47 research outputs found
Topological Floquet edge states in periodically curved waveguides
We study the Floquet edge states in arrays of periodically curved optical
waveguides described by the modulated Su-Schrieffer-Heeger model. Beyond the
bulk-edge correspondence, our study explores the interplay between band
topology and periodic modulations. By analysing the quasi-energy spectra and
Zak phase, we reveal that, although topological and non-topological edge states
can exist for the same parameters, \emph{they can not appear in the same
spectral gap}. In the high-frequency limit, we find analytically all boundaries
between the different phases and study the coexistence of topological and
non-topological edge states. In contrast to unmodulated systems, the edge
states appear due to either band topology or modulation-induced defects. This
means that periodic modulations may not only tune the parametric regions with
nontrivial topology, but may also support novel edge states.Comment: 11 pages, 5 figure
Modulation-induced long-range magnon bound states in one-dimensional optical lattices
Magnon excitations play an important role in understanding quantum magnetism and magnon bound states observed with ultracold atoms in optical lattices. Here, we investigate how gradient magnetic field and periodically modulated spin-exchange strength affect the two-magnon excitations. In the Stark resonance where the driving frequency matches and smooths the potential bias, the system gains translational invariance in both space and time in the rotating frame, and thus we can develop a Floquet-Bloch band theory for two magnons. We find a new kind of bound states with relative distance no less than two sites, apart from the conventional bound states with relative distance at one site, which indicates the modulation-induced long-range interaction. We analytically derive an effective Hamiltonian via the many-body perturbation theory for a deeper understanding of such novel bound states and explore the interplay between these two types of bound states. Moreover, we propose to probe modulation-induced bound states via quantum walks. Our study not only provides a scheme to form long-range magnon bound states, but also lays a cornerstone for engineering exotic quantum states in multi-particle Floquet systems.This work is supported by the Key-Area Research and Development Program of GuangDong Province
under Grants No. 2019B030330001, the National Natural Science Foundation of China (NNSFC) under
Grants [No. 11874434, No. 11574405], and the Science and Technology Program of Guangzhou (China)
under Grants No. 201904020024. YK is partially supported by the Office of China Postdoctoral Council
(Grant No. 20180052), the National Natural Science Foundation of China (Grant No. 11904419), and the
Australian Research Council (DP200101168)