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arXiv:2205.06441 · Nano Letters

Emergence and Dynamical Stability of a Charge Time-Crystal in a Current-Carrying Quantum Dot Simulator

Subhajit Sarkar, Yonatan Dubi

Published May 17, 2022• 17 citations
arXivHTMLPDF

Abstract

Periodically driven open quantum systems that never thermalize exhibit a discrete time-crystal behavior, a nonequilibrium quantum phenomenon that has shown promise in quantum information processing applications. Measurements of time-crystallinity are currently limited to (magneto-) optical experiments in atom-cavity systems and spin-systems making it an indirect measurement. We theoretically show that time-crystallinity can be measured directly in the charge-current from a spin-less Hubbard ladder, which can be simulated on a quantum-dot array. We demonstrate that one can dynamically tune the system out and then back on a time-crystal phase, proving its robustness against external forcings. These findings motivate further theoretical and experimental efforts to simulate the time-crystal phenomena in current-carrying nanoscale systems.

DOI
10.1021/acs.nanolett.2c00976

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Periodically driven open quantum systems that never thermalize exhibit a discrete time-crystal behavior, a nonequilibrium quantum phenomenon that has shown promise in quantum information processing applications. Measurements of time-crystallinity are currently limited to (magneto-) optical experiments in atom-cavity systems and spin-systems making it an indirect measurement. We theoretically show that time-crystallinity can be measured directly in the charge-current from a spin-less Hubbard ladder, which can be simulated on a quantum-dot array. We demonstrate that one can dynamically tune the system out and then back on a time-crystal phase, proving its robustness against external forcings. These findings motivate further theoretical and experimental efforts to simulate the time-crystal phenomena in current-carrying nanoscale systems.
Abstract 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 discrete time-crystalline order are currently limited to magneto-optical experiments and it was never observed in a transport experiment performed on systems connected to external electrodes. Here we demonstrate that both discrete time-crystal and quasi-crystal survive a very general class of environments corresponding to single-particle gain and loss through system-electrode coupling over experimentally relevant timescales. Using dynamical symmetries, we analytically identify the conditions for observing time-crystalline behavior in a periodically driven open Fermi-Hubbard chain attached to electrodes. We show that the spin-polarized transport current directly manifests the existence of a time-crystalline behavior. Our findings are verifiable in present-day experiments with quantum-dot arrays and Fermionic ultra-cold atoms in optical lattices.
Discrete time-crystals are periodically driven quantum many-body systems with broken discrete-time translational symmetry. Measurements of time-crystallinity are currently limited to optical experiments due to the conception that the presence of an environment destroys the time-crystal behavior. We demonstrate that a periodically driven quantum dot array attached to electrodes exhibits both stable and meta-stable discrete time-crystal and quasi-crystal behaviors. These behaviors are manifested in spin-current measurable in transport set-up. The present-day availability of quantum dot arrays with electrically controllable sites makes our findings experimentally verifiable.
A discrete time crystal is a recently discovered nonequilibrium phase of matter that has been shown to exist in disordered, periodically driven Ising spin chains. In this phase, if the system is initially prepared in one of a certain class of pure multispin product states, it periodically returns to this state over very long timescales despite the presence of interactions, disorder, and pulse imperfections. Here, we show that this phase occurs in GaAs quantum dot spin arrays containing as few as three quantum dots, each confining one electron spin, for naturally occurring levels of nuclear spin noise and charge noise. Although the physical interaction in these arrays is a nearest-neighbor Heisenberg exchange interaction, we show that this can be effectively converted into an Ising interaction by applying additional pulses during each drive period. We show that by changing the rotation axis of these pulses, we can select the direction of the Ising interaction and, consequently, the quantization axis of the stabilized multispin states. Moreover, we demonstrate that it is possible to perform coherent rotations of the stabilized states while remaining in the time-crystal phase. These findings open up the intriguing possibility of using time-crystal phases to extend the lifetime of quantum states for information applications.
Time crystals are nonequilibrium phases of matter characterized by the emergence of temporal ordering, in which an interacting many-body system develops robust structure in its time evolution that is not trivially dictated by the external driving or environment. While related phenomena have long been studied in classical nonlinear systems, their realization in entangled quantum matter represents a distinct frontier. The theoretical understanding of discrete time crystals has substantially advanced, yet recent experiments using modern quantum devices and quantum processors reveal regimes beyond established paradigms. These developments call for an extended classification of time-crystalline phases according to both their stabilization mechanisms and their physical character, including discrete and continuous, closed and open, critical, topological, quasiperiodic, and controlled realizations. We review recent implementations of time crystals on quantum platforms and propose such a classification framework, identifying promising directions for the discovery of novel time-crystalline phases of matter.
A time crystal is a state of periodically driven matter that breaks discrete time-translation symmetry.Time crystals have been demonstrated experimentally in various programmable quantum simulators, and they exemplify how nonequilibrium, driven quantum systems can exhibit intriguing and robust properties absent in systems at equilibrium.These robust driven states need to be stabilized by some mechanism, with the preeminent candidates being many-body localization and prethermalization.This introduces additional constraints that make it challenging to experimentally observe time crystallinity in naturally occurring systems.Recent theoretical work has developed the notion of prethermalization without temperature, expanding the class of time-crystal systems to explain time-crystalline observations at (or near) infinite temperature.In this work, we conclusively observe the emergence of a prethermal Uð1Þ time-crystalline state at quasi-infinite temperature in a solid-state NMR quantum emulator by verifying the requisites of prethermalization without temperature.In addition to observing the signature period-doubling behavior, we show the existence of a long-lived prethermal regime whose lifetime is significantly enhanced by strengthening an emergent Uð1Þ conservation law.Not only do we measure this enhancement through the global magnetization, but we also exploit on-site disorder to measure local observables, ruling out the possibility of many-body localization and confirming the emergence of long-range correlations.
Time crystals, a unique nonequilibrium 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 systems, pursuing alternative nanoscale platforms for time crystals is crucial. Here we theoretically predict discrete time crystals in a periodically driven molecular magnet array, modeled by a spin-S Heisenberg Hamiltonian with significant quadratic anisotropy, taken with realistic and experimentally relevant physical parameters. Surprisingly, we find that the time crystal response frequency correlates with the energy levels of the individual magnets and is essentially independent of the exchange coupling. The latter is unexpectedly manifested through a pulse-like oscillation in the magnetization envelope, signaling a many-body response. These results show that molecular magnets can be a rich platform for studying time-crystalline behavior and possibly other out-of-equilibrium quantum many-body dynamics.