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Chaos Solitons & Fractals

Transport and Fano resonance in a one-dimensional weakly-interacting periodically driven fermionic system

Vincenzo Bruno, R. Citro

Published Jun 20, 2025• 1 citation
Publisher

Abstract

We investigate the transport properties of a one-dimensional weakly interacting spin-1/2 fermionic lattice with a periodically driven impurity. Using the mean-field approximation, we extend the analysis of a noninteracting system to include weak on-site interactions. In a system without interactions and for small driving amplitude, a Fano resonance emerges in the transmission spectrum at the energy of the incoming particle equal to the driving frequency. The effect of weak interactions consists of a shift and deformation of the resonance. Moreover, for higher values of the drive amplitude, the interplay between interactions and periodic driving results in the formation of two distinct Fano resonances, highlighting the non-trivial effects of interactions on quantum transport. Our results could be relevant on optical platforms to achieve light sensing and manipulation.

DOI
10.1016/j.chaos.2025.116688

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We investigate the transport properties of a one-dimensional weakly interacting spin-1/2 fermionic lattice with a periodically driven impurity. Using the mean-field approximation, we extend the analysis of a noninteracting system to include weak on-site interactions. In a system without interactions and for small driving amplitude, a Fano resonance emerges in the transmission spectrum at the energy of the incoming particle equal to the driving frequency. The effect of weak interactions consists of a shift and deformation of the resonance. Moreover, for higher values of the drive amplitude, the interplay between interactions and periodic driving results in the formation of two distinct Fano resonances, highlighting the non-trivial effects of interactions on quantum transport. Our results could be relevant on optical platforms to achieve light sensing and manipulation.
Floquet engineering offers powerful tools to manipulate quantum states by periodically driving physical parameters. In this work, we investigate the quantum transport through two periodically driven impurities in a mesoscopic one-dimensional channel. By mapping the time-dependent Hamiltonian into an effective multichannel scattering problem, we unveil a rich landscape of transport phenomena arising from the interplay between Fabry-Perot cavity modes and Fano interference. We demonstrate that the inter-impurity distance acts as a critical control parameter, allowing for the formation of Bound States in the Continuum (BICs). Furthermore, we identify Quasi-BICs, extremely narrow resonances with finite lifetimes, that can be dynamically tuned by the drive amplitude. We show that these states enable a robust coherent trapping mechanism, allowing the system to switch from perfect transparency or reflection to strong localization with giant Wigner time delays. Our results suggest possible applications for tunable delay lines and quantum memories, with feasible experimental realizations in the context of cold atoms.
We investigate the effect of periodic driving by an external field on systems with attractive pairing interactions. These include spin systems (such as the ferromagnetic XXZXXZXXZ model) as well as ultracold fermionic atoms described by the attractive Hubbard model. We show that a well-known phenomenon seen in periodically driven systems---the renormalization of the exchange coupling strength---acts selectively on bound pairs of spins (atoms), relative to magnon (bare atom) states. Thus one can control the direction and speed of transport of bound pair relative to magnon (unpaired) atom states, and thus coherently achieve spatial separation of these components. Applications to recent experiments on transport with fermionic atoms in optical lattices which consist of mixtures of bound pairs and bare atoms are discussed.
For a periodically driven quantum system, an effective time-independent Hamiltonian is derived with an eigenenergy spectrum, which in the regime of large driving frequencies approximates the quasienergies of the corresponding Floquet Hamiltonian. The effective Hamiltonian is evaluated for the case of optical lattice models in the tight-binding regime subjected to strong periodic driving. Three scenarios are considered: a periodically shifted one-dimensional (1D) lattice, a two-dimensional (2D) square lattice with inversely phased temporal modulation of the well depths of adjacent lattice sites, and a 2D lattice subjected to an array of microscopic rotors commensurate with its plaquette structure. In the 1D scenario, the rescaling of the tunneling energy, previously considered by Eckardt et al. [Phys. Rev. Lett. 95, 260404 (2005)] is reproduced. The 2D lattice with well-depth modulation turns out as a generalization of the 1D case. In the 2D case with staggered rotation, the expression previously found in the case of weak driving by Lim et al. [Phys. Rev. Lett. 100, 130402 (2008)] is generalized, such that its interpretation in terms of an artificial staggered magnetic field can be extended into the regime of strong driving.
We study if the interplay between dynamical localization and interactions in periodically driven quantum systems can give rise to anomalous thermalization behavior. Specifically, we consider one-dimensional models with interacting spinless fermions with nearest-neighbor hopping and density-density interactions, and a periodically driven on-site potential with spatial periodicity m=2 and m=4. At a dynamical localization point, these models evade thermalization either due to the presence of an extensive number of conserved quantities (for weak interactions) or due to the kinetic constraints caused by drive-induced resonances (for strong interactions). Our models therefore illustrate interesting mechanisms for generating constrained dynamics in Floquet systems which are difficult to realize in an undriven system.
In this thesis, we theoretically investigate exotic quantum phenomena underlying periodically-driven systems.We discuss three distinct systems, noninteracting Dirac systems, lattice systems with a strong repulsive interaction, and lattice systems with a strong attractive interaction.We reveal various novel phenomena underlying these systems, and provide clear understanding of them.Periodically-driven systems, i.e., systems with a discrete time-translational symmetry, are described by the Floquet formalism, which maps the time-dependent Hamiltonian to a static "photon-dressed Hamiltonian".While a perturbative expansion of this Hamiltonian from the limit of high driving frequency has clarified various novel phenomena peculiar to periodically-driven systems, such an approach suffers from serious heating or damage when it is applied to realistic condensed matters.In this thesis, we focus on a lower-frequency regime, especially when the heating should be suppressed due to the small driving amplitude or an energy gap larger than the driving frequency.There, the high-frequency expansion cannot capture the relevant physics, so that we first formulate various perturbative expansions for three distinct regimes, i.e., high-frequency, small-amplitude, and strong-coupling regimes.We apply the small-amplitude expansion to two-and three-dimensional Dirac electrons driven by a circularly-polarized light to explore their behavior in the lowfrequency regime.We find an emergence of infinite numbers of topological gaps for the former and Weyl nodes for the latter.We also discuss how a regularization of the model affects this topological structure.We then introduce a strong repulsive interaction, and discuss behaviors of spins using the strong-coupling expansion.We predict an emergence of scalar spin chirality when a circularly-polarized light is illuminated, and discuss possible applications to photo-induced chiral spin liquids, and optical probing of spin chirality.Finally we turn to a strong attractive interaction to discuss the fate of the ordinary s-wave superconductivity under the periodic driving.We demonstrate an emergence of long sought-after η-pairing superconductivity, first as a ground state of the photon-dressed Hamiltonian, and then as a consequence of a dynamical phase transition in an isolated system such as an optical lattice system.
Abstract The out-of-equilibrium dynamics of finite ultracold bosonic ensembles in periodically driven one-dimensional optical lattices is investigated. Our study reveals that the driving enforces the bosons in different wells to oscillate in-phase and to exhibit a dipole-like mode. A wide range from weak-to-strong driving frequencies is covered and a resonance-like behavior of the intra-well dynamics is discussed. In the proximity of the resonance a rich intraband excitation spectrum is observed. The single particle excitation mechanisms are studied in the framework of Floquet theory elucidating the role of the driving frequency. The impact of the interatomic repulsive interactions is examined in detail yielding a strong influence on the tunneling period and the excitation probabilities. Finally, the dependence of the resonance upon a variation of the tunable parameters of the optical lattice is examined. Our analysis is based on the ab initio multi-configuration time-dependent Hartree method for bosons.