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arXiv:2311.04899 · Physical Review Research

Floquet engineering of binding in doped and photo-doped Mott insulators

Madhumita Sarkar, Zala Lenarčič, Denis Golež

Published Sep 24, 2024• 3 citations
arXivHTMLPDF

Abstract

We investigate the emergence of bound states in chemically and photo-doped Mott insulators, mediated by spin and η -pairing fluctuations within both 2-leg ladder and 2D systems. To effectively describe the photo and chemically doped state on the same footings, we employ the Schrieffer-Wolff transformation, resulting in a generalized t − J model. Our results demonstrate that the binding energies and localization length in the chemically and photo-doped regimes are comparable, with η -pairing fluctuations not playing a crucial role. Furthermore, we show that manipulating the binding is possible through external periodic driving, a technique known as Floquet engineering, leading to significantly enhanced binding energies. We also roughly estimate the lifetime of photo-doped states under periodic driving conditions based on the Fermi golden rule. Lastly, we propose experimental protocols for realizing Hubbard excitons in cold-atom experiments. Published by the American Physical Society 2024

DOI
10.1103/physrevresearch.6.033331

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We investigate the emergence of bound states in chemically and photo-doped Mott insulators, mediated by spin and η -pairing fluctuations within both 2-leg ladder and 2D systems. To effectively describe the photo and chemically doped state on the same footings, we employ the Schrieffer-Wolff transformation, resulting in a generalized t − J model. Our results demonstrate that the binding energies and localization length in the chemically and photo-doped regimes are comparable, with η -pairing fluctuations not playing a crucial role. Furthermore, we show that manipulating the binding is possible through external periodic driving, a technique known as Floquet engineering, leading to significantly enhanced binding energies. We also roughly estimate the lifetime of photo-doped states under periodic driving conditions based on the Fermi golden rule. Lastly, we propose experimental protocols for realizing Hubbard excitons in cold-atom experiments. Published by the American Physical Society 2024
We investigate the pairing state in a doped band insulator under a periodic driving field. We employ a correlated fermionic model on a honeycomb lattice, in which pairing glue is obtainable via repulsive interactions, and derive an effective model under circularly polarized light. We demonstrate that the effective pairing interaction for doped fermions obtained with the second-order perturbation theory is tunable by the frequency and amplitude of the driving field. We find the optimal frequency range to enhance the pairing interaction and show that the modified effective system can strengthen the two-body bound state. Our study suggests that external driving light can reinforce superconducting pair states in strongly correlated electron systems.
The study of nonequilibrium phenomena in interacting lattice systems can provide new perspectives on correlation effects, and information on metastable states of matter. Mott insulators are a promising class of systems for nonequilibrium studies, since they exhibit exotic phenomena and complex phase diagrams upon doping, and because a large Mott gap provides protection against fast thermalization and heating after photo-excitations. We can thus expect the emergence of interesting transient states and photo-induced phases in Mott systems. This review presents the current understanding of the mechanisms which control the time evolution of photo-doped charge carriers and the properties of photo-induced metastable states. We focus on recent theoretical progress, identify the relevant underlying concepts, and link them to experimental observations. The review starts with a general discussion of field-induced nonequilibrium setups and an overview of key experiments which revealed characteristic properties of photo-excited Mott states, proceeds with a compact overview of the theoretical tools which have been developed to investigate these strongly correlated nonequilibrium states, and then analyzes Mott insulators driven out of equilibrium by static electric fields, periodic fields, and short laser pulses. We also discuss the appearance of nonthermal electronic orders in photo-excited Mott systems, including nonthermal spin and orbital orders, ηηη pairing states, and novel types of excitonic orders.
The present thesis is devoted to quantum simulation of strongly interacting systems of ultra-cold atoms in optical lattices. It is a theoretical work which focuses on the possibility to employ strong time-periodic forcing for the coherent control of these system. This form of quantum engineering is called Floquet engineering. Experimentally, time-periodic forcing has been successfully applied to realize a variety of physical models and phenomena, especially in the regime of weak interactions. We describe two novel proposals for interesting phenomena in the regime of strong interactions that rely on lattice shaking: melting of a Mott-insulator into an excited-state superfluid via coherent coupling of Bloch bands and the creation of 1D lattice anyons. Furthermore, the role of multiphoton excitations in a driven lattice is analyzed since these processes can lead to unwanted heating and thereby impeding of successful Floquet engineering in the experiment. The introductory Chapter 1 gives an overview over the field of quantum simulations with ultra-cold atoms in optical lattices and describes the experimental progress that has been made in the recent years. In Chapter 2, Floquet theory is reviewed, which provides an excellent framework to deal with time-periodic Hamiltonians and which is the basis of the analysis presented in the following chapters. Chapter 3 deals with the proposal of coherently coupling Bloch bands of an optical lattice via resonant lattice shaking. In particular, the orbital-driven phase transition from a Mott insulating to a superfluid ground state is described in detail. In Chapter 4, a proposal of realizing 1D lattice anyons from strongly interacting bosons in a shaken and tilted lattice is worked out. Furthermore, Friedel oscillations are proposed to provide a measurable real-space signature for the anyonization. Finally, in Chapter 5 multiphoton excitations to higher Bloch bands are analyzed for the cases of a shaken and an amplitude-modulated lattice. The strength and the location of resonances, which are associated with heating, are described theoretically and numerically.
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.
Higher-order topological insulators have attracted significant interest in both static single-particle and many-body lattice systems. While periodically driven (Floquet) higher-order topological phases have been explored at the single-particle level, the role of interactions in such systems remains less understood. In this paper, we extend previous studies by investigating interaction-induced higher-order topological phases through Floquet engineering. To achieve this, we construct an extended Bose-Hubbard model on a square lattice subjected to periodic driving. We demonstrate the emergence of interaction-induced normal Floquet second-order topological corner states for doublons (i.e., bound boson pairs) from a trivial phase, which exhibit robustness against disorder. Notably, beyond the normal phase, we reveal an interaction-induced anomalous Floquet second-order topological phase, where in-gap corner states of doublons emerge within the $\ensuremath{\pi}/T$ gap (TTT being the driving period). Our model, accessible with state-of-the-art ultracold atom techniques, provides a platform for realizing interaction-driven higher-order topological phases uniquely enabled by periodic driving, with no direct counterparts in static or single-particle systems.
The concept of “Floquet engineering” relies on an external periodic drive to realize novel, effectively static Hamiltonians. This technique is being explored in experimental platforms across physics, including ultracold atoms, laser-driven electron systems, nuclear magnetic resonance, and trapped ions. The key challenge in Floquet engineering is to avoid the uncontrolled absorption of photons from the drive, especially in interacting systems in which the excitation spectrum becomes effectively dense. The resulting dissipative coupling to higher-lying modes, such as the excited bands of an optical lattice, has been explored in recent experimental and theoretical works, but the demonstration of a broadly applicable method to mitigate this effect is lacking. Here, we show how two-path quantum interference applied to strongly correlated fermions in a driven optical lattice suppresses dissipative coupling to higher bands and increases the lifetime of double occupancies and spin correlations by 2 to 3 orders of magnitude. Interference is achieved by introducing a weak second modulation at twice the fundamental driving frequency with a definite relative phase. This technique is shown to suppress dissipation in both weakly and strongly interacting regimes of an offresonantly driven Hubbard system, opening an avenue to realizing low-temperature phases of matter in interacting Floquet systems.