The Quantum Description of Light and X-Rays

The wave theory of the 19th century played an important role in the thinking of the early pioneers of the quantum era in the early 20th century. When Albert Einstein presented his revolutionary idea that light must be composed of light quanta, Max Planck strongly objected. He argued that light diffraction patterns extend over macroscopic dimensions and therefore cannot be produced by point-like light particles. This argument entails the very core of what became known as the wave-particle dilemma.?

The formal quantum description of light emerged in the late 1920s through Paul Dirac’s formulation of quantum mechanics, which he called “quantum electro-dynamics”. The word “quantum” describes discrete small units which when all added simulate a continuous distribution. An example are the discrete pixels of a digital camera that add up to a smooth looking picture. Dirac’s quantization of the continuous classical EM field resulted in tiny building blocks of light called “photons”. While the concept of the photon is all but trivial and is still debated by physics fundamentalists, the simplest mental picture is a small massless particle ?ying through space at the speed of light.

It was later recognized that Dirac’s formulation was incomplete and constituted only the simplest form of a more complete theory developed around 1950 by Sin-Itiro Tomonaga, Julian Schwinger, Richard Feynman, and Freeman Dyson (only the first three won the Nobel Prize in 1965). It is this complete theory of light and matter that we today call quantum electro-dynamics (QED).? QED has been found to agree with all measured electro-magnetic phenomena with amazing accuracy (up to one part in a trillion), and today is regarded as the theory that describes all EM phenomena. Its extension to include nuclear processes by quantum field theory is the basis for today’s “Standard Model” of Physics. The inclusion of gravity still evades us.

The complexity of QED led Feynman to call it “the strange theory of light and matter”. Indeed, some of its predictions can blow your mind and sound like science fiction. In QED, the lowest energy state is denoted by the label zero-point (ZP), leading to names like “ZP energy”, “ZP field”, “ZP state”, or “quantum vacuum”. The last name is misleading since the ZP state is not “empty” but contains so-called “virtual photons” which pop in and out of existence quasi-instantaneously. Their lifetime is so short that we cannot measure these virtual photons directly, but their existence manifests itself in observable effects. Each charged particle is surrounded by a cloud of such virtual photons and the overlap of the clouds gives rise to the classical electromagnetic coupling between charged particles (the Coulomb interaction). The ZP virtual photons also lead to a tiny shift in the energy levels of atoms, called Lamb-shift, and to a small anomaly in the magnetic moment of an electron, both discovered in the late 1940s. ?

QED includes both the photon and matter (particles with mass and charge) contributions and may be regarded as an extension of Dirac’s first order theory to higher order. ?This is today visualized by so-called Feynman diagrams which extend the description of single charges and photons to increasingly higher numbers or “orders”. The invention of the laser around 1960, led Roy Glauber in the early 1960s to develop a theory that specifically describes the light-only part of QED. In his quantum optics, Glauber maintained the QED notion of ordering processes in terms of the number of particles involved. First order describes the coherence properties of single non-interacting photons, as first done by Dirac around 1930. It gives the same results as the wave theory. ?Second order describes the correlations between 2 photons in time and space and is particularly important because the wave theory cannot explain all second order phenomena. In order to compare theory to experiments one typically assumes space-time separability and then considers the simultaneous (same-time) correlations between two photons. For example, the two photons can pool their energy in an instantaneous joint act, which is an example of a ??non-linear effect (in contrast to a linear = first order = single photon effect). Amazingly, two photons can also interfere to create new kinds of diffraction patterns, as I will explain in future blogs. ?Third and even higher orders describe correlations between increasing numbers of photons (3, 4, 5…).

Since quantum optics is based on QED, the ZP state also plays an important role. As in QED, it contains no real (measurable) photons. Observable photons are born through excitations of the ZP state through energy transfer from charged particles like electrons. In the reverse process, photons decay back into the ZP state (are destroyed) by transferring their energy back to charged particles.?

Photon birth and destruction are abstractly (mathematically) described through photon creation and destruction operators. Their repeated actions can create an arbitrary number of photons out of the ZP state and can similarly destroy them again. The ZP state in quantum optics represents darkness, while the excited states containing photons represent light. Thus quantum optics predicts the existence of different forms of light that can be created from the ZP state. Light is not simply composed of photons, but for a given number of photons (or ”order”) a substructure exists, expressed by different quantum states of light. This is the revolutionary new paradigm for the nature of light that earned Glauber the 2005 Nobel Prize in Physics.

Glauber’s theory has been beautifully verified experimentally through the manipulation of laser light over the last 50+ years. Laser light comes in a so-called “coherent state” or “Glauber state” containing a large number of photons. In experiments, the properties of a laser beam may be altered through its interaction with a sample. It can simply be attenuated to a coherent state containing less photons or used to create new types of quantum states (see below). In all quantum optics experiments, photon detection and counting plays a key role. A complete experiment consists of averaging over many observations of the behavior of single or few photons to obtain a statistical average.

The counting of photons is enabled by the so-called photoelectric effect, whose explanation won Einstein the Nobel Prize in 1921. In the process an incident photon is converted by a detector atom into an electron which is then amplified to produce a measurable electronic pulse. Each pulse reflects a single destroyed photon. In typical quantum optics experiments, one measures how many photons arrive within an “open” time period of a detector, which may be as short as 1 nanosecond. When more than single photons arrive within the detector time window, the photons are said to be detected in coincidence (at the same time). Quantum optics experiments typically deal with the arrivals of only few photons and the most studied cases involve the coincident arrival of only two photons.

The most famous two-photon state is created by splitting an incident photon into two photons with half the original energy. The creation of such photon pairs has a very low probability but they can be readily created by a laser. The simultaneous birth of such a photon pair has the amazing consequence that the two photons remain coupled after birth - they are said to be “entangled”. This phenomenon was famously disputed by Einstein as “spooky action at a distance” in the mid 1930s, but the modern proof of entanglement was honored by the 2022 Nobel Prize in Physics awarded to Alain Aspect, John Clauser and Anton Zeilinger. ??

In my next blog, I will describe in simple terms how diffraction is formulated in quantum optics, and then show how a statistical accumulation of many single photon bright spots evolves into the continuous ?pattern predicted by the wave theory. In a later blog I will discuss the remarkable two-photon diffraction case which reveals the limitation of the wave theory.