Theorist **Murray Holland** and his students have figured out a way to understand the quantum behavior of atoms inside every laser in JILA, including two superradiant lasers in the Thompson lab that work entirely differently from all the others. Their secret: the application of SU(4) group theory, originally used to explain quark physics, to the quantum behavior of atoms in a laser.

Before this seminal insight, most theorists believed the behavior of atoms in a laser was too complex to ever be described. For instance, three hundred atoms, each with two possible states, would have as many different combinations of quantum states in a laser as there are atoms in the Universe. The pathway through this complexity is something called invariance.

Invariance is responsible for the familiar laws of conservation of energy and momentum that govern the classical world. The two laws state that if no external forces are acting on a system, (1) the amount of energy remains constant over time, and (2) an object will continue moving at the same speed forever. The fact that energy remains constant is due to the invariance of choosing the origin of time. The fact that an object just keeps traveling at the same speed is due to the invariance of choosing the origin of space.

Holland and his group discovered an intricate invariance that governs the quantum physics of lasers. Only a relatively small number of possible quantum states are compatible with a particular value of the invariant quantity once it’s determined by a laser system itself.

It’s as if a laser can “chose to be made of only one color such as red, blue, green, yellow, black, grey, or clear Legos. But, once decided, the laser obeys a conservation law that says that the color of the Lego blocks won’t change in time. The constancy of the color represents the invariance. Once the invariance is in place, any state of the laser can be made from just four shapes of quantum Lego blocks such as a square, a corner piece, a thin arch piece, and a rectangle. These shapes correspond to the up, down, strange, and charm quarks, respectively.

Like quarks, the laser Lego shapes are actually quantum mechanical states. Even so, it’s possible to construct quite complicated things from four elementary building blocks. In fact, it’s possible to make everything you need to describe a laser. Holland and his group proved this by using SU(4) group theory to solve the quantum master equations for both ordinary and superradiant lasers.

The group is currently working to see how far they can push this new idea.