Sung to the abbess’s lines in “Maria” from The Sound of Music:
“How do you catch a wave like Maria? How do you grab a cloud and pin it down? Oh, how do you solve a particle like Maria? How do you hold a moonbeam in your hand?”
Through our expeditions into the wilderness of quantum mechanics so far, we’ve seen particles that are wild and free. But most particles spend their lives in more constrained circumstances: electrons caught in the embrace of nuclei, atoms shackled into molecules, or the regimented lines of crystals. Confinement is not necessarily bad—only strings tightly tied into a musical instrument can make music.
In today’s hike into the quantum-mechanical woods, we are going to carry along some traps so we can see how particles behave when you confine them. (Being sensitive sorts, we’ll treat them kindly and release them when we’re done.) In the process, we’ll discover the origin of emission spectra from stars and encounter artificial atoms and quantum dots, which play leading roles in everything from quantum computing to consumer televisions.
Why the caged bird sings
As we’ve seen a number of times, all particles move like waves. But what happens when we trap a wave? How does a particle’s behavior change when we confine it?
A great everyday example of a trapped wave is a guitar string. Before being attached to a guitar, a string can wiggle any way it feels like. Fast waves, slow waves—every kind of wave is possible. But when we tie the string to a guitar and pluck it, the resulting wave is trapped by the ends that are attached to the guitar. The wave can bounce between the ends, but it can’t escape.
As shown in the diagram above, some sets of waves (harmonics) are allowed, but only waves of the right length are possible. When we trapped the wave, we went from any note being possible to a state where only those waves that fit within the trap—and the notes they correspond to—can exist. In other words, the pitches of the guitar string are caused by the trap. And when we put a finger on a fret to change the size of the trap, the size of the waves that fit changes, and the notes we hear change.
We can see the same thing happen with electrons. In 1993, Don Eigler and colleagues made an electron trap by placing 48 iron atoms into a ring on top of a copper sheet. The ring of iron atoms creates a quantum corral—a circular electron trap. When imaged with a scanning tunneling microscope, the wave of a trapped electron can be clearly seen inside the ring of iron atoms.
Since particles move like waves, they respond just like any other kind of wave when caught—they sing with specific notes. The electron in the quantum corral looks like the vibrations of a drum head. That is not an accident: a drum also creates a circular trap for waves analogous to the quantum corral. The observation that quantum particles pick up specific notes when trapped is a consequence of them moving like waves. So by catching particle waves, we can make music.