NonHermitian Topological Phases in a Hermitian Modified Bosonic Kitaev Chain

TL;DR

This work shows that a Hermitian modification of the bosonic Kitaev chain can host both non-Hermitian skin effect (NHSE) and nontrivial topological edge modes in its excitation spectrum. By establishing an exact mapping to two copies of a non-Hermitian SSH model, the authors achieve analytic topological classification via winding-number invariants and zero-energy edge states. They demonstrate that NHSE and some edge modes are destroyed by any nonzero onsite bosonic frequency, yet disorder can partially recover certain features, revealing a robust interplay between topology and NHSE. An experimental route based on parametric driving of coupled optical cavities and Floquet engineering is proposed to realize and explore the full parameter space with high control.

Abstract

We present a modification to the bosonic Kitaev chain that, despite being Hermitian, supports both nonHermitian skin effect and nontrivial topological edge modes in its excitation Hamiltonian. We establish an exact mapping between the excitation Hamiltonian of our system and a nonHermitian Su-Schrieffer-Heeger (SSH) model, which allows for a completely analytical characterization of its topology. In particular, topological phase transition points separating a topologically trivial and nontrivial regime were identified analytically by the appropriate winding number invariant and the presence of zero energy modes. Similarly to the regular bosonic Kitaev chain, the nonHermitian skin effect and some (but not all) topological edge modes are quickly destroyed at nonzero bosonic onsite potential (harmonic oscillator frequency). Remarkably, however, disorder partially recovers some of these features. This work thus demonstrates the potential of a modified bosonic Kitaev chain as a platform to generate rich nonHermitian topological phenomena from a completely Hermitian system's perspective. Lastly, we suggest a possible experimental realization of the model, which could allow for total control over the parameter space.

Figures (10)

• Figure 1: The eigenvalue spectrum of the Hatano-Nelson Hamiltonian under OBC (red) and under PBC (blue). In all panels, the system parameters are set as $\Delta_0=1$, $N=100$, (a,b) $\omega=0$, (c,d) $\omega=0.5$.
• Figure 2: The excitation energy spectrum of $\mathcal{H}'$ under OBC (red) and under PBC (blue) at varying $\Delta_1$. In all panels, the system parameters are set as $J_1=1.4$, $J_2=1.2$, $\Delta_2=1$, $N=100$, (a,b) $\omega=0$, (c,d) $\omega=0.5$.
• Figure 3: The excitation energy spectrum of $\mathcal{H}'$ under OBC (red) and under PBC (blue) at varying $\omega$. In all panels, the system parameters are set as $J_1=0.4$, $J_2=0.1$, $\Delta_1=1$$\Delta_2=0.5$, and $N=100$.
• Figure 4: The spatial profiles of all eigenstates of $\mathcal{H}'$ at $N=100$ (see Eq. (\ref{['sprof']}) for definitions). System parameters are chosen as (a) $J_1=0.4$, $J_2=0.1$, $\Delta_1=1$, $\Delta_2=0.5$, $\omega=0$, (b) $J_1=0.4$, $J_2=0.1$, $\Delta_1=1$, $\Delta_2=0.5$, $\omega=0.1$, (c) $J_1=0.4$, $J_2=0.1$, $\Delta_1=0.5$, $\Delta_2=1$, $\omega=0$, (d) $J_1=0.1$, $J_2=0.4$, $\Delta_1=1$, $\Delta_2=0.5$, $\omega=0$.
• Figure 5: The spatial profiles of all eigenstates of $\mathcal{H}'$ and their energy excitation spectrum at varying $J_1$. In panels (a,b,c), the system parameters are taken as $\Delta_2=1.5$, $\Delta_1=1$, and $N=100$ ($J_1=0.5$ is additionally taken in panels (a,b)). The system parameters in panel (d) are $\Delta_1=1.5$, $\Delta_2=1$, and $N=100$. We set $\omega=0$ in panels (a,c,d) and $\omega=0.05$ in panel (b).