One cat and three masters

It might be pushing ninety, yet still it slinks through the physics laboratories of the modern age: Schrödinger’s Cat. Probably the most famous animal in physics, it was born of a thought experiment and manages to be both dead and alive at the same time. As part of a Branco Weiss Fellowship, Matteo Fadel is researching what all the fuss is about with this cat – or, rather, the transition between quantum mechanics and classical physics, for which it has become a symbol.

A cat is born

In the 1930s, the era’s most famous physicists – among them Erwin Schrödinger – discussed how to reconcile the theory of quantum mechanics with the reality we observe in everyday life. In quantum mechanical terms, a particle can assume what are known as superposition states. This means that rather than being in either state A or state B, the particle can also be in both at the same time.

Take the example of radioactive materials, whose atomic nuclei emit radiation when they decay. The only way to state whether or not a given nucleus has already decayed after a certain time is with the help of a probability distribution. As long as nobody measures the emitted particle – that is, for as long as it does not interact with its environment – the nucleus is in a superposition state of “intact” and “decayed”.

Schrödinger found this idea absurd and suggested imagining a cat in a sealed box. Alongside it in the box sits a “hell machine”, as Schrödinger called it: a radioactive substance for which the probability that one atom will have decayed after one hour is 50 percent. Should this come to pass, the resulting radiation triggers a signal in a detector. This, in turn, causes a hammer to smash a bottle containing hydrogen cyanide, which kills the cat. However, it is just as likely that no atom will decay, the hydrogen cyanide will remain in the bottle, and the cat will stay alive. According to the rules of quantum mechanics, this setup would put the cat in a superposition state, i.e. dead and alive at the same time – until someone looks inside the box and finds it either dead or alive.

In reality, cats have never been reported to be dead and alive at the same time. And so the big question is why an atom can be in a superposition state but a cat cannot. The answer lies in mass and temperature: the more atoms that are involved and the faster they are moving, which is to say the heavier and warmer the object, the faster the superposition state loses its coherence. It interacts with the environment and can therefore no longer be observed. With a domestic cat and at room temperature, this happens many times faster than anything the most precise clocks could measure, let alone what we humans could observe.

The music of quantum mechanics

It is precisely such fundamental problems of physics that have long intrigued Matteo Fadel. At ETH Zurich, he is now trying to explore the mysterious grey area between the microscopic world of quantum mechanics and the macroscopic world of our everyday lives. Cats might be out of the question, but how big and heavy can objects become and still let us observe their quantum mechanical behaviour?

Fadel, a physicist, works as a postdoc in the laboratory of ETH Professor Yiwen Chu, who is one of the pioneers of quantum acoustics. While quantum states are otherwise often observed in photons – i.e. light particles – or electrons, this relatively young field deals with quantum mechanical effects in sound waves. To this end, researchers use piezo crystals to couple superconducting qubits – the old hands of experimental quantum physics – with what are known as HBARs (high overtone bulk acoustic wave resonators). These might for instance be fine flakes of sapphire. The piezo crystals deform when placed in an electric field; in this case, the electric signal comes from the qubits. The vibration generated by periodic deformations in the piezo crystal is passed on to the sapphire, which can store it as an acoustic standing wave.

For Fadel and his question about the transition between the microscopic and macroscopic worlds, such experiments are particularly interesting because, although the vibrations in the HBAR do not involve the whole sapphire, they do involve several orders of magnitude more atoms than in other quantum mechanical experiments. Or, to put it another way: the cat in this box might not be full-grown, but it still weighs in at 50 micrograms.

If the HBAR is now cooled to just above absolute zero, it becomes possible to excite individual phonons, the acoustic counterparts of photons. Fadel – himself a passionate violinist – likes to compare it to a guitar player who plucks on a single string. Just as the tone on the guitar will fade, so too will the sapphire interact with its environment after excitation and lose the phonon, and thus its quantum mechanical behaviour, over time. However, this process is slow enough for physicists to still prove it.

Advancing into new fields

Fadel and his colleagues now plan to realise the said superposition states and have the atoms that make up the sapphire vibrate in different directions simultaneously. Furthermore, there are other interesting quantum states that physicists hope to explore using the acoustic resonator. Some of these could be used, for example, for quantum teleportation or for building quantum computers.

Fadel himself is particularly interested in the states that will shed new light on the connection between quantum mechanics and gravity. According to Isaac Newton, who illustrated the principle of gravity with an apple rather than a cat, the force is stronger the closer two objects come to each other. Albert Einstein, in turn, postulated in his theory of relativity that gravitational fields stretch time. If this is true, then time passes more quickly for the live cat that has climbed the wall of the box than for the dead cat lying on its floor. This might be one reason why the quantum mechanical superposition state loses its coherence over time, even in a hermetically sealed container.

Can such effects now finally be demonstrated by means of quantum acoustics? Fadel’s research aims to break precisely this new ground in fundamental physics. Ground where quantum mechanics, gravitation and relativity come together; or, to put it another way, where the famous animal is no longer only Schrödinger’s but, in a sense, Newton’s and Einstein’s cat, too.