Confined non-Hermitian skin effect in a semi-infinite Fock-state lattice

TL;DR

This paper explores a novel confined non-Hermitian skin effect in a semi-infinite Fock-state lattice with inhomogeneous coupling, revealing how engineered profiles alter eigenmode localization and quantum state evolution.

Contribution

It analytically demonstrates the confined skin effect caused by inhomogeneous coupling and nonreciprocity, and proposes an experimental scheme using trapped ions.

Findings

Eigenmodes are confined within a finite spatial range.

Probability distribution evolution is doubly confined and skewed.

Engineered coupling profiles enable new quantum state manipulation protocols.

Abstract

In this paper, we investigate the non-Hermitian skin effect in a semi-infinite Fock-state lattice, where the inherent coupling scales as \sqrt{n}. By analytically solving a non-uniform, non-reciprocal SSH model, we demonstrate that the intrinsic inhomogeneous coupling, in combination with nonreciprocity, fundamentally modifies the conventional skin effect. Instead of accumulating at the physical boundary, all eigenmodes become compressed and skewed within a finite spatial range determined by the inhomogeneous profile-a phenomenon we term the confined non-Hermitian skin effect. Consequently, the evolution of the probability distribution on the lattice starting from a single site is doubly confined: it is spatially bounded to a finite range by the inhomogeneous coupling, and further restricted to a one-sided trajectory at the edge of this range by the non-reciprocity. Moreover, a feasible experimental scheme based on a single trapped ion is also proposed. This work reveals how engineered coupling profiles in synthetic dimensions can reshape non-Hermitian properties and enable new protocols for quantum state manipulation.