Atoms and Molecules Interacting With Light:
Atomic Physics for the Laser Era

by Peter van der Straten and Harold Metcalf
Cambridge, 2016, 515 pages
reviewed by T. Nelson

n chemistry courses, we're all taught that an excited atom spontaneously decays to a ground state by emitting a photon. We learn the selection rules that describe whether the transition is allowed by quantum mechanics. And we learn all the formulas that allow us to predict the rate.

But how does an atom know it's supposed create a photon instead of, say, a popsicle? They never tell us that. Indeed, it took the development of quantum mechanics just to get as far as a description. All we really have so far are models.

One famous model, called the Wigner-Weisskopf model of spontaneous emission, considers spontaneous decay as an interaction between the atom's excited state |e⟩ and an empty radiation field |0⟩. The combined system |e;0⟩ is a super­position of the the atom and the field.

This model says that to understand why an atom's state decays to the ground state, we can't consider the atom by itself. We must also understand how it interacts with space, or what is called the atom-field interaction. The atom's electric dipole moment interacts with an electro­magnet­ic field. The decay is irreversible, so the theory says, because there are an infinite number of reverse modes that add destructively so the probability of reversing the process is zero. The transition occurs at a specific frequency, called a line, which comes from the fact that an atom can only exist in certain quantized states.

It's a sophisticated model, and it's still used today. But where does the field come from? How does a photon propagate in space? How empty is ‘empty’ space (which physicists call the quantum vacuum), anyway, if it's stuffed to the gills with all these fields and excitations, some of which come out of the vacuum spontaneously to create phenomena like the Casimir effect? We talk about photons all the time, yet we still don't really know why they're created.

These ideas show that space isn't just a background on which things happen, but an active participant in particle interactions that determines the properties of whatever is created or destroyed.

Some parts of this book, like the formulas for the hydrogen atom, will be familiar. But there's much more to the subject than we're taught. For instance, the Darwin term, named after Charles Galton Darwin, the grandson of the famous biologist, is a purely relativistic effect. It was thought to come from the overlap of the wavefunc­tion with the nucleus, and was added to help understand the fine structure in an atom's emission spectrum. The authors say it has no intuitive explanation whatsoever and was superseded by the Lamb shift, which started out as a correction for the interaction between hydrogen and empty space but may end up as something a lot bigger (see also this excellent mostly non-technical description here).

Another oddity is the Sommerfeld fine-structure constant (α) which is almost—but not quite—1/137. It's thought of as a coupling constant for electro­magnetic interactions between particles, but nobody knows why it has its particular value. At one time there was some speculation that the value of α could have changed since the Big Bang.

The authors give reasonably good explanations of concepts like Rabi frequency (Ω), which is a measure of how strongly the atom is coupled to the incoming coherent light, as from a laser. That is to say, the atom cyclically absorbs a photon, then gets rid of it by stimulated emission back to the driving field. If the incoming light is close to the transition wavelength, Ω is stronger. A Rabi frequency is not the frequency of the emitted photon but is much lower, often in the range of 50 kHz. It's important in lasers. Anthony Siegman explains it better in his 1986 book Lasers, which has a whole chapter on Rabi oscillations, though he tells us not to read it.

Another important concept is the Rotating Wave Approximation (RWA), which has nothing to do with rotating waves, but is a simplification needed to calculate the famously unsolvable Schrödinger equation. You need this to understand anything on the topic in the literature.

They also describe interesting phenomena, such as the non-crossing theorem. A transition splits into two energies, one higher than the starting energy and one lower, when you put it in a magnetic field. This is called a Zeeman shift. If you have two transitions starting at different energies, you might expect them eventually to overlap, but they don't. They're never allowed to cross, but instead ‘bounce’ off each other, giving very weird-looking graphical plots.

The non-crossing theorem is related to spin-orbit interaction, so we also need to understand the Aufbau principle for electronic structure of atoms. But even here the authors take care to discuss unfamiliar phenomena, such as ‘dark states’ and electromagnetically induced transparency; and exotic analogues of hydrogen like positronium, muonium, and pionic hydrogen, where the usual proton + electron composition is changed.

Of course what people are really interested in these days are things like optical molasses, which is when two laser beams slightly detuned from each other are pointed toward each other to create a standing wave. In optical molasses, it's not the light that slows down, but light causing atoms to stop moving, which is to say cooling them off. It turned out that this type of optical cooling worked much better than the theory predicted. In trying to explain it, physicists invented an even better way, known as sub-Doppler cooling, which is now widely used in studying Bose-Einstein condensates (BECs), where the atoms all occupy the same ground state. This only happens if they happen to be bosons; fermions aren't ‘allowed’ to be in the same state. In a BEC, huge numbers of atoms move as if they were one single atom.

This requires temperatures below a millionth of a degree above absolute zero, so even the most robust cooling trap, called a magneto-optical trap, which only gets your atoms down to 0.001K, isn't good enough. The magneto-optical trap is popular because it doesn't need high polarization or precise lasers, so cheaper diode lasers and modest quadrupoles are good enough. But to get the final cooling to a μK, you need to add evaporative cooling, which is a sort of Maxwell's demon that throws away anything warm. Unlike optical molasses, a BEC can slow down light to walking speed and even stop it entirely.

That makes laser cooling a hot topic these days, but to understand why it works you need to understand the basics. There are many formulas and graphs, but a deep knowledge of quantum mechanics isn't necessary for this book (though it couldn't hoit). Persevering through the familiar early chapters is well worth the effort, and it pays to keep in mind that there has to be another level of explanation for all this that remains to be discovered. This book will give you a better understanding of auroras, but the unknown stuff is what makes it exciting.

jun 09, 2025. updated jun 10 2025