# Phase space crystals: a new way to create a quasienergy band structure.

@article{Guo2013PhaseSC, title={Phase space crystals: a new way to create a quasienergy band structure.}, author={Lingzhen Guo and Michael Marthaler and Gerd Sch{\"o}n}, journal={Physical review letters}, year={2013}, volume={111 20}, pages={ 205303 } }

A novel way to create a band structure of the quasienergy spectrum for driven systems is proposed based on the discrete symmetry in phase space. The system, e.g., an ion or ultracold atom trapped in a potential, shows no spatial periodicity, but it is driven by a time-dependent field coupling highly nonlinearly to one of its degrees of freedom (e.g., ∼q(n)). The band structure in quasienergy arises as a consequence of the n-fold discrete periodicity in phase space induced by this driving field…

## 45 Citations

### Synthesizing lattice structures in phase space

- Physics
- 2016

In one dimensional systems, it is possible to create periodic structures in phase space through driving, which is called phase space crystals (Guo et al 2013 Phys. Rev. Lett. 111 205303). This is…

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### Time Crystal Platform: From Quasicrystal Structures in Time to Systems with Exotic Interactions.

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Here it is shown that condensed matter problems ranging from single particles in potentials of quasicrystal structure to many-body systems with exotic long-range interactions can be realized in the time domain with an appropriate periodic driving.

### On the long-term stability of space-time crystals

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- 2020

We investigate a space-time crystal in a superfluid Bose gas. Using a well-controlled periodic drive we excite only one crystalline mode in the system, which can be accurately modeled in the rotating…

### Topological time crystals

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- 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…

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

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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.

### Time crystals: Analysis of experimental conditions

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- 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.…

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- 2019

A space-time crystal has recently been observed in a superfluid Bose gas. Here we construct a variational model that allows us to describe from first principles the coupling between the radial…

### Fractional time crystals

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- 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…

### Floquet many-body engineering: topology and many-body physics in phase space lattices

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- 2017

Hamiltonians which are inaccessible in static systems can be engineered in periodically driven many-body systems, i.e., Floquet many-body systems. We propose to use interacting particles in a…

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