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Discrete time crystals (DTCs) are emergent non-equilibrium phases of periodically driven many-body systems, with potential applications ranging from quantum computing to sensing and metrology. There has been significant recent interest in…

We analyse quasi-periodically driven quantum systems that can be mapped exactly to periodically driven ones and find Floquet Time Spirals in analogy with spatially incommensurate spiral magnetic states. Generalising the mechanism to…

Disordered Systems and Neural Networks · Physics 2019-10-09 Hongzheng Zhao , Florian Mintert , Johannes Knolle

Crystals form regular and robust structures that under extreme conditions can melt and recrystallize into different arrangements in a process that is called crystal metamorphism. While crystals exist due to the breaking of a continuous…

Quantum Physics · Physics 2021-01-04 Victor M. Bastidas , Marta P. Estarellas , Tomo Osada , Kae Nemoto , William J. Munro

Despite being forbidden in equilibrium, spontaneous breaking of time translation symmetry can occur in periodically driven, Floquet systems with discrete time-translation symmetry. The period of the resulting discrete time crystal is…

Disordered Systems and Neural Networks · Physics 2017-06-21 Norman Y. Yao , Andrew C. Potter , Ionut-Dragos Potirniche , Ashvin Vishwanath

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

In this work we use optimal control to generate Discrete Time Crystals (DTC) in generic many-body quantum systems. We define appropriate cost functions, which, when optimized, result in the formation of DTCs. This hitherto unexplored method…

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 be spontaneously broken to form a…

Mesoscale and Nanoscale Physics · Physics 2019-06-11 James O'Sullivan , Oliver Lunt , Christoph W. Zollitsch , M. L. W. Thewalt , John J. L. Morton , Arijeet Pal

Discrete time crystals (DTCs) are new phases of matter characterized by the presence of an observable evolving with $nT$ periodicity under a $T$-periodic Hamiltonian, where $n>1$ is an integer insensitive to small parameter variations. In…

Quantum Physics · Physics 2020-01-17 Pekik Nurwantoro , Raditya Weda Bomantara , Jiangbin Gong

The compelling original idea of a time crystal has referred to a structure that repeats in time as well as in space, an idea that has attracted significant interest recently. While obstructions to realize such structures became apparent…

Strongly Correlated Electrons · Physics 2020-12-03 A. Kshetrimayum , J. Eisert , D. M. Kennes

Discrete time-crystals are periodically driven quantum many-body systems with broken discrete-time translational symmetry, a non-equilibrium steady state representing self-organization of motion of quantum particles. Observations of…

Mesoscale and Nanoscale Physics · Physics 2022-06-28 Subhajit Sarkar , Yonatan Dubi

In this work we introduce {\it boundary time-crystals}. Here {\it continuous} time-translation symmetry breaking occurs only in a macroscopic fraction of a many-body quantum system. After introducing their definition and properties, we…

Quantum Physics · Physics 2018-07-23 F. Iemini , A. Russomanno , J. Keeling , M. Schirò , M. Dalmonte , R. Fazio

Time crystals, a unique non-equilibrium quantum phenomenon with promising applications in current quantum technologies, mark a significant advance in quantum mechanics. Although traditionally studied in atom-cavity and optical lattice…

Quantum Physics · Physics 2024-10-07 Subhajit Sarkar , Yonatan Dubi

The spontaneous breaking of time translation symmetry has led to the discovery of a new phase of matter - the discrete time crystal. Discrete time crystals exhibit rigid subharmonic oscillations, which result from a combination of many-body…

Chimera states are a captivating occurrence in which a system composed of multiple interconnected elements exhibits a distinctive combination of synchronized and desynchronized behavior. The emergence of these states can be attributed to…

Statistical Mechanics · Physics 2024-06-27 Mahbub Rahaman , Akitada Sakurai , Analabha Roy

A discrete time crystal is a phase unique to nonequilibrium systems, where discrete time translation symmetry is spontaneously broken. Most of conventional time crystals proposed so far rely on spontaneous breaking of on-site symmetries and…

Mesoscale and Nanoscale Physics · Physics 2018-08-30 Kaoru Mizuta , Kazuaki Takasan , Masaya Nakagawa , Norio Kawakami

We report the observation of a symmetry-protected topological time crystal, which is implemented with an array of programmable superconducting qubits. Unlike the time crystals reported in previous experiments, where spontaneous breaking of…

Open many-body quantum systems can exhibit intriguing nonequilibrium phases of matter, such as time crystals. In these phases, the state of the system spontaneously breaks the time-translation symmetry of the dynamical generator, which…

Discrete time crystals are a many-body state of matter where the extensive system's dynamics are slower than the forces acting on it. Nowadays, there is a growing debate regarding the specific properties required to demonstrate such a…

Classical Physics · Physics 2019-09-25 Toni L. Heugel , Matthias Oscity , Alexander Eichler , Oded Zilberberg , R. Chitra

Symmetries are well known to have had a profound role in our understanding of nature and are a critical design concept for the realization of advanced technologies. In fact, many symmetry-broken states associated with different phases of…

Quantum Physics · Physics 2021-04-01 A. Sakurai , V. M. Bastidas , W. J. Munro , Kae Nemoto

Sensing periodic-fields using quantum sensors has been an active field of research. In many of these scenarios, the quantum state of the probe is flipped regularly by the application of $\pi$-pulses to accumulate information about the…

Quantum Physics · Physics 2025-11-19 Rozhin Yousefjani , Saif Al-Kuwari , Abolfazl Bayat