A Curious Observer Guide to Quantum Mechanics, pt. 5: Catch a wave

A Curious Observer Guide to Quantum Mechanics, pt. 5: Catch a wave

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A Curious Observer Guide to Quantum Mechanics, pt. 5: Catch a wave

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One of the quietest revolutions of our present century was the entry of quantum mechanics into our everyday technology. It was previously that quantum effects were limited to physics laboratories and delicate experiments. But modern technology is increasingly relying on quantum mechanics for its basic operation, and the importance of quantum effects will only grow in the coming decades. As such, physicist Miguel F. Morales has taken on the powerful task of explaining quantum mechanics to laymen in this seven-part series (no math, we promise). Below is the fifth story in the series, but you can always find the start story plus a landing page for the entire series so far on the site.

Sung after the abbots’ rules in “Maria” The sound of music:

“How do you catch a wave like Mary? How do you grab a cloud and capture it? Oh, how do you solve a particle like Mary? How do you hold a moonbeam in your hand?”

Through our expeditions into the wilderness of quantum mechanics so far, we have seen particles that are wild and free. But most particles spend their lives in more limited conditions: electrons trapped in the embrace of nuclei, atoms bound in molecules, or the regimental lines of crystals. Lock-up is not necessarily bad – only strings tied to a musical instrument can make music.

In today’s hike to quantum mechanical wood we are going to take some traps with us so we can see how particles behave if you limit them. (Because we are sensitive species, we treat it kindly and release it when we are done.) In the process, we will discover the origin of emission spectra of stars and encounter artificial atoms and quantum dots, which play a major role in everything from quantum computers to consumer televisions. .

Why the cage bird sings

As we have seen several times, all particles move like waves. But what happens if we catch a wave? How does the behavior of a particle change when we limit it?

A great everyday example of a trapped wave is a guitar string. Before attaching a string to a guitar, it can wrap as it feels. Fast waves, slow waves – every kind of wave is possible. But if we tie the string to a guitar and pluck it, the wave from it is caught by the points attached to the guitar. The wave can bounce off between the ends, but it cannot escape.

The trapped waves of a guitar string. Clockwise from top left are the fundamental, 2nd harmonics and 3rd harmonics of an open string. Only waves that fit neatly into the trap are allowed, and the increasing frequency is associated with higher energy (higher pitch). We can also shorten the trap by using one of the guitar bands, which changes the frequency of the fundamental (bottom left) and all the harmonics.
Enlarge / The trapped waves of a guitar string. Clockwise from top left are the fundamental, 2nd harmonics and 3rd harmonics of an open string. Only waves that fit neatly into the trap are allowed, and the increasing frequency is associated with higher energy (higher pitch). We can also shorten the trap by using one of the guitar bands, which changes the frequency of the fundamental (bottom left) and all the harmonics.

Miguel Morales

As shown in the diagram above, some sets of waves (harmonics) are allowed, but only waves of the correct length are possible. When we trap the wave, we go from any possible note to a state where only the waves that fit into the trap – and the notes that match it – can exist. In other words, the pitches of the guitar string are cause through the snare. And if we put a finger on the ferret 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 happening with electrons. In 1993, Don Eigler and colleagues made an electron collector by placing 48 iron atoms in a ring on top of a copper plate. The ring of iron atoms creates a quantum grain – a circular electron trap. If imaged with a scanning tunnel microscope, the wave of a trapped electron can be clearly seen inside the ring of iron atoms.

A circular coral of 48 iron atoms (sharp peaks) on a copper plate. The wave of an electron trapped in the bead can be clearly seen.
Enlarge / A circular coral of 48 iron atoms (sharp peaks) on a copper plate. The wave of an electron trapped in the bead can be clearly seen.

As particles move like waves, they react just like any other wave when caught – it sings with specific notes. The electron in the quantum corral looks like the vibrations of a drumhead. This is not an accident: a drum also creates a circular snare for waves analogous to the quantum bead. The observation that quantum particles pick up specific notes when trapped is the result of them moving like waves. By capturing particle waves, we can therefore make music.

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