arXiv subjects

Carlo Danieli

Publications and source records attributed to Carlo Danieli.

At least 19 recordsLinked to original sources

arXiv2026

Thermodynamics of photonic nonlinear Aharonov-Bohm cages

We investigate equilibrium and non-equilibrium thermodynamics of one-dimensional photonic diamond lattices with Kerr nonlinearity. The equilibrium phase diagram is obtained as a function of the synthetic magnetic flux acting on each plaquette. In the linear regime, the magnetic flux can induce Aharonov-Bohm caging, flattening all Bloch bands and suppressing particle and energy currents. In this caging regime, non-vanishing currents are enabled by nonlinearity. By imposing stationary temperature- and chemical potential- imbalances at the system boundaries, we show that at weak nonlinearity fine tuning the flux at the Aharonov-Bohm caging transforms the system from a conductor to an insulator. For intermediate nonlinear strength, the system remains conducting for all magnetic fluxes; however, the caging condition significantly enhances the Seebeck coefficient and thermoelectric figure of merit, improving the thermoelectric features of the system. Our results give evidence of a novel route towards optimization of coupled transport devices, based on the control of linear versus nonlinear conduction channels via a synthetic magnetic flux.

cond-mat.stat-mech↗

arXiv2026

Progress on artificial flat band systems: classifying, perturbing, applying

We highlight recent progress in the study of artificial flat band systems with a threefold focus. First, we discuss single-particle flat band physics, which has advanced through the design of various flat band generators. These generators rely on the classification of flat bands in terms of compact localized states - their fundamental building blocks. A related development is the complete real-space description of flat band projectors. Next, we review studies on perturbations of flat bands, which provide new insights into the effects of disorder and, more importantly, the intricate interplay between many-body interactions and flat band physics. Finally, we survey the growing number of experimental realizations of flat bands across diverse physical platforms.

cond-mat.mes-hall↗

arXiv2025

Holonomic multi-controlled gates for single-photon states

Controlled and multi-controlled quantum gates, whose action on a target qubit depends on the state of multiple control qubits, represent a fundamental logical building block for complex quantum algorithms. We propose a scheme for realizing this class of gates based on non-Abelian holonomies in modulated photonic waveguide networks. Our approach relies on linear photonic cicuits formed by two star networks coupled via a two-path circuit. A star network with M peripheral waveguides coupled to a single central site, or M-pod, naturally generalizes the tripod structure used in non-Abelian Thouless pumping and stimulated Raman adiabatic passage (STIRAP). In the present work, we first analyze the minimal case of two connected tripods and design adiabatic driving loops that implement single-qubit, CNOT, and SWAP gates. We then show how extending the approach to larger M-pod structures enables the realization of multiply controlled operations, which we exemplify by designing Toffoli and the OR gate on two coupled pentapods. Finally, we demonstrate that networks of connected tripods can implement the Deutsch quantum query algorithm.

quant-ph↗

arXiv2025

Compact localized currents in flat bands with broken time-reversal symmetry

We develop a systematic framework for constructing all-bands-flat (ABF) lattice Hamiltonians that explicitly break time-reversal symmetry (TRS). By threading magnetic flux through disconnected polygonal plaquettes and applying local entangling unitary transformations, we map plaquettes onto families of ABF models in one, two, and three dimensions. This procedure preserves the flux configuration while converting semi-detangled geometries into ABF lattices with nontrivial hopping structure. The resulting flat bands admit compact localized states (CLSs) whose support includes both the flux-threaded plaquettes and auxiliary sites introduced by the unitary transformations. In these TRS-broken constructions, the CLSs host localized circulatory currents whose magnitude depends on the applied flux. We further extend the framework to lattices with coexisting flat and dispersive bands, illustrating cases with both orthogonal and non-orthogonal CLSs. Our results provide a controlled route for generating dispersionless lattices supporting flux-induced local currents.

cond-mat.mes-hall↗

arXiv2025

Quantum storage with flat bands

The realization of robust quantum storage devices relies on the ability to generate long-lived, spatially localized quantum states. In this work, we introduce a method for the targeted creation of compact excitations in flat-band lattices. By injecting in-plane radiation waves from the system's edge and applying a localized on-site potential at the desired storage position, we induce hybridization between compact localized states (CLSs) of the flat-band and resonant dispersive plane waves. This hybridization enables the formation of spatially compact, stable excitations suitable for quantum memory applications. We experimentally validate this mechanism using photonic waveguide arrays, focusing on two representative geometries: the diamond chain and the one-dimensional Lieb ladder. Our approach is broadly applicable to any platform supporting flat-band physics.

