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A spacetime crystal is a phase of matter that spontaneously develops periodic order in both space and time. Spacetime crystals have been experimentally observed in microscopic quantum many-body systems and, very recently, in a mesoscopic…

Soft Condensed Matter · Physics 2026-03-11 Guoqing Liu , Jimin Bai , Matteo Baggioli , Jie Zhang

Transition metal dichalcogenides (TMDs) combine interesting optical and spintronic properties in an atomically-thin material, where the light polarization can be used to control the spin and valley degrees-of-freedom for the development of…

Mesoscale and Nanoscale Physics · Physics 2021-03-10 Carmem M. Gilardoni , Freddie Hendriks , Caspar H. van der Wal , Marcos H. D. Guimarães

The study of phases is useful for understanding novel states of matter. One such state of matter are time crystals which constitute periodically driven interacting many-body systems that spontaneously break time translation symmetry. Time…

Quantum Gases · Physics 2021-12-24 Arkadiusz Kuros , Rick Mukherjee , Florian Mintert , Krzysztof Sacha

Photonic media modulated periodically in time, termed photonic time crystals (PTCs), have attracted considerable attention for their ability to open momentum bandgaps hosting amplifying modes. These momentum gaps, however, generally appear…

Temporal cavity solitons (CSs) are stable, localized particle-like objects in the form of optical pulses that circulate indefinitely in coherently driven nonlinear resonators. In the spectral domain, they form highly coherent frequency…

Second-order time correlation measurements with a temporal resolution better than 3 ps were performed on a CdTe microcavity where spontaneous Bose-Einstein condensation is observed. After the laser pulse, the nonresonantly excited thermal…

This paper investigates the possibility of generating Floquet-time crystals in higher dimensions ($d\geq 2$) through the time-periodic driving of integrable free-fermionic models. The realization leads to rigid time-crystal phases that are…

Strongly Correlated Electrons · Physics 2024-05-13 Rahul Chandra , Analabha Roy

Between space crystals and amorphous materials there exists a third class of aperiodic structures which lack translational symmetry but reveal long-range order. They are dubbed quasi-crystals and their formation, similarly as the formation…

Quantum Gases · Physics 2019-06-19 Krzysztof Giergiel , Arkadiusz Kuroś , Krzysztof Sacha

When matter undergoes a phase transition from one state to another, usually a change in symmetry is observed, as some of the symmetries exhibited are said to be spontaneously broken. The superconducting phase transition in the underdoped…

Strongly Correlated Electrons · Physics 2009-11-07 A. Kaminski , S. Rosenkranz , H. M. Fretwell , J. C. Campuzano , Z. Li , H. Raffy , W. G. Cullen , H. You , C. G. Olson , C. M. Varma , H. H"ochst

We present the theory of spontaneous symmetry breaking (SSB) of discrete time translations as recently realized in the space-time crystals of an atomic Bose-Einstein condensate. The non-equilibrium physics related to such a…

Quantum Gases · Physics 2021-11-10 J. N. Stehouwer , J. Smits , P. van der Straten , H. T. C. Stoof

Strong measurements usually restrict the dynamics of measured finite dimensional systems to the Zeno subspace, where subsequent evolution is unitary due to the suppression of dissipative terms. Here we show qualitatively different behaviour…

Quantum Physics · Physics 2023-09-07 Midhun Krishna , Parvinder Solanki , Michal Hajdušek , Sai Vinjanampathy

Crystals of repulsively interacting ions in planar traps form hexagonal lattices, which undergo a buckling instability towards a multi-layer structure as the transverse trap frequency is reduced. Numerical and experimental results indicate…

Quantum Gases · Physics 2016-09-13 Daniel Podolsky , Efrat Shimshoni , Giovanna Morigi , Shmuel Fishman

In analogy with crystalline solids around us, Wilczek recently proposed the idea of "time crystals" as phases that spontaneously break the continuous time translation into a discrete subgroup. The proposal stimulated further studies and…

Statistical Mechanics · Physics 2015-06-26 Haruki Watanabe , Masaki Oshikawa

Synthetic crystal lattices provide ideal environments for simulating and exploring the band structure of solid-state materials in clean and controlled experimental settings. Physical realisations have, so far, dominantly focused on…

Mesoscale and Nanoscale Physics · Physics 2020-10-12 L. Pickup , H. Sigurdsson , J. Ruostekoski , P. G. Lagoudakis

We describe a possible general and simple paradigm in a classical thermal setting for discrete time crystals (DTCs), systems with stable dynamics which is subharmonic to the driving frequency thus breaking discrete time-translational…

Statistical Mechanics · Physics 2020-01-22 F. M. Gambetta , F. Carollo , A. Lazarides , I. Lesanovsky , J. P. Garrahan

We introduce a boundary condition twisted by time translation as a novel probe to characterize dynamical phases in periodically driven (Floquet) quantum systems. Inspired by twisted boundary conditions in equilibrium systems, this approach…

Statistical Mechanics · Physics 2025-11-17 Ryota Nakai , Taozhi Guo , Shinsei Ryu

We show that geometrically coupled polariton condensates fabricated in semiconductor devices are versatile systems capable of simulating molecules with given characteristics. In particular, we consider oscillatory and stationary symmetric…

Mesoscale and Nanoscale Physics · Physics 2021-03-03 Alexander Johnston , Kirill P. Kalinin , Natalia G. Berloff

We investigate the conditions under which periodically driven quantum systems subject to dissipation exhibit a stable subharmonic response. Noting that coupling to a bath introduces not only cooling but also noise, we point out that a…

Statistical Mechanics · Physics 2020-04-08 Achilleas Lazarides , Sthitadhi Roy , Francesco Piazza , Roderich Moessner

Temporal coherence of driven-dissipative condensates is limited by phase noise. We show that mirror-mediated time-delayed self-feedback enables control of coherence in a trapped exciton-polariton condensate. Reinjecting a small fraction of…

Optics · Physics 2026-04-29 I. Smirnov , S. Alyatkin , P. G. Lagoudakis

Polariton condensates provide a versatile platform for exploring non-equilibrium phase transitions and collective phenomena in open quantum systems. Near the condensation threshold, these systems are particularly sensitive to fluctuations…