# Quantum Bootcamp Part V: Quantum Optics, Illuminating the Invisible

**Research Area:**

*Undergraduate Wonju Lee contributes the entirety of this fifth column in our Quantum Bootcamp series, which details the journey he and Ethan Wang ’26 are pursuing in their independent study of quantum computing under Department of Chemistry postdoc Benjamin Lienhard of the Rabitz Group. *

*This will be Wonju’s final column. He has temporarily suspended his undergraduate degree at Princeton University in order to serve in the South Korean Marine Corps for 18 months. He plans to return to campus in the Fall of 2025 to resume his studies, joining the Class of 2028. Below, his observations on historical developments in quantum optics.*

Following our study of quantum mechanics, Ethan and I delved into quantum optics, the quantum interpretation of light. Under Ben’s instruction, we reviewed *Quantum Optics: An Introduction* by Mark Fox (Oxford University Press, 2006). Unlike the classical understanding of light as electromagnetic waves, quantum optics elucidates optical phenomena by viewing light as a stream of photons or quanta of electromagnetic energy. The birth of quantum optics was a rather natural theoretical progression to explain effects not covered by classical physics.

Undergraduate Wonju Lee, formerly a member of the Class of 2026, leaves Princeton for a two-year stint in the South Korean Marine Corps. He plans to return to campus in the Fall of 2025.

As we explored the various aspects of quantum optics, I was astonished by how rigorous mathematical observations and theories served as a basis for ideas proposed decades before being experimentally verified. In the following, we present some of the historic milestones showcasing how intellectual visionaries conceived the concepts of quantum optics with no more than their imaginations and an application of mathematics.

At the dawn of the 20th century, German physicist Max Planck hypothesized that blackbody radiation is emitted in discrete packets of energy, or quanta, which marked a cornerstone in the transition from classical to quantum optics. Black-body radiation is emitted by a black body (a hypothetical body that absorbs all incident electromagnetic radiation). Previously, physicists had struggled to describe the spectral distribution of black-body radiation, as classical physics predicted infinite intensities as the emission wavelength decreases, known as the ultraviolet catastrophe. Planck approached this problem by proposing a radiation law in 1901 that assumed energy to be quantized in discrete energy packets instead of a continuous stream, a rather displeasing assumption and interpretation even for him.

Then, in 1905, fellow physicist **Albert Einstein** explained the photoelectric effect by applying Planck’s quantum theory. The photoelectric effect refers to the ejection of electrons from a metal surface under electromagnetic radiation. Einstein predicted that the atoms were absorbing energy from the radiation in quantized packets, and that the electric current created by the incident light particles knocking out the electrons from atoms differed based on the frequency of the light instead of the intuitively expected intensity. American physicist Robert Millikan, who won the Nobel Prize in Physics in 1923, experimentally verified Einstein’s prediction a decade later. It was no other than this theory that earned Einstein his own Nobel Prize in Physics in 1921, not his Theory of Relativity or the famous equation demonstrating the relationship between energy and mass, E=mc^{2}.

In 1948, Dutch physicist Hendrik Casimir predicted what became known as the Casimir effect, which opened new doors in quantum field theory and electrodynamics. Light can be treated as quantized electromagnetic fields and can be viewed as quantum harmonic oscillators. The zero-point energy state, also the minimum uncertainty state of this oscillator, originates from the vacuum field fluctuations.

Essentially, the Casimir effect is a radiation theory where energy in an empty vacuum produces a force between two objects separated by a narrow vacuum gap. The Casimir effect was only experimentally demonstrated several decades later; in 1997, Steven Lamoreaux, today a professor of physics at Yale University, measured the force experimentally, and Casimir’s theory predicted the force with high precision.

In 1963, American physicist Roy Glauber introduced coherent states in quantum optics. While the concept of coherent states was initially presented in 1926, Glauber demonstrated their significance to the field of quantum optics, which led to his Nobel Prize in Physics in 2005. Coherent states are the quantum-mechanical equivalent of a classical electromagnetic field, which lies at the interface between quantum and classical. A coherent state is a minimum uncertainty state. It is often explained as a displaced vacuum state for its uncertainty circle of the vacuum displaced from the origin.

Glauber’s theories were later verified with the development of lasers producing coherent light.

Quantum theories have continuously developed and spread across multiple disciplines in recent years. Theories have not only been verified but also refined and extended by experimental discoveries. The insights of these quantum optical theories have led to the birth of new technologies, such as quantum computing and quantum communications.

The counterintuitive nature of the quantum world renders the discoveries reported above particularly astounding. Despite the technological limitations of their eras and the inability to experimentally test their ideas, countless theories were advanced from various physicists’ innovative thinking and creativity that were only years later experimentally verified.

The basis of all these discoveries is mathematics. Mathematical derivations served as a bridge between theories and experimental realities, connecting the abstract with the empirical. With the evolution of the field of quantum optics, further mathematical insights will continue to illuminate the undiscovered and support optical theories as physicists take leaps of faith. As Einstein once said: “A theory can be proved by experiment, but no path leads from experiment to the birth of a theory.”

As I transition from the quantum boot camp to the Korean Marine Corps boot camp, I seek to continue my quantum journey. I hope to return in two years to share further insights and discoveries.

*Wonju Lee and Ethan Wang have been writing the Quantum Bootcamp series since last spring. Here are columns one, two, three, and four. We continue next month with a new piece by Ethan on quantum computing. We wish Wonju all the best in his pursuits, and will look forward to seeing him back on campus in two years.*