Inseparable Time-Crystal Geometries on the Möbius Strip

Giergiel, Krzysztof; Kuroś, Arkadiusz; Kosior, Arkadiusz; Sacha, Krzysztof

doi:10.1103/physrevlett.127.263003

Cited by 13 publications

(29 citation statements)

References 70 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Although time is a single degree of freedom, crystalline structures in time with the properties of 2D (or 3D) condensed matter systems can be created by a BEC bouncing resonantly between two (or three) oscillating atom mirrors [32,44,[47][48][49].…”

Section: Higher-dimensional Time Latticesmentioning

confidence: 99%

“…We now consider the case when the two mirrors are oriented at 45 o to each other to form a wedge with one mirror located in the vertical direction x−y = 0 and the other located at x = 0 [49]. When a particle strikes the vertical mirror, its momenta are exchanged p x ↔ p y , whereas when it strikes the mirror located at x = 0, the momentum p y remains the same while the momentum p x → −p x .…”

Section: Möbius Strip Geometrymentioning

confidence: 99%

“…Transforming to the action-angle variables I ± = I y ± I x and θ ± = (θ y ± θ x )/2 and switching to the frame oscillating with the mirrors, Θ + = θ + − ωt/s and Θ − = θ − , leads to the classical secular effective Hamiltonian [49]…”

Section: Möbius Strip Geometrymentioning

confidence: 99%

“…Such a system has been shown to exhibit dramatic breaking of discrete time-translation symmetry in which the bouncing atoms can evolve with periods up to about 100 times longer than the period of the drive [34,35] (see also [11,36,37]). This allows the creation of big discrete time crystals possessing a large number of temporal lattice sites, which are suitable for realizing a broad range of condensed matter phenomena in the time dimension [38][39][40][41][42][43][44][45][46][47][48][49]. It has been shown for the case s = 2 that such discrete time crystals are robust against external perturbations [50] and quantum fluctuations [50,51] and live for extremely long times [51,52].…”

Section: Introductionmentioning

confidence: 99%

“…Temporal condensed matter phenomena that have been predicted to date include Mott insulator phases in the time dimension [38]; Anderson localization [34,[38][39][40][41]54] and many-body localization in the time dimension [42]; topologically protected edge states in time [43,53]; quasi-crystal structures in time [44,45]; two-dimensional time lattices supporting a Möbius strip geometry and flat-band physics [49]; and time-space crystals exhibiting a six-dimensional quantum Hall effect [47].…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Condensed matter physics in big discrete time crystals

Hannaford,

Sacha

2022

Preprint

Self Cite

View full text Add to dashboard Cite

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 matter phenomena in the time dimension. Such a bouncing BEC system can exhibit dramatic breaking of time-translation symmetry, allowing the creation of discrete time crystals having up to about 100 temporal lattice sites and suitable for hosting a broad range of temporal condensed matter phenomena. We first consider single-particle condensed matter phenomena in the time dimension which include Anderson localization due to temporal disorder, topological time crystals, and quasi-crystal structures in time. We then discuss many-body temporal condensed matter phenomena including Mott insulator phases in time, manybody localization in time, many-body topological time crystals and time crystals having long-range exotic interactions. We also discuss the construction of two (or three) dimensional time lattices, involving the bouncing of a BEC between two (or three) orthogonal oscillating mirrors and between two oscillating mirrors oriented at 45-degrees. The latter configuration supports a versatile Möbius strip geometry which can host a variety of two-dimensional time lattices including a

show abstract

Section: Higher-dimensional Time Latticesmentioning

confidence: 99%

Section: Möbius Strip Geometrymentioning

confidence: 99%

Section: Möbius Strip Geometrymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Condensed matter physics in big discrete time crystals

Hannaford,

Sacha

2022

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

Condensed matter physics in big discrete time crystals

Hannaford

Sacha

2022

AAPPS Bull.

Self Cite

View full text Add to dashboard Cite

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 matter phenomena in the time dimension. Such a bouncing BEC system can exhibit dramatic breaking of time-translation symmetry, allowing the creation of discrete time crystals having up to about 100 temporal lattice sites and suitable for hosting a broad range of temporal condensed matter phenomena. We first consider single-particle condensed matter phenomena in the time dimension which include Anderson localization due to temporal disorder, topological time crystals, and quasi-crystal structures in time. We then discuss many-body temporal condensed matter phenomena including Mott insulator phases in time, many-body localization in time, many-body topological time crystals and time crystals having long-range exotic interactions. We also discuss the construction of two (or three) dimensional time lattices, involving the bouncing of a BEC between two (or three) orthogonal oscillating mirrors and between two oscillating mirrors oriented at 45∘. The latter configuration supports a versatile Möbius strip geometry which can host a variety of two-dimensional time lattices including a honeycomb time lattice and a Lieb square time lattice. Finally, we discuss the construction of a six-dimensional time-space lattice based on periodically driven BECs trapped in a three-dimensional optical lattice.

show abstract

Synthetic dimensions for topological and quantum phases

Argüello-Luengo,

Bhattacharya,

Celi

et al. 2024

Commun Phys

View full text Add to dashboard Cite

The concept of synthetic dimensions works particularly well in atomic physics, quantum optics, and photonics, where the internal degrees of freedom (Zeeman sublevels of the ground state, metastable excited states, or motional states for atoms, and angular momentum states or transverse modes for photons) provide the synthetic space. In this Perspective article we report on recent progress on studies of synthetic dimensions, mostly, but not only, based on the research realized around the Barcelona groups (ICFO, UAB), Donostia (DIPC), Poznan (UAM), Kraków (UJ), and Allahabad (HRI). We describe our attempts to design quantum simulators with synthetic dimensions, to mimic curved spaces, artificial gauge fields, lattice gauge theories, twistronics, quantum random walks, and more.

show abstract

Inseparable Time-Crystal Geometries on the Möbius Strip

Cited by 13 publications

References 70 publications

Condensed matter physics in big discrete time crystals

Condensed matter physics in big discrete time crystals

Condensed matter physics in big discrete time crystals

Synthetic dimensions for topological and quantum phases

Contact Info

Product

Resources

About