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arXiv:2507.06305

Entanglement switching via mobility edges in a quasiperiodic chain

Joung, YouYoung, Junmo Jeon, SungBin Lee

Published Jul 8, 2025• 0 citations
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Abstract

We propose quasiperiodic chains with tunable mobility edge physics, as a promising platform for engineering long-range quantum entanglement. Using the generalized Aubry-André model, we show that the mobility edges play a key role in manipulating long-range indirect interactions in these systems. Near the mobility edge, critical states exhibit unexpectedly strong correlations between sites that share similar local structures, regardless of their spatial separation. Remarkably, by tuning the mobility edge across the Fermi level, one can induce both adiabatic transport and abrupt switching of entanglement between distant sites. These results highlight the potential of aperiodic structures for controlling nonlocal quantum correlations, opening new avenues for entanglement-based applications in quasiperiodic systems.

DOI
10.48550/arxiv.2507.06305

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We propose quasiperiodic chains with tunable mobility edge physics, as a promising platform for engineering long-range quantum entanglement. Using the generalized Aubry-André model, we show that the mobility edges play a key role in manipulating long-range indirect interactions in these systems. Near the mobility edge, critical states exhibit unexpectedly strong correlations between sites that share similar local structures, regardless of their spatial separation. Remarkably, by tuning the mobility edge across the Fermi level, one can induce both adiabatic transport and abrupt switching of entanglement between distant sites. These results highlight the potential of aperiodic structures for controlling nonlocal quantum correlations, opening new avenues for entanglement-based applications in quasiperiodic systems.
We investigate localization phenomena and exact mobility edges in a quasiperiodic Aharonov-Bohm chain, where the 1D canonical diagonal and off-diagonal Aubry-André-Harper models are laterally coupled to an auxiliary sublattice threaded by a synthetic magnetic flux. By analytically computing the Lyapunov exponent via Avila's global theory of one-frequency Schrödinger operators, we derive exact expressions for mobility edges. In the diagonal limit, the coupling to the auxiliary sublattice generates hyperbolic mobility edges that exhibit a sign-changing divergence and can be continuously tuned by the magnetic flux. In the off-diagonal regime, the interference between quasiperiodic hopping and indirect tunneling through the auxiliary sublattice gives rise to exact anomalous mobility edges that separate critical and extended states. Critical states and anomalous mobility edges emerge even in the absence of incommensurately distributed zeros in the hopping modulation, a behavior distinct from that of conventional off-diagonal models. Our results establish a rigorous theoretical framework for engineering controllable mobility edges, with the synthetic flux providing a tunable experimental knob that paves the way for realizations in platforms such as superconducting quantum circuits and photonic waveguides.
We investigate the quantum dynamics of a one-dimensional quasiperiodic system featuring a single-particle mobility edge (SPME), described by the generalized Aubry-André (GAA) model. This model offers a unique platform to study the consequences of coexisting localized and extended eigenstates, which contrasts sharply with the abrupt localization transition in the standard Aubry-André model. We analyze the system's response to a quantum quench through two complementary probes: entanglement entropy (EE) and subsystem information capacity (SIC). We find that the SPME induces a smooth crossover in all dynamical signatures. The EE saturation value exhibits a persistent volume-law scaling in the mobility-edge phase, with an entropy density that continuously decreases as the number of available extended states decreases. Complementing this, the SIC profile interpolates between the linear ramp characteristic of extended systems and the information trapping behavior of localized ones, directly visualizing the mixed nature of the underlying spectrum. Our results establish unambiguous dynamical fingerprints of a mobility edge, providing a crucial non-interacting benchmark for understanding information and entanglement dynamics in more complex systems with mixed phases.
A mobility edge, a critical energy separating localized and extended excitations, is a key concept for understanding quantum localization. The Aubry-André (AA) model, a paradigm for exploring quantum localization, does not naturally allow mobility edges due to self-duality. Using the momentum-state lattice of quantum gas of Cs atoms to synthesize a nonlinear AA model, we provide experimental evidence for a mobility edge induced by interactions. By identifying the extended-to-localized transition of different energy eigenstates, we construct a mobility-edge phase diagram. The location of a mobility edge in the low- or high-energy region is tunable via repulsive or attractive interactions. Our observation is in good agreement with the theory and supports an interpretation of such interaction-induced mobility edge via a generalized AA model. Our Letter also offers new possibilities to engineer quantum transport and phase transitions in disordered systems.
The manipulation of localization in quasiperiodic systems by mobility edges or localization transition holds significant physical importance. In this letter, we demonstrated that the dissipation can induce the emergence of anomalous mobility edges and extended-localized transition in emitter-cavity arrays controlled by quasiperiodic potentials. Specifically, we observe that the localization properties of emitters is governed by the nature of quantum bound states, either discrete or embedded in continuum, providing a unified mechanism linking the emitter-photon bound physics to quasiperiodic criticality. Depending on the bound state discrete or continuumlike, the induced effective excitation hopping exhibits either exponentially decaying or sinusoidally oscillating, giving rise to the formation of localized or critical states, respectively. Through a generalized duality transformation, we analytically determine the anomalous mobility edges and the critical strength of potential, enabling the construction of a full phase diagram. The study reveals that the physical characteristics of cavity exert a significant influence on excitation localization. Therefore, the manipulation of excitation localization can be achieved solely by adjusting the cavity fields.
We develop a theoretical scheme to perform a readout of the properties of a quasiperiodic 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 one-dimensional quasiperiodic 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 models and evidence the transition between them. By attaching two qubits at distinct sites of the system, we demonstrate that the transport property of the quasiperiodic 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. In addition, the localization length of the SPEs can also be gleaned from the exponential decay of correlations at long times as a function of distance between qubits. 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 behavior and the scaling of the threshold time with qubit separation are governed by the fastest spreading states.
Cold atom arrays in optical lattices offer a highly tunable platform for exploring complex quantum phenomena that are difficult to realize in conventional materials. Here, we investigate the emergence of controllable long-range quantum correlations in a simulated twisted bilayer structure with fermionic cold atoms. By exploiting the incommensurate nature of the twisted bilayer, we observe a significant enhancement of long-range susceptibility, suggesting the formation of stable entangled states between spatially distant localized spins. We further show that the tunability of the interlayer coupling in terms of driving fields enables us to manipulate these entangled states without deformation of lattice structure and extra doping. Our findings provide a pathway for overcoming challenges in establishing strong correlations across distant sites, highlighting the potential of optical lattices as a versatile platform for advanced quantum technologies.