Mutual interactions between atoms are responsible for self-organization of atoms and formation of space crystals. In 2012 Frank Wilczek posed a question if a similar phenomenon can occur in the time domain. In other words, if a quantum many-body system can self-organize in time and spontaneously start periodic motion. The original Wilczek's idea turned out to be impossible to realize, however, it became an inspiration to scientists and a novel research area was initiated.
We got interested in the time crystals shortly after the publication of Wilczek's seminal paper and we proposed realization of a discrete time crystal in a closed periodically driven atomic system. Later similar phenomena were rediscovered in condensed matter systems. Apart from the research of spontaneous formation of crystalline structures in time, we are interested in various condensed matter phases in the time domain. It turns out that Anderson and many-body localization and topological phases can be realized in the time dimension. For more information see the monograph Time Crystals
|Time lattice (left) created by ultra-cold atoms bouncing between two oscillating atom mirrors (right).|
We also do theoretical research on ultra-cold atomic gases. Our interests concern: collective excitation in atomic gases (such as solitons and vortices), ultra-cold gases in optical lattice potentials, disordered systems, topological systems and analysis of a measurement problem in quantum many body systems.