Condensed matter physics in big discrete time crystals

• Published in: AAPPS bulletin Vol. 32; no. 1; pp. 1 - 16
• Main Authors: Hannaford, Peter, Sacha, Krzysztof
• Format: Journal Article
• Language: English
• Published: Singapore Springer Nature Singapore 02.05.2022; Springer
• Subjects: Astronomy; Astrophysics and Cosmology; Atomic; Bose-Einstein condensate; Condensed matter; Molecular; Optical and Plasma Physics; Particle and Nuclear Physics; Physics; Physics and Astronomy; Review Article; Time crystals; Ultracold atoms; Time crystals; Condensed matter; Ultracold atoms; Bose-Einstein condensate
• ISSN: 2309-4710; 2309-4710
• DOI: 10.1007/s43673-022-00041-8

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.