Challenging quantum mechanics with a crystal

Dr. Matteo Fadel, Branco Weiss Fellow at ETH, together with the group of Prof. Yiwen Chu at the Laboratory of Solid State Physics and colleagues in Denmark and Germany, has now managed to put a microgram-mass crystal into a quantum superposition state in order to test the validity of quantum mechanics in this macroscopic regime. The results of his research, recently published in the scientific journal Physical Review Letters, should make it possible to test quantum mechanics – and possible modifications of it – using heavier objects than ever before.

Over the past decades, much progress has been made in testing quantum mechanics by making atoms and ever larger molecules interfere. In the case of molecules, this was achieved by using diffraction gratings. In such a grating, the quantum mechanical wave associated with the molecule is split into many parts, which are then recombined and – if coherence between the parts is maintained for long enough – create an interference pattern. Such interference patterns have been observed for molecules consisting of as many as 2000 atoms. “Using larger and larger molecules, however, means that the slits of the diffraction grating need to be closer and closer together, which at some point will make this approach unfeasible”, says Fadel. This is because the wavelength of the quantum mechanical wavefunction of a particle becomes smaller as it mass increases.

Quantum states of a vibrating crystal

To test quantum mechanics for more massive objects, therefore, he and his team used a different approach: so-called acoustic wave resonators. Those are essentially little slabs of sapphire that are made to vibrate, and those vibrations are then measured. In order to induce vibrations that represent quantum mechanical superposition states – the equivalent of an atom or molecule being in two places at the same time – the crystal is coupled via the piezoelectric effect (which creates an electric field when a material is deformed) to a superconducting circuit that acts as a quantum bit, or qubit, which is also used in quantum computers. A qubit can take on one of two possible quantum states, or a superposition of the two. By coupling the qubit to the crystal one can transfer the superposition state of the qubit to the collective vibration of the atoms in the crystal. Furthermore, the qubit can subsequently be used to detect the vibrational state of the crystal.

With this procedure, Fadel and his collaborators were able to create quantum mechanical superposition states of a sapphire crystal consisting of ten thousand trillion atoms (a number with 16 zeroes). They cooled the crystal, which vibrated around six billion times per second, down to a hundredth of a degree above absolute zero so as to minimize thermal fluctuations. After putting the crystal into a specific quantum state, the researchers detected its state after a variable time via the qubit. This allowed them to determine whether the vibrational state of the crystal was truly quantum mechanical or whether it could be described by classical mechanics. In their experiment, they found quantum features in the vibration of the crystal for up to 40 microseconds.

Possible modifications of quantum mechanics

“Combined with the large mass of the crystal, this coherence time indicates a test of the quantum superposition principle at a level that is close to what can currently be achieved with molecule interferometers”, Fadel explains. “With some improvements we should be able to create even more macroscopic states in the near future, surpassing the results obtained with molecules and thus testing quantum mechanics in as yet unexplored regimes.” Fadel’s ultimate aim is to find out what happens to quantum effects in the intermediate mass regime between atoms or molecules on the one hand and truly macroscopic objects on the other hand. Some current theories assume that the loss of quantum coherence as objects become larger is somehow built into quantum mechanics. This, however, would mean that the famous Schrödinger equation – a mathematical tool used by physicists to describe quantum systems – is incomplete and needs to be modified by adding an extra term.   

The results now obtained by Fadel and his collaborators at ETH put an upper bound on how large such a hypothetical term might be. Finding out whether the Schrödinger equation needs to be modified is of great interest not just for basic science, as Fadel points out: “This would have important implications, for example, for quantum computers and sensors.” As the numbers of qubits in those quantum devices become increasingly large, decoherence effects due to their sheer size could put as yet unforeseen constraints on their functionality.