physics.optics↗

arXiv2024

Thouless quantum walks in topological flat bands

Non-Abelian gauge symmetries are cornerstones of modern theoretical physics, underlying fundamental interactions and the geometric structure of quantum mechanics. However, their potential to control quantum coherence, entangle- ment, and transport in engineered quantum systems remains to a large extent unexplored. In this work, we propose utilizing non-Abelian Thouless pumping to realize one-dimensional discrete-time quantum walks on topological lattices char- acterized by degenerate flat bands. Through carefully designed pumping cycles, we implement different classes of holonomic coin and shift operators. This frame- work allows for the construction of quantum walks that encode the topological and geometric properties of the underlying system. Remarkably, the resulting evolution exhibits parity symmetry breaking and gives rise to a dynamical pro- cess governed by a Weyl-like equation, highlighting the deep connection between parity and time-reversal symmetry breaking in the system.

cond-mat.mes-hall↗

arXiv2024

Non-Abelian Thouless pumping in a Rice-Mele ladder

Non-Abelian Thouless pumping intertwines adiabatic quantum control and topological quantum transport and it holds potential for quantum metrology and computing. In this work, we introduce a ladder model featuring two doubly-degenerate bands and we show that adiabatic manipulation of the lattice parameters results in non-Abelian Thouless pumping, inducing both the displacement of an initially localized state and a geometric unitary transformation within the degenerate subspace. Additionally, we show that the structure and symmetry of the ladder model can be understood through its connection to a Yang monopole model. The proposed Hamiltonian can be realized using cold atoms in optical lattices, enabling the experimental demonstration of non-Abelian Thouless pumping in a genuinely quantum many-body system.

cond-mat.mes-hall↗

arXiv2024

Flat band fine-tuning and its photonic applications

Flat bands - single-particle energy bands - in tight-binding networks have attracted attention due to the presence of macroscopic degeneracies and their extreme sensitivity to perturbations. This makes them natural candidates for emerging exotic phases and unconventional orders. The challenging part however is to construct flat band networks, whose existence relies on symmetries and fine-tuning. In this review we consider the recently proposed systematic ways to construct flat band networks based on symmetries or fine-tuning. We then discuss how the fine-tuning constructions can be further extended, adapted or exploited in presence of perturbations, both single-particle and many-body. This strategy has lead to the discovery of non-perturbative metal-insulator transitions, fractal phases, nonlinear and quantum caging and many-body nonergodic quantum models. We discuss what implications these results may have for the design of fine-tuned nanophotonic systems including photonic crystals, nanocavities, and metasurfaces.

physics.optics↗

arXiv2023

Quantum engineering for compactly localized states in disordered Lieb lattices

Blending ordering within an uncorrelated disorder potential in families of 3D Lieb lattices preserves the macroscopic degeneracy of compact localized states and yields unconventional combinations of localized and delocalized phases -- as shown in Phys.Rev.B 106, 214204 (2022). We proceed to reintroduce translation invariance in the system by further ordering the disorder, and discuss the spectral structure and eigenstates features of the resulting perturbed lattices. We restore order in steps by first (i) rendering the disorder binary -- i.e. yielding a randomized checkerboard potential, then (ii) reordering the randomized checkerboard into an ordered one, and at last (iii) realigning all the checkerboard values yielding a constant potential shift, but only on a sub-lattice. Along this path, we test the influence of additional random impurities on the order restoration. We find that in each of these steps, sub-families of states are projected upon the location of the degenerate compact states, while the complementary ones are localized in the perturbed sites with energy determined by the strength of checkerboard. This strategy, herewith implemented in the 3D Lieb, highlights order restoration as experimental pathway to engineer spectral and states features in disordered lattice structures in the pursuit of quantum storage and memory applications.

