# Time crystals in periodically driven systems

@article{Yao2018TimeCI, title={Time crystals in periodically driven systems}, author={Norman Y. Yao and C. Nayak}, journal={Physics Today}, year={2018} }

When the discrete time-translation symmetry of isolated, periodically driven systems is spontaneously broken, a new phase of matter can emerge.

## 46 Citations

### Floquet theory for temporal correlations and spectra in time-periodic open quantum systems: Application to squeezed parametric oscillation beyond the rotating-wave approximation

- Physics
- 2021

The authors develop a general method for the computation of temporal correlation functions and the corresponding spectra in time-periodic open quantum systems based on the Floquet theory. The authors…

### An inexpensive crystal makes a fine quantum time machine

- PhysicsPhysics Today
- 2019

To understand the intricacies of thermodynamics in the quantum regime, it helps to be able to turn back the clock.

### Classical discrete time crystals

- PhysicsNature Physics
- 2020

The spontaneous breaking of time-translation symmetry in periodically driven quantum systems leads to a new phase of matter: the discrete time crystal (DTC). This phase exhibits collective…

### Emergent limit cycles and time crystal dynamics in an atom-cavity system

- PhysicsPhysical Review A
- 2019

We propose an experimental realization of a time crystal using an atomic Bose-Einstein condensate in a high finesse optical cavity pumped with laser light detuned to the blue side of the relevant…

### Classical Many-Body Time Crystals.

- Physics, Computer SciencePhysical review letters
- 2019

This work provides a simple and pedagogical framework by which to obtain many-body time crystals using parametrically coupled resonators and presents a clear distinction between single-mode time-translation symmetry breaking and a situation where an extensive number of degrees of freedom undergo the transition.

### Supplemental Material for Classical many-body time crystals

- Physics
- 2019

Discrete time crystals are a many-body state of matter where the extensive system’s dynamics are slower than the forces acting on it. Nowadays, there is a growing debate regarding the specific…

### 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…

### The role of fluctuations in quantum and classical time crystals

- Physics
- 2022

Discrete time crystals (DTCs) are a many-body state of matter whose dynamics are slower than the forces acting on it. The same is true for classical systems with period-doubling bifurcations. Hence,…

### Building Continuous Time Crystals from Rare Events.

- PhysicsPhysical review letters
- 2020

Using Doob's transform as a tool, this work provides a mechanism to build classical time-crystal generators from the rare event statistics of some driven diffusive systems and uncovers striking similarities, but also key differences, with the Kuramoto synchronization transition.

### Time crystal dynamics in a weakly modulated stochastic time delayed system

- PhysicsScientific reports
- 2022

Time crystal oscillations in interacting, periodically driven many-particle systems are highly regular oscillations that persist for long periods of time, are robust to perturbations, and whose…

## References

SHOWING 1-10 OF 17 REFERENCES

### Floquet Time Crystals.

- PhysicsPhysical review letters
- 2016

This work defines what it means for time translation symmetry to be spontaneously broken in a quantum system and shows that this occurs in a large class of many-body localized driven systems with discrete time-translation symmetry.

### 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.

### Quantum time crystals.

- PhysicsPhysical review letters
- 2012

Some subtleties and apparent difficulties associated with the notion of spontaneous breaking of time-translation symmetry in quantum mechanics are identified and resolved. A model exhibiting that…

### Impossibility of spontaneously rotating time crystals: a no-go theorem.

- PhysicsPhysical review letters
- 2013

A "no-go theorem" is proved, rigorously ruling out the possibility of spontaneous ground-state rotation for a broad class of systems.

### 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.

### 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…

### 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.

### 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.

### 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.