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Signatures of discrete time-crystallinity in transport through quantum dot arrays

Subhajit Sarkar, Yonatan Dubi

Published Jul 9, 2021• 5 citations
OpenAlex

Abstract

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.

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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.

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Time-crystalline behavior in an engineered spin chain

Robin Schäfer, Götz Silvester Uhrig, Joachim Stolze

Time crystals break the discrete time translational invariance of an external periodic drive by oscillating at an integer multiple of the driving period. In addition to this fundamental property, other aspects are often considered to be essential characteristics of a time crystal, such as the presence of disorder or interactions, robustness against small variations of system parameters, and the free choice of the initial quantum state. We study a finite-length polarized XX spin chain engineered to display a spectrum of equidistant energy levels without drive and show that it keeps a spectrum of equidistant Floquet quasienergies when subjected to a large variety of periodic driving schemes. Arbitrary multiples of the driving period can then be reached by adjusting parameters of the drive, for arbitrary initial states. This behavior is understood by mapping the XX spin chain with $N+1$ sites to a single large spin with $S=N/2$ invoking the closure of the group SU(2). Our simple model is neither intrinsically disordered nor is it an interacting many-body system (after suitable mapping), and it does not have a thermodynamic limit in the conventional sense. It does, however, show controllable discrete time translational symmetry breaking for arbitrary initial states and a degree of robustness against perturbations, thereby carrying some characteristic traits of a discrete time crystal.

arXiv:1904.12328•Physical review. B./Physical review. B•Nov 5, 2019•10 citations
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.
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.
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.
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.
Abstract Discrete time crystals (DTCs) are out-of-equilibrium quantum states of matter which break time translational symmetry. DTCs have been extensively realized in experiments, particularly their subclass that is characterized by period-doubling dynamics due to its natural occurrence in a system of periodically driven two-level, e.g. spin-1/2, particles. The realization of DTCs beyond period-doubling, including their generalizations termed discrete quasicrystals has also been made in recent years, though such experiments typically involve higher spin particles. Constructing and observing DTCs beyond period-doubling in systems of two-level particles are generally still considered an open challenge due to the latter’s Z 2 symmetry that natively only leads to period-doubling. In this work, we developed an intuitive interacting system of two-level particles (qubits) that supports the more non-trivial period-quadrupling DTCs (4 T -DTCs). Remarkably, by utilizing a variational algorithm, we are able to observe clear signatures of such 4 T -DTCs in a quantum processor despite the presence of considerable noise and the small number of available qubits. Our findings extend the landscape of time crystalline behavior by demonstrating a distinct realization of time crystallinity beyond standard period-doubling dynamics with qubits (two-level particles) on a NISQ-era digital quantum computer, as well as the potential of existing noisy intermediate-scale quantum devices for simulating exotic non-equilibrium quantum states of matter.
Discrete time crystals (DTCs) are novel out-of-equilibrium quantum states of matter which break time translational symmetry. DTCs have been extensively realized in experiments, particularly their subclass that is characterized by period-doubling dynamics due to its natural occurrence in a system of periodically driven two-level, e.g., spin-1/2, particles. The realization of DTCs beyond period-doubling, including their generalizations termed discrete quasicrystals has also been made in recent years, though such experiments typically involve higher spin particles. Constructing and observing DTCs beyond period-doubling in systems of two-level particles are generally still considered an open challenge due to the latter's Z2\mathbb{Z}_2Z2​ symmetry that natively only leads to period-doubling. In this work, we developed an intuitive interacting system of two-level particles (qubits) that supports the more non-trivial period-quadrupling DTCs (4T4T4T-DTCs). Remarkably, by utilizing a variational algorithm, we are able to observe clear signatures of such 4T4T4T-DTCs in a quantum processor despite the presence of considerable noise and the small number of available qubits. Our findings extend the landscape of time crystalline behavior by demonstrating a distinct realization of time crystallinity beyond standard period-doubling dynamics with qubits (two-level particles) on a NISQ-era digital quantum computer, as well as the potential of existing noisy intermediate-scale quantum devices for simulating exotic non-equilibrium quantum states of matter.
Time crystals break the discrete time translational invariance of an external periodic drive by oscillating at an integer multiple of the driving period. In addition to this fundamental property, other aspects are often considered to be essential characteristics of a time crystal, such as the presence of disorder or interactions, robustness against small variations of system parameters, and the free choice of the initial quantum state. We study a finite-length polarized XX spin chain engineered to display a spectrum of equidistant energy levels without drive and show that it keeps a spectrum of equidistant Floquet quasienergies when subjected to a large variety of periodic driving schemes. Arbitrary multiples of the driving period can then be reached by adjusting parameters of the drive, for arbitrary initial states. This behavior is understood by mapping the XX spin chain with N+1N+1N+1 sites to a single large spin with S=N/2S=N/2S=N/2 invoking the closure of the group SU(2). Our simple model is neither intrinsically disordered nor is it an interacting many-body system (after suitable mapping), and it does not have a thermodynamic limit in the conventional sense. It does, however, show controllable discrete time translational symmetry breaking for arbitrary initial states and a degree of robustness against perturbations, thereby carrying some characteristic traits of a discrete time crystal.