Although spontaneously broken time-translation symmetry has never been observed before, almost every other type of spontaneous symmetry breaking has been. One very common example of a spontaneously broken symmetry occurs in magnets. The laws of nature do not impose which side of a magnet will be the north pole and which will be the south pole. The distinguishing feature of any magnetic material, however, is that it spontaneously breaks this symmetry and chooses one side to be the north pole. Another example is ordinary crystals. Although the laws of nature are invariant under rotating or shifting (translating) space, crystals spontaneously break these spatial symmetries because they look different when viewed from different angles and when shifted a little bit in space.
In their new study, the physicists specifically define what it would take to spontaneously break time-translation symmetry, and then use simulations to predict that this broken symmetry should occur in a large class of quantum systems called “Floquet-many-body-localized driven systems.” The scientists explain that the key aspect of these systems is that they remain far from thermal equilibrium at all times, so the system never heats up.
The new definition of broken time-translation symmetry is similar to the definitions of other broken symmetries. Basically, when the size of a system (such as a crystal) grows, the time taken for a symmetry-breaking state to decay into a symmetry-respecting state increases, and in an infinite system the symmetry-respecting state can never be reached. As a result, symmetry for the entire system is broken.
“The significance of our work is two-fold: on one hand, it demonstrates that time-translation symmetry is not immune to being spontaneously broken,” said coauthor Bela Bauer, a researcher at Microsoft Station Q. “On the other hand, it deepens our understanding that non-equilibrium systems can host many interesting states of matter that cannot exist in equilibrium systems.”
According to the physicists, it should be possible to perform an experiment to observe time-translation symmetry breaking by using a large system of trapped atoms, trapped ions, or superconducting qubits to fabricate a time crystal, and then measure how these systems evolve over time. The scientists predict that the systems will exhibit the periodic, oscillating motion that is characteristic of time crystals and indicative of spontaneously broken time-translation symmetry.