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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. Published by the American Physical Society2025
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Universality classes of thermalization for mesoscopic Floquet systems
We identify several distinct phases of thermalization that describe regimes of behavior in isolated, periodically driven (Floquet), mesoscopic quantum chaotic systems. In doing so, we also identify a Floquet thermal ensemble, the “ladder ensemble,” that is qualitatively distinct from the “featureless infinite-temperature” state that has long been assumed to be the appropriate maximum-entropy equilibrium ensemble for driven systems. The phases we find can be coarsely classified by (i) whether or not the system irreversibly exchanges energy of order ω with the drive, i.e., Floquet thermalizes, and (ii) the Floquet thermal ensemble describing the final equilibrium in systems that do Floquet thermalize. These phases are representative of regimes of behavior in mesoscopic systems, but they are sharply defined in a particular large-system limit where the drive frequency ω scales up with system size N as the N → ∞ limit is taken: we examine frequency scalings ranging from a weakly N-dependent ω(N)∼logN, to stronger scalings ranging from ω(N)∼√N to ω(N)∼N. We show that the transition where Floquet thermalization breaks down happens at an extensive drive frequency and, beyond that, systems that do not Floquet thermalize are distinguished based on the presence or absence of rare resonances across Floquet zones. We produce a thermalization phase diagram that is relevant for numerical studies of Floquet systems and experimental studies on small-scale quantum simulators, both of which lack a clean separation of scales between N and ω. A striking prediction of our work is that, under the assumption of perfect isolation, certain realistic quench protocols from simple pure initial states can show Floquet thermalization to a type of Schrodinger-cat state that is a global superposition of states at distinct temperatures. Our work extends and organizes the theory of Floquet thermalization, heating, and equilibrium into the setting of mesoscopic quantum systems.
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- Award ID(s):
- 2120757
- PAR ID:
- 10505920
- Publisher / Repository:
- American Physical Society
- Date Published:
- Journal Name:
- Physical Review B
- Volume:
- 108
- Issue:
- 17
- ISSN:
- 2469-9950
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1103/PhysRevB.108.174303
