# Discrete Time-Crystalline Order in Cavity and Circuit QED Systems.

@article{Gong2018DiscreteTO, title={Discrete Time-Crystalline Order in Cavity and Circuit QED Systems.}, author={Zongping Gong and Ryusuke Hamazaki and Masahito Ueda}, journal={Physical review letters}, year={2018}, volume={120 4}, pages={ 040404 } }

Discrete time crystals are a recently proposed and experimentally observed out-of-equilibrium dynamical phase of Floquet systems, where the stroboscopic dynamics of a local observable repeats itself at an integer multiple of the driving period. We address this issue in a driven-dissipative setup, focusing on the modulated open Dicke model, which can be implemented by cavity or circuit QED systems. In the thermodynamic limit, we employ semiclassical approaches and find rich dynamical phases on…

## 98 Citations

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

- Physics, MedicinePhysical 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.

Dissipative discrete time crystals

- Physics
- 2018

Periodically driven quantum systems host a range of non-equilibrium phenomena which are unrealizable at equilibrium. Discrete time-translational symmetry in a periodically driven many-body system can…

Signatures of discrete time crystalline order in dissipative spin ensembles

- PhysicsNew Journal of Physics
- 2020

Discrete time-translational symmetry in a periodically driven many-body system can be spontaneously broken to form a discrete time crystal, an exotic new phase of matter. We present observations…

Time crystals in a shaken atom-cavity system

- Physics
- 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…

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.…

Dynamical phase transition in Floquet optical bistable systems: An approach from finite-size quantum systems

- Physics
- 2019

Dynamical response of an optical bistable system to a time-periodic driving field is studied. We found a phase transition in the structure of limit cycle as a function of the frequency of the driving…

Dynamical quantum phase transitions in discrete time crystals

- PhysicsPhysical Review A
- 2018

Discrete time crystals are related to non-equilibrium dynamics of periodically driven quantum many-body systems where the discrete time translation symmetry of the Hamiltonian is spontaneously broken…

Period-n Discrete Time Crystals and Quasicrystals with Ultracold Bosons.

- Physics, MedicinePhysical review letters
- 2019

A Floquet driving that induces clockwise circulation of the particles among the odd sites of the ring which can be mapped to a fully connected model of clocks of two counterrotating species and can be realized with state-of-the-art ultracold atoms experiments.

Dicke time crystals in driven-dissipative quantum many-body systems

- PhysicsNew Journal of Physics
- 2019

The Dicke model -- a paradigmatic example of superradiance in quantum optics -- describes an ensemble of atoms which are collectively coupled to a leaky cavity mode. As a result of the cooperative…

Time Crystals in Open Systems Experiments successfully capture signatures of a discrete time crystal phase in an open , quantummany-body system

- 2021

T ime crystals, as proposed by Frank Wilczek in 2012, are temporal analogs of conventional space crystals [1]. Just as conventional crystals require the breaking of space translation symmetry, time…

## References

SHOWING 1-10 OF 150 REFERENCES

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

- Physics, Materials ScienceNature
- 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.

Discrete Time Crystals: Rigidity, Criticality, and Realizations.

- Physics, MedicinePhysical 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 a discrete time crystal

- Physics, MedicineNature
- 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.

Dynamical many-body phases of the parametrically driven, dissipative Dicke model

- Physics
- 2015

The dissipative Dicke model exhibits a fascinating out-of-equilibrium many-body phase transition as a function of a coupling between a driven photonic cavity and numerous two-level atoms. We study…

Dynamics of nonequilibrium Dicke models

- Physics
- 2012

Motivated by experiments observing self-organization of cold atoms in optical cavities, we investigate the collective dynamics of the associated nonequilibrium Dicke model. The model displays a rich…

Equilibrium states of generic quantum systems subject to periodic driving.

- Mathematics, PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2014

It is shown that for generic nonintegrable interacting systems, local observables become independent of the initial state entirely.

Prethermal time crystals in a one-dimensional periodically driven Floquet system

- Physics
- 2017

Motivated by experimental observations of time-symmetry breaking behavior in a periodically driven (Floquet) system, we study a one-dimensional spin model to explore the stability of such Floquet…

Chaos and the quantum phase transition in the Dicke model.

- Physics, MedicinePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2003

A semiclassical Dicke model is derived that exhibits analogues of all the important features of the quantum model, such as the phase transition and the concurrent onset of chaos, and it is demonstrated that the system undergoes a transition from quasi-integrability to quantum chaotic.

Critical Time Crystals in Dipolar Systems.

- Physics, MedicinePhysical 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.

Critical dynamical properties of a first-order dissipative phase transition

- Physics
- 2017

We theoretically investigate the critical properties of a single driven-dissipative nonlinear photon mode. In a well-defined thermodynamical limit of large excitation numbers, the exact quantum…