# Clean Floquet Time Crystals: Models and Realizations in Cold Atoms.

@article{Huang2017CleanFT, title={Clean Floquet Time Crystals: Models and Realizations in Cold Atoms.}, author={Biao Huang and Ying-Hai Wu and W. Vincent Liu}, journal={Physical review letters}, year={2017}, volume={120 11}, pages={ 110603 } }

Time crystals, a phase showing spontaneous breaking of time-translation symmetry, has been an intriguing subject for systems far away from equilibrium. Recent experiments found such a phase in both the presence and the absence of localization, while in theories localization by disorder is usually assumed a priori. In this work, we point out that time crystals can generally exist in systems without disorder. A series of clean quasi-one-dimensional models under Floquet driving are proposed to…

## 67 Citations

### Time crystals: Analysis of experimental conditions

- PhysicsPhysical Review A
- 2018

Time crystals are quantum many-body systems which are able to self-organize their motion in a periodic way in time. Discrete time crystals have been experimentally demonstrated in spin systems.…

### Time crystals in a shaken atom-cavity system

- PhysicsPhysical Review A
- 2019

We demonstrate the emergence of a time crystal of atoms in a high-finesse optical cavity driven by a phase-modulated transverse pump field, resulting in a shaken lattice. This shaken system exhibits…

### Realizing time crystals in discrete quantum few-body systems

- PhysicsPhysical Review B
- 2019

The exotic phenomenon of time translation symmetry breaking under periodic driving - the time crystal - has been shown to occur in many-body systems even in clean setups where disorder is absent. In…

### Discrete Time Crystals in the Absence of Manifest Symmetries or Disorder in Open Quantum Systems.

- PhysicsPhysical review letters
- 2019

A semiclassical approach reveals the emergence of a robust discrete time-crystalline phase in the thermodynamic limit in which metastability, dissipation, and interparticle interactions play a crucial role.

### Topological time crystals

- PhysicsNew Journal of Physics
- 2019

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…

### 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.

### Fractional time crystals

- PhysicsPhysical Review A
- 2019

Time crystals are quantum systems that are able to reveal condensed matter behavior in the time domain. It is known that crystallization in time can be observed in a periodically driven many-body…

### Ju l 2 01 9 Continuous time crystals from static Hamiltonians with long-range interactions

- Physics
- 2019

Time crystals correspond to a phase of matter where time-translational symmetry (TTS) is broken. Up to date, they are well studied in open quantum systems, where external drive allows to break…

### Observation of a Space-Time Crystal in a Superfluid Quantum Gas.

- PhysicsPhysical review letters
- 2018

The observation of a space-time crystal using ultracold atoms, where the periodic structure in both space and time is directly visible in the experimental images, paving the way for the usage of space- time crystals for the discovery of novel nonequilibrium phases of matter.

### 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…

## References

SHOWING 1-10 OF 123 REFERENCES

### Discrete Time Crystals: Rigidity, Criticality, and Realizations.

- PhysicsPhysical review letters
- 2017

A simple model for a one-dimensional discrete time crystal which explicitly reveals the rigidity of the emergent oscillations as the drive is varied is considered and a blueprint based upon a one dimensional chain of trapped ions is proposed.

### Observation of discrete time-crystalline order in a disordered dipolar many-body system

- PhysicsNature
- 2017

This work observes long-lived temporal correlations, experimentally identifies the phase boundary and finds that the temporal order is protected by strong interactions, which opens the door to exploring dynamical phases of matter and controlling interacting, disordered many-body systems.

### Observation of a discrete time crystal

- PhysicsNature
- 2017

The experimental observation of a discrete time crystal, in an interacting spin chain of trapped atomic ions, is presented, which opens the door to the study of systems with long-range spatio-temporal correlations and novel phases of matter that emerge under intrinsically non-equilibrium conditions.

### Critical Time Crystals in Dipolar Systems.

- PhysicsPhysical review letters
- 2017

The authors demonstrate the existence of a novel, critical DTC regime that is stabilized not by many-body localization but rather by slow, critical dynamics, and shows that the DTC response can be used as a sensitive probe of nonequilibrium quantum matter.

### Absence of Quantum Time Crystals.

- PhysicsPhysical review letters
- 2015

A no-go theorem is proved that rules out the possibility of time crystals defined as such, in the ground state or in the canonical ensemble of a general Hamiltonian, which consists of not-too-long-range interactions.

### Long-time behavior of periodically driven isolated interacting lattice systems

- Physics
- 2014

We study the dynamics of isolated interacting spin chains that are periodically driven by sudden quenches. Using full exact diagonalization of finite chains, we show that these systems exhibit three…

### Topological Thouless pumping of ultracold fermions

- Physics
- 2016

Charge transport in a cyclically time-modulated periodic potential, also known as a topological Thouless pump, has been realized in an ultracold gas of fermionic atoms. An electron gas in a…

### Absolute stability and spatiotemporal long-range order in Floquet systems

- Physics
- 2016

Recent work has shown that a variety of novel phases of matter arise in periodically driven Floquet systems. Among these are many-body localized phases which spontaneously break global symmetries and…

### Space-time crystals of trapped ions.

- Physics, Materials SciencePhysical review letters
- 2012

The proposed space-time crystals of trapped ions provide a new dimension for exploring many-body physics and emerging properties of matter and are robust for direct experimental observation.

### Phase Structure of Driven Quantum Systems.

- PhysicsPhysical review letters
- 2016

It is shown that their disordered Floquet many-body localized counterparts can exhibit distinct ordered phases delineated by sharp transitions, and these are analogs of equilibrium states with broken symmetries and topological order.