cond-mat.dis-nn↗

arXiv2023

Dynamical chaos in the integrable Toda chain induced by time discretization

We use the Toda chain model to demonstrate that numerical simulation of integrable Hamiltonian dynamics using time discretization destroys integrability and induces dynamical chaos. Specifically, we integrate this model with various symplectic integrators parametrized by the time step $\tau$ and measure the Lyapunov time $T_{\Lambda}$ (inverse of the largest Lyapunov exponent $\Lambda$). A key observation is that $T_{\Lambda}$ is finite whenever $\tau$ is finite but diverges when $\tau \rightarrow 0$. We compare the Toda chain results with the nonitegrable Fermi-Pasta-Ulam-Tsingou chain dynamics. In addition, we observe a breakdown of the simulations at times $T_B \gg T_{\Lambda}$ due to certain positions and momenta becoming extremely large (``Not a Number''). This phenomenon originates from the periodic driving introduced by symplectic integrators and we also identify the concrete mechanism of the breakdown in the case of the Toda chain.

nlin.CD↗

arXiv2022

Unconventional delocalization in a family of 3D Lieb lattices

Uncorrelated disorder in generalized 3D Lieb models gives rise to the existence of bounded mobility edges, destroys the macroscopic degeneracy of the flat bands and breaks their compactly-localized states. We now introduce a mix of order and disorder such that this degeneracy remains and the compactly-localized states are preserved. We obtain the energy-disorder phase diagrams and identify mobility edges. Intriguingly, for large disorder the survival of the compactly-localized states induces the existence of delocalized eigenstates close to the original flat band energies -- yielding seemingly divergent mobility edges. For small disorder, however, a change from extended to localized behavior can be found upon decreasing disorder -- leading to an unconventional ``inverse Anderson" behavior. We show that transfer matrix methods, computing the localization lengths, as well as sparse-matrix diagonalization, using spectral gap-ratio energy-level statistics, are in excellent quantitative agreement. The preservation of the compactly-localized states even in the presence of this disorder might be useful for envisaged storage applications.

cond-mat.dis-nn↗

arXiv2021

Higher-order exceptional point and Landau-Zener Bloch oscillations in driven non-Hermitian photonic Lieb lattices

We propose a scheme to realize parity-time (PT) symmetric photonic Lieb lattices of ribbon shape and complex couplings, thereby demonstrating the higher-order exceptional point (EP) and Landau-Zener Bloch (LZB) oscillations in presence of a refractive index gradient. Quite different from non-Hermitian flatband lattices with on-site gain/loss, which undergo thresholdless PT symmetry breaking, the spectrum for such quasi-one-dimensional Lieb lattices has completely real values when the index gradient is applied perpendicular to the ribbon, and a triply degenerated (third-order) EP with coalesced eigenvalues and eigenvectors emerges only when the amplitude of gain/loss ratio reaches a certain threshold value. When the index gradient is applied parallel to the ribbon, the LZB oscillations exhibit intriguing characteristics including asymmetric energy transition and pseudo-Hermitian propagation as the flatband is excited. Meanwhile, a secondary emission occurs each time when the oscillatory motion passes through the EP, leading to distinct energy distribution in the flatband when a dispersive band is excited. Such novel phenomena may appear in other non-Hermitian flatband systems. Our work may also bring insight and suggest a photonic platform to study the symmetry and topological characterization of higher-order EPs that may find unique applications in for example enhancing sensitivity.

physics.optics↗

arXiv2021

Compact breathers generator in one-dimensional nonlinear networks

Nonlinear networks can host spatially compact time periodic solutions called compact breathers. Such solutions can exist accidentally (i.e. for specific nonlinear strength values) or parametrically (i.e. for any nonlinear strength). In this work we introduce an efficient generator scheme for one-dimensional nonlinear lattices which support either types of compact breathers spanned over a given number U of lattice's unit cells and any number of sites v per cell - scheme which can be straightforwardly extended to higher dimensions. This scheme in particular allows to show the existence and explicitly construct examples of parametric compact breathers with inhomogeneous spatial profiles -- extending previous results which indicated that only homogeneous parametric compact breathers exist. We provide explicit d=1 lattices with different v supporting compact breather solutions for U=1,2.

