Non-Hermitian Topological Phase Transition of the Bosonic Kitaev Chain

Abstract: The bosonic Kitaev chain, just like its fermionic counterpart, has extraordinary properties. For example, it displays the non-Hermitian skin effect even without dissipation when the system is Hermitian. This means that all eigenmodes are exponentially localized to the edges of the chain. This is possible since the $\hat{x}$ and $\hat p$ quadratures decouple such that each of them is governed by a non-Hermitian dynamical matrix. In the topological phase of the model, the modes conspire to lead to exponential amplification of coherent light that depends on its phase and direction. In this work, we study the robustness of this topological amplification to on-site dissipation. We look at uniform and non-uniform dissipation and study the effect of different configurations. We find remarkable resilience to dissipation in some configurations, while in others the dissipation causes a topological phase transition which eliminates the exponential amplification. For example, when the dissipation is placed on every other site, the system remains topological even for very large dissipation which exceeds the system's non-Hermitian gap and the exponential amplification persists. On the other hand, dividing the chain into unit cells of an odd number of sites and placing dissipation on the first site leads to a topological phase transition at some critical value of the dissipation. Our work thus provides insights into topological amplification of multiband systems and sets explicit limits on the bosonic Kitaev chain's ability to act as a multimode quantum sensor.