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College Physics

A new kind explaination of polarization of Zeeman spectrum

Fang Wen

Published Jan 1, 2005• 0 citations
OpenAlex

Abstract

According to the electromagnetic theory of light and the graphic method of vector,the characteristic of σ and π polarizations of the transition of atom is analyzed.

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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.
Zeeman split takes place for the hyperfine level structure of neutral atoms where magnetic field exists. In addition, being excited by right circularly polarized light and left circularly polarized light, atoms obey different transition rules. So, the absorption peak between the hyperfine Zeeman level shifts with respect to the absorption peak without magnetic field. Accordingly, the authors demonstrated a kind of simple and flexible method to stabilize the frequency of diode laser. The linewidth of diode laser was reduced to less than 1 MHz using this method. Through analyzing the experiment results, the authors found that when the sum of both shifts of the hyperfine level of atoms excited by right circularly polarized light and left circularly polarized light was equal to the FWHM (Full Width at Half Maximum) of the saturated absorption peak, the laser frequency was stabilized best.
The unitary transformation from linearly to elliptically polarized states of photons is determined in a scheme of the second quantization (\textsection{}1). It is given by ${\mathbf{e}}_{l}={\mathbf{e}}_{1}cos\ensuremath{\phi}+i{\mathbf{e}}_{2}sin\ensuremath{\phi}$, ${\mathbf{e}}_{r}=i{\mathbf{e}}_{1}sin\ensuremath{\phi}+{\mathbf{e}}_{2}cos\ensuremath{\phi}$ where e1{\mathbf{e}}_{1}e1​ and e2{\mathbf{e}}_{2}e2​ are orthogonal unit vectors corresponding to linearly polarized states of photons and el{\mathbf{e}}_{l}el​ and er{\mathbf{e}}_{r}er​ are those corresponding to left and right elliptically polarized states of photons. A general formula for a probability of an emission of light from an atom is deduced on the basis of the Dirac electron theory so as to include up to both a magnetic dipole and an electric quadrupole term (\textsection{}2). Its general form is improved as compared with the hitherto obtained one. The general theory is applied to electric dipole and quadrupole and magnetic dipole spectral lines (\textsection{}3 and \textsection{}4). Polarization states of the Zeeman components corresponding to all combinations of magnetic and orbital magnetic quantum numbers of an atom are completely determined for an arbitrary given direction of an observation on the basis of quantum mechanics.