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arXiv:2112.07964 · Physical Review A

Floquet-engineered pair and single-particle filters in the Fermi-Hubbard model

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

Published Oct 5, 2022• 15 citations
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Abstract

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 $U$. 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.

DOI
10.1103/physreva.106.043303

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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 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 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 investigate how the driving field affects the bound states in the one-dimensional two-particle Bose–Hubbard model with an impurity. In the high-frequency regime, compared with the static lattice [Phys. Rev. Lett. 109 (2012) 116405], a new type of Floquet bound state can be obtained even for a weak particle–particle interaction by tuning the driving amplitude. Moreover, the localization degree of the Floquet bound molecular state can be adjusted by tuning the driving frequency, and even the Floquet bound molecular state can be changed into the Floquet extended state when the driving frequency is below a critical value. Our results provide an efficient way to manipulate bound states in the many-body systems.
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.
The Sachdev-Ye-Kitaev (SYK) model has attracted widespread attention due to its relevance to diverse areas of physics, such as high temperature superconductivity, black holes, and quantum chaos. The model is, however, extremely challenging to realize experimentally. In this work, we show how a particular form of Floquet engineering, termed ``kinetic driving'', effectively eliminates single-particle processes and creates quasi-random all-to-all interactions when applied to models of Hubbard type. For the specific case of the Bose-Hubbard model, we explicitly verify that the driven system indeed reproduces SYK physics by direct comparison of the spectral form factor and out-of-time ordered correlation functions (OTOCs). Our findings indicate that a cold-atom realization of kinetic driving -- achieved through modulation of hopping amplitudes in an optical lattice -- offers a practical and accurate platform for quantum simulation of the SYK model.
Intense time-periodic laser fields can transform the electronic structure of a solid into strongly modified Floquet-Bloch bands. While this suggests multiple pathways to induce electronic orders such as superconductivity or charge density waves, the possibility of preparing low-energy phases of Floquet Hamiltonians remains unclear because of the energy absorption at typical experimentally accessible driving frequencies. Here we investigate a realistic pathway towards laser control of electronic orders, which is the transient enhancement of fluctuating orders. Using a conserving Keldysh Green's function formalism, we simulate the buildup of short range Cooper-pair correlations out of a normal metal in the driven attractive Hubbard model. Even for frequencies only slightly above or within the bandwidth, a substantial enhancement of correlations can be achieved before the system reaches a high electronic temperature. This behavior relies on the nonthermal nature of the driven state. The effective temperature of the electrons at the Fermi surface, which more closely determines the superconducting correlations, remains lower than an estimate from the global energy density. Even though short ranged, the fluctuations can have marked signatures in the electronic spectra.