Experimental Proposal on Non-Hermitian Skin Effect by Two-dimensional Quantum Walk with a Single Trapped Ion

Abstract

Non-Hermitian Hamiltonians are widely used in describing open systems with gain and loss, among which a key phenomenon is the non-Hermitian skin effect. Here we report an experimental scheme to realize a two-dimensional (2D) discrete-time quantum walk with non-Hermitian skin effect in a single trapped ion. We show the coin and 2D walker states can be labeled in the spin of the ion and the coherent-state lattice of the ion motion, respectively. We numerically observe a directional bulk flow, whose orientations are controlled by dissipative parameters, showing the emergence of the non-Hermitian skin effect. We then discuss an experimental implementation of our scheme in a lasercontrolled trapped Ca+ ion. Our experimental proposal may be applicable to studies of dissipative quantum walk systems, and may be able to generalize to other platforms such as superconducting circuits and atoms in cavity.