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arXiv:2305.16743 · Physical Review A

Momentum-resolved Floquet-engineered pair and single-particle filter in the Fermi-Hubbard model

Friedrich Hübner, Christoph Dauer, Sebastian Eggert, Corinna Kollath, Ameneh Sheikhan

Published Aug 8, 2023• 8 citations
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Abstract

We investigate the transport properties of a Fermi-Hubbard chain with an impurity which is formed by a site with a periodically modulated chemical potential. We determine the momentum-resolved transmission through this impurity in dependence of the modulation frequency and strength for a single particle and a pair of fermions. We find that the pair transmission has a very distinct behavior from the single-particle transmission. Different situations can occur, where only the single particle or the pair with a certain momentum is transmitted or filtered out.

DOI
10.1103/physreva.108.023307

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We investigate the transport properties of a Fermi-Hubbard chain with an impurity which is formed by a site with a periodically modulated chemical potential. We determine the momentum-resolved transmission through this impurity in dependence of the modulation frequency and strength for a single particle and a pair of fermions. We find that the pair transmission has a very distinct behavior from the single-particle transmission. Different situations can occur, where only the single particle or the pair with a certain momentum is transmitted or filtered out.
We investigate the Fermi-Hubbard model with a Floquet-driven impurity in the form of a local time-oscillating potential. For strong attractive interactions a stable formation of pairs is observed. These pairs show a completely different transmission behavior than the transmission that is observed for the single unpaired particles. Whereas in the high-frequency limit the single particles show a maximum of the transition at low driving amplitudes, the pairs display a pronounced maximum transmission when the amplitude of the driving is close to the interaction amplitude UUU. We use the distinct transmission behavior to design filters for pairs or single particles, respectively. For example, one can totally block the transmission of single particles through the driven impurity and allow only for the transmission of pairs. We quantify the quality of the designed filters.
We investigate scattering phenomena in a one-dimensional attractive Bose-Hubbard model with a time-periodically modulated impurity. We analyze both single-particle and pair (doublon) transmission, exploring a range of interaction strengths and drive amplitudes. Our exact numerical results reveal excellent quantitative agreement with analytical predictions in the high-frequency limit. At intermediate and weak attractive interactions, we observe significant pair dissociation and the emergence of dynamically localized single-particle modes. These features are reminiscent of Floquet Bound States in the Continuum (BICs). These findings provide new avenues for engineering controllable quantum transport and localized states in ultracold atom experiments.
We study solutions to the Lippmann-Schwinger equation in systems where a slow subsystem is coupled to a fast subsystem via an impurity. Such situations appear when a high-frequency Floquet-driven impurity is introduced into a low-energy system, but the driving frequency is at resonance with a high-energy band. In contrast to the case of resonant bulk driving, where the particles in the low-energy system are excited into the high-energy band, we surprisingly find that these excitations are suppressed for resonantly driven impurities. Still, the transmission through the impurity is strongly affected by the presence of the high-energy band in a universal way that does not depend on the details of the high-energy band. We apply our general result to two examples and show the suppression of excitations from the low-energy band into the high-energy band: a) bound pairs in a Fermi-Hubbard chain scattering at a driven impurity, which is at resonance with the Hubbard interaction and b) particles in a deep optical lattice described by the tight-binding approximation, which scatter at a driven impurity, whose driving frequency equals the band gap between the two lowest energy bands.
We investigate the dynamics of bound pairs in an extended Hubbard model at resonance. We show that a single fermion and a singlet bound pair possess identical dispersion relations and scatter off each other. In contrast, a neighboring doublon pair is dynamically pinned in the strong-interaction regime. Remarkably, a single fermion and a singlet bound pair exhibit fundamentally different scattering behaviors when encountering a pinned doublon pair acting as a scattering center. While the singlet bound pair undergoes perfect transmission, the single fermion is completely reflected. These results demonstrate that a neighboring doublon pair functions as an efficient filter that separates bound pairs from single particles. Numerical simulations fully support the analytical predictions. Our findings provide a dynamical mechanism for generating and manipulating bound-pair states.
We investigate pair superfluidity in a generalized Bose-Hubbard model, extending the framework to include pair hopping and direct on-site pair interactions. Our study reveals unique features of the pair superfluid phase, such as reentrant behavior and pockets of the normal state within the superfluid region---phenomena absent in single-particle superfluid models. Through compressibility analysis, we identify Mott insulating features at zero temperature and a complex interplay between temperature, chemical potential, and pair hopping. We highlight the importance of the occupation basis size in accurately modeling pair-superfluid dynamics, demonstrating that excessive truncation leads to unphysical artifacts. Additionally, we present phase diagrams contrasting pair and single-particle superfluidity, showing the distinct nature of their respective transitions and phase boundaries. Our findings provide theoretical insights relevant to experimental platforms, such as ultracold atomic gases and Josephson junction systems, and utilize Floquet engineering as a justification for achieving and controlling pair-hopping dynamics. This paper enhances our understanding of pair superfluidity and paves the way for further exploration of complex quantum many-body systems.
We study low-temperature transport properties of a doped two-chain ladder system of interacting fermions in the presence of a barrier or of a low concentration of impurities. The conductance is suppressed above a certain value of the interaction as in a single chain, despite the presence of dominant superconducting correlations. There is, however, a region of repulsive interaction where perfect transmission across the barrier occurs unlike that in the single-chain case. We provide a possible explanation for the temperature maximum of the resistivity in the normal state of ${\mathrm{Sr}}_{0.4}{\mathrm{Ca}}_{13.6}{\mathrm{Cu}}_{24}{\mathrm{O}}_{42\ensuremath{-}\ensuremath{\delta}}$.