Floquet Bosonic Kitaev Chain

TL;DR

The paper addresses how Floquet engineering can yield non-Hermitian topological phenomena in Hermitian bosonic lattices by mapping to an excitation-level non-Hermitian problem and applying Floquet theory. It analyzes two solvable driven models of a modified bosonic Kitaev chain, revealing coexistence of NHSE with topological zero and π edge modes and, in Model 2, tunable proliferation of edge modes. The edge modes demonstrate robustness to onsite frequency and disorder with model-dependent NHSE behavior, illustrating a route to realize Floquet non-Hermitian phases without actual non-Hermiticity in the Hamiltonian. These results provide a framework for exploring richer Floquet non-Hermitian phases, potential 2D extensions, and experimental realizations in Hermitian systems.

Abstract

We propose a class of periodically driven (Hermitian) modified bosonic Kitaev chains that effectively hosts rich nonHermitian Floquet topological phenomena. Two particular models are investigated in details as case studies. The first of these represents a minimal topologically nontrivial model in which nonHermitian skin effect, topological zero modes, and topological $π$ modes coexist. The other displays a more sophisticated model that supports multiple topological zero modes and topological $π$ modes in a tunable manner. By subjecting both models to perturbations such as a finite onsite bosonic frequency and spatial disorder, these features exhibit distinct responses. In particular, while generally all topological edge modes are robust against such perturbations, the nonHermitian skin effect is easily suppressed and revived by, respectively, the onsite bosonic frequency and spatial disorder in the first model, but it could be insensitive to both perturbations in the second model. Our studies thus demonstrate the prospect of a periodically driven bosonic Kitaev chain as a starting point in exploring various nonHermitian Floquet topological phases through the lens of a Hermitian system.

Figures (8)

• Figure 1: (a,b) The real and imaginary parts of the system's quasienergy excitation spectrum under OBC (red) and PBC (blue). (c,d) The spatial profiles of all quasienergy excitation eigenstates under (c) $J_0=0.5$ and (d) $J_0=3$. The other system parameters are taken as $j_0=0.5$, $\Delta_0=1$, $\delta_0=4$, (a,b) $N=100$, (c,d) $N=250$.
• Figure 2: The upper panels depict the system's quasienergy excitation spectrum for model 1 under OBC as a system parameter is varied. The bottom panels present the numerically calculated winding numbers $\nu_0$ and $\nu_\pi$. The remaining system parameters are chosen as $N=100$, (a) $\Delta_0 = 1$, $\delta_0 = 0.5$, $j_0 = 4$, (b) $J_0 = 3$, $j_0 = 0.5$, $\delta_0 = 4$, (c) $J_0 =2$, $\Delta_0 =1$, $\delta_0 =0.5$, (d) $J_0 =3$, $j_0 =0.5$, $\Delta_0 =4$.
• Figure 3: The upper panels depict the system's quasienergy excitation spectrum for model 2 under OBC as a system parameter is varied according to case(i) in Sec. \ref{['Mod2']}. The bottom panels present the numerically calculated winding numbers $\nu_0$ and $\nu_\pi$. The remaining system parameters are chosen as $N=100$, (a) $\Delta_a = 0.6$, $\Delta_b=1.6$, $J_a = \sqrt{\Delta_a^2 +1}$, $J_b = \sqrt{\Delta_b^2 +1}$, (b) $J_a = 0.6$, $\Delta_b=1.6$, $\Delta_a = \sqrt{J_a^2 +1}$, $J_b = \sqrt{\Delta_b^2 +1}$, (c) $\Delta_a = 0.6$, $J_b=1.6$, $J_a = \sqrt{\Delta_a^2 +1}$, $\Delta_b = \sqrt{J_b^2 +1}$, (d) $J_a = 0.6$, $J_b=1.6$, $\Delta_a = \sqrt{J_a^2 +1}$, $\Delta_b = \sqrt{J_b^2 +1}$.
• Figure 4: The system's quasienergy excitation spectrum under OBC at finite onsite bosonic frequency for (a,b) model 1 and (c,d) model 2. (a,b) Model 1 system parameters are chosen as (a) $\Delta_0=0.5$$\delta_0=1$, $J_0=\sqrt{1.8^2+\Delta_0^2}$, and $j_0=\sqrt{2.5^2+\delta_0^2}$, (b) $J_0=0.5$, $\delta_0=1$, $\Delta_0=\sqrt{1.8^2+J_0^2}$, and $j_0=\sqrt{(\pi-0.2)^2+\delta_0^2}$. (c,d) Model 2 system parameters are chosen as (c) $\Delta_a=-\frac{\delta_a}{m}=0.6$, $\Delta_b=\frac{\delta_b}{m}=0.6$, $J_a=-\frac{j_a}{m}=\sqrt{1^2+0.6^2}$, and $J_b=\frac{j_b}{m}=\sqrt{1^2+0.6^2}$, (d) $\Delta_a=-\frac{\delta_a}{m}=1$, $\Delta_b=\frac{\delta_b}{m}=0.6$, $J_a=-\frac{j_a}{m}=\sqrt{2}$, and $J_b=\frac{j_b}{m}=\sqrt{1^2+0.6^2}$. The system size is taken as $N=100$ in all panels, and $\omega=0.01\pi$ in panels (c,d).
• Figure 5: The spatial profiles of all quasienergy excitation eigenstates (see Eq. (\ref{['sprof']}) for its definition) under (a,b) model 1, (c,d) model 2. The insets of each panel depict the zoomed-in view of all localized quasienergy excitation eigenstates, which include nontopological bulk modes (panel (d3)) and genuine topological edge modes (all the other panels). The system parameters are taken as $N=250$ in all panels, $\omega=0.05$ in panels (a,b), $m=1.8\pi$ in panel (c), and $m=1.1\pi$ in panel (d). The remaining system parameters respectively match those of Fig. \ref{['fig:finw']}(a)-(d).