of photon.

The history of the discovery, study, and explanation of the effect discovered fifty years ago by the German physicist Hanle and its development and generalization by the French school of physicists led by Kastler are described. The effect is observed optically in an increase in the degree of depolarization of the resonance fluorescence. It is studied in the range of magnetic fields in which the Zeeman splitting of the atomic magnetic sublevels does not exceed the level widths determined by thermal relaxation mechanisms and electromagnetic interaction. It is a direct optical manifestation of interference of degenerate atomic states and is intimately connected with the conservation law for the angular momentum of the photon-atom system. In the review, different applications of the effect to the measurement of mean lifetimes, linewidths, and Stark splitting constants of atoms in excited states are given. The resonance scattering of light by atoms in the ground state in a weak magnetic field is considered in detail—in particular, in the presence of radio-frequency magnetic fields oriented in different ways. The different possible types of parametric resonances in one or two radio-frequency fields for arbitrary orientation of the constant magnetic field are interpreted as the effect of crossing of the levels of an atom that is dressed by the radio-frequency field. Applications of the effect in the quantum magnetometry of ultraweak fields (down to 10-10 Oe) are examined.

Many teachers like to introduce the Bohr atom toward the end of an introductory physics course. This is an excellent idea, given the historic importance of Bohr’s 1913 work, which provided the bridge from Planck’s quantized interaction of matter and radiation (1900) to the full theory of quantum mechanics (1925-28). Unfortunately, the version of the Bohr atom that appears in many textbooks and is no doubt often presented to students is more wrong than right and may leave both teachers and students wondering why, more than a hundred years later, it is still being taught. This “pedagogic” version postulates that an electron in a stationary state moves in a circular orbit with an angular momentum that is an integral multiple of h/2π (L = nh/2π = nħ)—ħ for the lowest-energy state, 2ħ for the next state, and so on. This picture of the hydrogen atom is wrong in two senses. First it doesn’t conform to our present understanding of the hydrogen atom. This, in itself, is not a reason to scrap it, for the historical development of quantum physics is certainly of interest. But second, it doesn’t conform to the essence of what Bohr actually did. That is a reason not to teach about circular orbits and L = nħ.

More than a century ago, pioneeringworks carried out by Poynting (1909) and other physicists have provided the evidence of the validity of Marxwell equations for an electromagnetic field, showing how a beam of light carries energy and momentum, both in the linear and angular components. In particular the angular momentum of light, related to the generator of rotations in quantum mechanics, has been typically associated with its polarization, and more specifically with its circular polarization components. An optical beam traveling in the positive direction of the z axis that is circularly polarized, carries a z-component angular momentum content σ = ±h per photon, which is positive if the circular polarization is left-handed and negative if it is right-handed. This angular momentum content is not just a formal property, but a very concrete one that can have significant mechanical effects as for example an observable induced rotation by absorption to amaterial particle Beth (1936); Friese et al. (1998)