Signatures of discrete time-crystallinity in transport through an open Fermionic chain

TL;DR

This paper demonstrates that discrete time-crystalline order can be observed in transport experiments on open fermionic chains, with spin-polarized current serving as a direct signature, even in the presence of environmental gain and loss.

Contribution

It analytically identifies conditions for observing time-crystalline behavior in open driven fermionic systems connected to electrodes, extending the experimental scope beyond magneto-optical setups.

Findings

Time-crystalline order persists in open systems with gain and loss.

Spin-polarized transport current reveals time-crystalline behavior.

Theoretical conditions for observing time-crystals in fermionic chains are established.

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. Crucially, 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 environment 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. Remarkably, 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.