# Topological time crystals

@article{Giergiel2018TopologicalTC, title={Topological time crystals}, author={Krzysztof Giergiel and Alexandre Dauphin and Maciej Lewenstein and Jakub J. Zakrzewski and Krzysztof Sacha}, journal={New Journal of Physics}, year={2018}, volume={21} }

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…

## 35 Citations

### Controlled preparation of phases in two-dimensional time crystals

- PhysicsPhysical Review Research
- 2021

The study of phases is useful for understanding novel states of matter. One such state of matter are time crystals which constitute periodically driven interacting many-body systems that…

### Two-dimensional Thouless pumping in time-space crystalline structures

- PhysicsPhysical Review B
- 2022

Dynamics of a particle in a resonantly driven quantum well can be interpreted as that of a particle in a crystal-like structure, with the time playing the role of the coordinate. By introducing an…

### Condensed matter physics in time crystals

- PhysicsNew Journal of Physics
- 2020

Time crystals are physical systems whose time translation symmetry is spontaneously broken. Although the spontaneous breaking of continuous time-translation symmetry in static systems is proved…

### Quantum Time Crystals from Hamiltonians with Long-Range Interactions.

- PhysicsPhysical review letters
- 2019

This study proposes a form of a Hamiltonian for which the unitary dynamics exhibits the time crystalline behavior and breaks continuous TTS, based on a spin-1/2 many-body Hamiltonian which has long-range multispin interactions in the form of spin strings, thus bypassing previously known no-go theorems.

### Time Crystals Protected by Floquet Dynamical Symmetry in Hubbard Models.

- PhysicsPhysical review letters
- 2020

These time crystals arise only from the Floquet dynamical symmetry and thus appear in both dissipative and isolated systems and in the presence of disorder as long as the FDS is respected, and their experimental realizations in cold atom experiments are discussed.

### Condensed matter physics in big discrete time crystals

- PhysicsAAPPS Bulletin
- 2022

We review the application of discrete time crystals created in a Bose-Einstein condensate (BEC) of ultracold atoms bouncing resonantly on an oscillating atom mirror to the investigation of condensed…

### Autonomous topological time crystals and knotty molecular motors

- PhysicsJournal of physics. Condensed matter : an Institute of Physics journal
- 2020

It is demonstrated how the time crystalline qualities of a closed string are greatly enhanced when the string becomes knotted, which means that physical realizations of Hamiltonian time crystals can be constructed in terms of knotted ring molecules.

### Phase diagram and optimal control for n-tupling discrete time crystal

- PhysicsNew Journal of Physics
- 2020

A remarkable consequence of spontaneously breaking the time translational symmetry in a system, is the emergence of time crystals. In periodically driven systems, discrete time crystals (DTC) can be…

### Time-crystalline phases and period-doubling oscillations in one-dimensional Floquet topological insulators

- Physics
- 2020

In this work, we reported a ubiquitous presence of topological Floquet time crystal (TFTC) in one-dimensional periodically-driven systems. The rigidity and realization of spontaneous discrete…

### Six-dimensional time-space crystalline structures

- Physics
- 2021

Time crystalline structures are characterized by regularity that single-particle or many-body systems manifest in the time domain, closely resembling the spatial regularity of ordinary space…

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