Topological Amplification of the Bosonic Kitaev Chain with Non-Uniform Loss

TL;DR

This paper investigates the robustness of topological exponential amplification in the bosonic Kitaev chain against various dissipation configurations, revealing conditions under which amplification persists or is suppressed.

Contribution

It provides a detailed analysis of how uniform and non-uniform losses affect topological amplification in the bosonic Kitaev chain, highlighting configurations with high resilience.

Findings

Exponential amplification persists with certain non-uniform losses.

Dissipation on every other site does not destroy topological amplification.

A phase transition occurs under specific dissipation arrangements, eliminating amplification.

Abstract

The bosonic Kitaev chain is known to have extraordinary properties distinct from its fermionic counterpart. For example, it exhibits the non-Hermitian skin effect -- its eigenmodes are exponentially localized to the edges of the chain -- even when the system is Hermitian. Such non-Hermitian effects originate from the fact that the dynamics of bosonic quadratic Hamiltonians is governed by a non-Hermitian matrix. In the topological phase of the model, the modes conspire to lead to phase-dependent and directional exponential amplification of a classical drive. In this work, we study the robustness of this topological amplification to on-site dissipations. We examine the effect of uniform and non-uniform losses under various configurations. We find a remarkable resilience to dissipation in some configurations, while in others the dissipation causes a topological phase transition which eliminates the exponential amplification. In particular, when the dissipation is placed on every other site, the system remains topological and the exponential amplification persists even for very large loss rates which exceed the system's non-Hermitian gap. On the other hand, we find that 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 a certain critical value of the dissipation. Our work thus provides insights into the robustness against losses of the topological amplification of non-Hermitian systems and sets explicit limits on the bosonic Kitaev chain's ability to act as a multimode quantum sensor in realistic lossy scenarios.