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arXiv:1807.02105 · Physical review. B./Physical review. B

Discrete time quasicrystals

Krzysztof Giergiel, Arkadiusz Kuroś, Krzysztof Sacha

Published Jun 11, 2019• 73 citations
arXivHTMLPDF

Abstract

Periodically driven quantum many-body systems can spontaneously reorganize their motion and start moving with a period different than the driving period. These are ``discrete time crystals'' and they have been realized already in the laboratory. It turns out that systems from the same class can spontaneously reveal quasicrystalline structures in time. The interaction between the particles forces them into a quasicrystal pattern in the time domain, in spite of the fact that the driving is periodic.

DOI
10.1103/physrevb.99.220303

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Periodically driven quantum many-body systems can spontaneously reorganize their motion and start moving with a period different than the driving period. These are ``discrete time crystals'' and they have been realized already in the laboratory. It turns out that systems from the same class can spontaneously reveal quasicrystalline structures in time. The interaction between the particles forces them into a quasicrystal pattern in the time domain, in spite of the fact that the driving is periodic.
Time crystals are quantum many-body systems that, due to interactions between particles, are able to spontaneously self-organize their motion in a periodic way in time by analogy with the formation of crystalline structures in space in condensed matter physics. In solid state physics properties of space crystals are often investigated with the help of external potentials that are spatially periodic and reflect various crystalline structures. A similar approach can be applied for time crystals, as periodically driven systems constitute counterparts of spatially periodic systems, but in the time domain. Here we show 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. Moreover, it is possible to create molecules where atoms are bound together due to destructive interference if the atomic scattering length is modulated in time.
Floquet (periodically driven) systems can give rise to unique nonequilibrium phases of matter without equilibrium analogs. The most prominent example is the realization of discrete time crystals. An intriguing question emerges: What other novel phases can manifest when the constraint of time periodicity is relaxed? In this study, we explore quantum systems subjected to a quasiperiodic drive. Leveraging a strongly interacting spin ensemble in diamond, we identify the emergence of long-lived discrete time quasicrystals. Unlike conventional time crystals, time quasicrystals exhibit robust subharmonic responses at multiple incommensurate frequencies. Furthermore, we show that the multifrequency nature of the quasiperiodic drive allows for the formation of diverse patterns associated with different discrete time quasicrystalline phases. Our findings demonstrate the existence of nonequilibrium phases in quasi-Floquet settings, significantly broadening the catalog of novel phenomena in driven many-body quantum systems.
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 system when interactions between particles force a system to evolve with a period that is an integer multiple of a driving period. This phenomenon is dubbed discrete time crystal formation. Here, we consider ultracold atoms bouncing on an oscillating atom mirror and show that the system can spontaneously form a discrete time crystal where the ratio of a period of its motion and a driving period is a rational number. This kind of discrete time crystal requires higher-order resonant driving, which is analyzed here with the help of an original approach.
Discrete time quasicrystals (DTQC) constitute a class of non-equilibrium matter characterized by temporal order without strict periodicity, in contrast to conventional time crystals. Investigating these phenomena is essential for expanding our fundamental understanding of far-from-equilibrium quantum matter and spontaneous symmetry breaking beyond periodic regimes. Here, we experimentally observe a DTQC in a driven-dissipative ensemble of strongly interacting Rydberg atoms, displaying non-equilibrium dynamical response with a different finite Abelian group symmetry Zm×Zn{{\mathbb{Z}}}_{m}\times {{\mathbb{Z}}}_{n}Zm​×Zn​. By applying a quasiperiodic drive using a dual-frequency drive with incommensurate frequencies, we demonstrate that the system exhibits a robust subharmonic response at multiple incommensurate frequencies, signifying the emergence of a DTQC phase. We map the full phase diagram of the system, which includes the DTQC phase, and demonstrate its rigidity against perturbations in both RF field intensity and laser detuning. Moreover, we observe a cyclic group symmetry effect that constrains the construction of Z2×Z3{{\mathbb{Z}}}_{2}\times {{\mathbb{Z}}}_{3}Z2​×Z3​-symmetric DTQC. This work establishes a versatile platform for studying non-equilibrium phases of matter and provides insights into the dynamics of time-translation symmetry breaking in quantum many-body systems. Time-crystal phases have raised both theoretical and experimental interest across various platforms. Here, the authors report the observation of a discrete time-quasicrystal in a driven-dissipative ensemble of interacting Rydberg atoms, advancing the understanding of symmetry breaking in these systems.
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 quantized to an integer multiple of the drive period, arising from a combination of collective synchronization and many body localization. Here, we consider a simple model for a one-dimensional discrete time crystal which explicitly reveals the rigidity of the emergent oscillations as the drive is varied. We numerically map out its phase diagram and compute the properties of the dynamical phase transition where the time crystal melts into a trivial Floquet insulator. Moreover, we demonstrate that the model can be realized with current experimental technologies and propose a blueprint based upon a one dimensional chain of trapped ions. Using experimental parameters (featuring long-range interactions), we identify the phase boundaries of the ion-time-crystal and propose a measurable signature of the symmetry breaking phase transition.
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. However, the first idea of spontaneous breaking of discrete time translation symmetry, in ultracold atoms bouncing on an oscillating mirror, still awaits experimental demonstration. Here, we perform a detailed analysis of the experimental conditions needed for the realization of such a discrete time crystal. Importantly, the considered system allows for the realization of dramatic breaking of discrete time translation symmetry where a symmetry broken state evolves with a period tens of times longer than the driving period. Moreover, atoms bouncing on an oscillating mirror constitute a suitable system for the realization of dynamical quantum phase transitions in discrete time crystals and for the demonstration of various nontrivial condensed-matter phenomena in the time domain. We show that Anderson localization effects, which are typically associated with spatial disorder and exponential localization of eigenstates of a particle in configuration space, can be observed in the time domain when ultracold atoms are bouncing on a randomly moving mirror.