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

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.

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

“…Moreover, there can be many DTC states corresponding to the same DTC eigenvalue, and depending on the initial density matrix the system reaches a particular DTC state. 61 We choose t ∥ hop = U = K = 20π MHz = 0.26 μeV, all being electrically tunable. The frequency of the external drive is ω = 2π × (10 MHz) [therefore, a period of T = 0.1 μs] assuming the typical resolution of nanoseconds in the time-dependent measurements in experiments with QD array.…”

“…The eigenvalues that lie on the complex unit circle confirms the existence of a DTC oscillation irrespective of any initial condition. 23,28,30,61 This means that any initial random density matrix would bring in the DTC oscillation in the long time limit. Moreover, there can be many DTC states corresponding to the same DTC eigenvalue, and depending on the initial density matrix the system reaches a particular DTC state.…”

“…We set γ L = γ R = γ = 10 −4 ω, and choose Γ = t hop for faster quantum-synchronization of oscillating effective dipoles residing on the (j, a) − (j, b) bonds (the choice of magnitude of Γ only determines the synchronization time scale). 61 In the long time limit between 85T − 100T, oscillations show clear signature of DTC with period 3T. This is further fingerprinted in the Discrete Fourier transform (DFT) |τ̃3 x (f)| of the effective-dipole oscillation in the form of a sharp peak at a frequency f = 2ω/3, as seen in Figure 2c.…”

“…, where [V in(out) , A loc ] ∝ γ makes the FDS weak. 61 This leads to the appearance of Floquet coherent states ρ m,n . The Floquet coherent states are built from the Floquet steady state ρ FSS as, ρ m,n = (τ loc,|E| + ) m ρ FSS (τ loc,|E| − ) n (with i n t e g e r v a l u e s o f m , n ) , s a t i s f y i n g…”

“…For γT ≪ 1, we find stable DTC oscillation in the long time limit, otherwise a metastable DTC emerges. 61 The characteristic frequency of Floquet coherence is given by…”