Read-out of Quasi-periodic Systems using Qubits

TL;DR

This paper presents a theoretical method to analyze quasi-periodic systems by coupling them to qubits, enabling the detection of different eigenstate regimes and transport properties through qubit decoherence and correlation dynamics.

Contribution

It introduces a novel qubit-based read-out scheme to distinguish localized, delocalized, and mixed regimes in quasi-periodic systems and to infer transport behaviors.

Findings

Qubit decoherence dynamics reveal eigenstate nature.

Scaling of qubit correlation time indicates transport regime.

Transport behavior in systems with mobility edges is dominated by fastest spreading states.

Abstract

We develop a theoretical scheme to perform a read-out of the properties of a quasi-periodic system by coupling it to one or two qubits. We show that the decoherence dynamics of a single qubit coupled via a pure dephasing type term to a 1D quasi-periodic system with a potential given by the Andr\'e-Aubry-Harper (AAH) model and its generalized versions (GAAH model) is sensitive to the nature of the single particle eigenstates (SPEs). More specifically, we can use the non-markovianity of the qubit dynamics as quantified by the backflow of information to clearly distinguish the localized, delocalized, and mixed regimes with a mobility edge of the AAH and GAAH model and evidence the transition between them. By attaching two qubits at distinct sites of the system, we demonstrate that the transport property of the quasi-periodic system is encoded in the scaling of the threshold time to develop correlations between the qubits with the distance between the qubits. This scaling can also be used to distinguish and infer different regimes of transport such as ballistic, diffusive and no transport engendered by SPEs that are delocalized, critical and localized respectively. When there is a mobility edge allowing the coexistence of different kinds of SPEs in the spectrum, such as the coexistence of localized and delocalized states in the GAAH models, we find that the transport behaviour and the scaling of the threshold time with qubit separation is governed by the fastest spreading states.