Floquet Time Crystals could exist and break time translation symmetry

Researchers have defined what it means for time translation symmetry to be spontaneously broken in a quantum system, and show with analytical arguments and numerical simulations that this occurs in a large class of many-body-localized driven systems with discrete time-translation symmetry.

In 2012 Nobel laureate Frank Wilczek first proposed the idea of time crystals. He argued that these hypothetical objects can exhibit periodic motion, such as moving in a circular orbit, in their state of lowest energy, or their “ground state.” Theoretically, objects in their ground states don’t have enough energy to move at all.

Physicists from the University of California, Santa Barbara (UCSB) and Microsoft Station Q (a Microsoft research lab located on the UCSB campus) have demonstrated that it may be possible for time crystals to physically exist.

The physicists have focused on the implication of time crystals that seems most surprising, which is that time crystals are predicted to spontaneously break a fundamental symmetry called “time-translation symmetry.” To understand what this means, the researchers explain what spontaneous symmetry breaking is.

If time crystals really do spontaneously break time-translation symmetry, then the laws of nature that govern time crystals wouldn’t change with time, but the time crystals themselves would change over time due to their ground-state motion, spontaneously breaking the symmetry.

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.

Arxiv – Floquet Time Crystals

Definition of Time Translation Symmetry-Breaking

Systems that spontaneously break time-translation symmetry (TTS) have been dubbed “time crystals,” in analogy with ordinary crystals, which break spatial translational symmetries. Even defining this notion correctly requires considerable care, and putative models have proven inconsistent. The most obvious definition of time-translation symmetry breaking (TTSB) would be that the expectation values of observables are time-dependent in thermal equilibrium. However, this is clearly impossible

We must look beyond strict thermal equilibrium. This should not be too surprising, as the state ρ preserves all the symmetries of H, which would suggest that no symmetry can be spontaneously broken. For symmetries other than time translation, the resolution to this paradox is well-known: in a system with a spontaneously broken symmetry, there is ergodicity-breaking and the lifetime of a symmetry-breaking state diverges as the system size grows. Thus, in the thermodynamic limit, the state ρ is unphysical and is never reached.

After defining time translation symmetry breaking, they used simulations to predict that this broken symmetry should occur in a large class of quantum systems called “Floquet-many-body-localized driven 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.

Signatures of MBL have been observed in trapped systems of neutral atoms and trapped ions, and signatures of single-particle localization have been seen in coupled superconducting qubits. In any of these systems, one can prepare an arbitrary initial product state, evolve to late times according to a drive in the class considered here, and measure the “spins” in the desired basis. Their prediction is that persistent oscillations will be observed at a fraction of the drive frequency.

“In collaboration with experimental research groups, we are exploring the possibility of realizing Floquet time crystals in systems of cold atomic gases,” said coauthor Chetan Nayak at Microsoft Station Q and UCSB.

SOURCES- Phys Org, Arxiv, Physical Review Letters