Topological Time Crystals

Abstract

By analogy with the formation of space crystals, crystalline structures can also appear in the time domain. While in the case of space crystals we often ask about periodic arrangements of atoms in space at a moment of a detection, in time crystals the role of space and time is exchanged. That is, we fix a space point and ask if the probability density for detection of a system at this point behaves periodically in time. Here, we show that in periodically driven systems it is possible to realize topological insulators, which can be observed in time. The bulk-edge correspondence is related to the edge in time, where edge states localize. We focus on two examples: Su-Schrieffer-Heeger (SSH) model in time and Bose Haldane insulator which emerges in the dynamics of a periodically driven many-body system.

Version accepted for publication in New Journal of Physics

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Cited by in corpus (36)

• Quantum Time Crystals from Hamiltonians with Long-Range Interactions
• The isolated Heisenberg magnet as a quantum time crystal
• Time Crystals Protected by Floquet Dynamical Symmetry in Hubbard Models
• Quantum time reflection and refraction of ultracold atoms
• Condensed Matter Physics in Time Crystals
• Discrete time crystal in a finite chain of Rydberg atoms without disorder
• Creating big time crystals with ultracold atoms
• Rigorous bounds on dynamical response functions and time-translation symmetry breaking
• Photonic Floquet time crystals
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• Topological Molecules and Topological Localization of a Rydberg Electron on a Classical Orbit
• Towards Timetronics with Photonic Systems
• Atomic Regional Superfluids in two-dimensional Moiré Time Crystals