nlin.PS↗

arXiv2021

Many-body localization transition from flatband fine-tuning

Translationally invariant flatband Hamiltonians with interactions lead to a many-body localization transition. Our models are obtained from single particle lattices hosting a mix of flat and dispersive bands, and equipped with fine-tuned two--body interactions. Fine-tuning of the interaction results in an extensive set of local conserved charges and a fragmentation of the Hilbert space into irreducible sectors. In each sector, the conserved charges originate from the flatband and act as an effective disorder inducing a transition between ergodic and localized phases upon variation of the interaction strength. Such fine-tuning is possible in arbitrary lattice dimensions and for any many-body statistics. We present computational evidence for this transition with spinless fermions.

cond-mat.stat-mech↗

arXiv2020

Nonlinear caging in All-Bands-Flat Lattices

We study the impact of classical short-range nonlinear interactions on transport in lattices with no dispersion. The single particle band structure of these lattices contains flat bands only, and cages non-interacting particles into compact localized eigenstates. We demonstrate that there always exist local unitary transformations that detangle such lattices into decoupled sites in dimension one. Starting from a detangled representation, inverting the detangling into entangling unitary transformations and extending to higher lattice dimensions, we arrive at an All-Bands-Flat generator for single particle states in any lattice dimension. The entangling unitary transformations are parametrized by sets of angles. For a given member of the set of all-bands-flat, additional short-range nonlinear interactions destroy caging in general, and induce transport. However, fine-tuned subsets of the unitary transformations allow to completely restore caging. We derive the necessary and sufficient fine-tuning conditions for nonlinear caging, and provide computational evidence of our conclusions for one-dimensional systems.

cond-mat.quant-gas↗

arXiv2020

Quantum Caging in Interacting Many-Body All-Bands-Flat Lattices

We consider translationally invariant tight-binding all-bands-flat networks which lack dispersion. In a recent work [arXiv:2004.11871] we derived the subset of these networks which preserves nonlinear caging, i.e. keeps compact excitations compact in the presence of Kerr-like local nonlinearities. Here we replace nonlinear terms by Bose-Hubbard interactions and study quantum caging. We prove the existence of degenerate energy renormalized compact states for two and three particles, and use an inductive conjecture to generalize to any finite number M of participating particles in one dimension. Our results explain and generalize previous observations for two particles on a diamond chain [Vidal et.al. Phys. Rev. Lett. 85, 3906 (2000)]. We further prove that quantum caging conditions guarantee the existence of extensive sets of conserved quantities in any lattice dimension, as first revealed in [Tovmasyan et al Phys. Rev. B 98, 134513 (2018)] for a set of specific networks. Consequently transport is realized through moving pairs of interacting particles which break the single particle caging.

cond-mat.quant-gas↗

arXiv2020

Fragile Many Body Ergodicity

Weakly nonintegrable many-body systems can restore ergodicity in distinctive ways depending on the range of the interaction network in action space. Action resonances seed chaotic dynamics into the networks. Long range networks provide well connected resonances with ergodization controlled by the individual resonance chaos time scales. Short range networks instead yield a dramatic slowing down of ergodization in action space, and lead to rare resonance diffusion. We use Josephson junction chains as a paradigmatic study case. We exploit finite time average distributions to characterize the thermalizing dynamics of actions. We identify a novel action resonance diffusion regime responsible for the slowing down. We extract the diffusion coefficient of that slow process and measure its dependence on the proximity to the integrable limit. Independent measures of correlation functions confirm our findings. The observed fragile diffusion is relying on weakly chaotic dynamics in spatially isolated action resonances. It can be suppressed, and ergodization delayed, by adding weak action noise, as a proof of concept.

nlin.CD↗

arXiv2020

Many-Body Flatband Localization

We generate translationally invariant systems exhibiting many-body localization from All-Bands- Flat single particle lattice Hamiltonians dressed with suitable short-range many-body interactions. This phenomenon - dubbed Many-Body Flatband Localization (MBFBL) - is based on symmetries of both single particle and interaction terms in the Hamiltonian, and it holds for any interaction strength. We propose a generator of MBFBL Hamiltonians which covers both interacting bosons and fermions for arbitrary lattice dimensions, and we provide explicit examples of MBFBL models in one and two lattice dimensions. We also explicitly construct an extensive set of local integrals of motion for MBFBL models. Our results can be further generalized to long-range interactions as well as to systems lacking translational invariance.

cond-mat.stat-mech↗