Steady-state skin effect in bosonic topological edge states under parametric driving

TL;DR

The work shows that a steady-state non-Hermitian skin effect can be realized in bosonic BdG systems by introducing parametric driving into edge states of a bosonic Chern insulator, without relying on dissipation. Using non-equilibrium Green's function methods, the authors demonstrate corner-localized accumulation and quadrature-anisotropic squeezing in the steady state under open boundary conditions, with the skin effect tied to boundary-driven spectral winding and symmetry considerations. The approach leverages the intrinsic non-Hermiticity of bosonic BdG Hamiltonians, providing a bridge between non-Hermitian spectral theory and concrete quantum platforms. These results offer a route to observe bosonic skin phenomena in photonic, magnonic, or phononic systems and raise questions about stability under perturbations and interactions in nonequilibrium settings.

Abstract

Non-Hermitian systems have attracted significant theoretical interest due to their extreme properties. However, realizations have mostly been limited to classical applications or artificial setups. In this study, we focus on the quantum nature inherent in bosonic Bogoliubov-de Gennes (BdG) systems, which from the perspective of spectral theory corresponds to non-Hermiticity. Based on this insight, we propose a steady-state skin effect in quantum condensed matter utilizing such BdG non-Hermiticity. Specifically, we introduce BdG quantum terms arising from parametric pumping to the edge states of an underlying bosonic Hermitian Chern insulator, thereby realizing non-Hermiticity without dissipation. This system design has the advantage of being largely independent of microscopic model details. Through analysis using non-equilibrium Green's functions, we find that under open boundary conditions, a steady state exhibiting the non-Hermitian skin effect is realized. The pronounced corner particle accumulation observed in this steady state shows quadrature anisotropy, which manifests the bosonic quantum nature. Our results bridge the gap between the fascinating mathematics of non-Hermitian matrices and practical quantum physical systems.

Figures (4)

• Figure 1: Schematic illustration of the non-Hermitian skin effects. Left panel: Relationship between spectral winding and the skin effect. Right panel: the skin effect on chiral edge states with edge-dependent dissipation.
• Figure 2: Non-Hermitian skin effect in bosonic chiral edge states under parametric driving. (a) Complex spectra and skin modes in the presence of the unitary symmetry (\ref{['unitary-sym']}). (b) Complex spectra under symmetry-breaking term. (c) Complex spectra and skin modes under one-edge driving at $y=1$.
• Figure 3: Steady-state accumulation caused by non-Hermitian skin effect. Left panel: Eigenspectra of the effective Hamiltonians and steady-state accumulation of $a$ bosons. Right panel: Spatial distribution of quadrature fluctuations, $\langle x^2_{i,\theta}\rangle$. The sublattice positions are plotted as (0,0) and (1/2,1/2) in each unit cell. For both one-edge and two-edge driving, the parameters are set as $L_x=L_y=16$, $\Delta=0.2$, $\epsilon=0$, and $\Gamma=0.12$.
• Figure 4: Complex energy spectra for different (a) perturbation strengths $(L_x\times L_y=16\times16)$ and (b) system sizes ($\epsilon=0.01$).