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arXiv:2602.01625

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

Nobuyuki Okuma

cond-mat.mes-hallcond-mat.mtrl-scicond-mat.quant-gasquant-phSubmitted Feb 2, 2026• Announced Feb 3, 2026
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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.

Comments
8 pages, 4figures, accepted by PRB

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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.
The non-Hermitian skin effect (NHSE), the accumulation of eigen-wave functions at boundaries of open systems, underlies a variety of exotic properties that defy conventional wisdom. While the NHSE and its intriguing impact on band topology and dynamics have been observed in classical or photonic systems, their demonstration in a quantum gas system remains elusive. Here we report the experimental realization of a dissipative Aharonov-Bohm chain-non-Hermitian topological model with NHSE-in the momentum space of a two-component Bose-Einstein condensate. We identify signatures of the NHSE in the condensate dynamics, and perform Bragg spectroscopy to resolve topological edge states against a background of localized bulk states. Our Letter sets the stage for further investigation on the interplay of many-body statistics and interactions with the NHSE, and is a significant step forward in the quantum control and simulation of non-Hermitian physics.
Non-Hermitian physics has emerged as a rapidly advancing field of research, revealing a range of novel phenomena and potential applications. Traditional non-Hermitian Hamiltonians are typically simulated by constructing asymmetric couplings or by introducing dissipation and gain to realize non-Hermitian systems. The quadratic bosonic system (QBS) with squeezing interaction is intrinsically Hermitian; however, its dynamical evolution matrix in both real and momentum spaces is non-Hermitian. Based on this, applying a field-operator transformation xp to the dynamical evolution matrix yields quadrature nonreciprocal transmission between the x and p operators. This nonreciprocal characteristic can be utilized in signal amplifiers. On the other hand, within the Bogoliubov-de Gennes framework in momentum space, one can observe non-Hermitian topological phenomena such as point-gap topology and the non-Hermitian skin effect, both induced by spectra with nonzero winding numbers. Additionally, QBS can be employed to realize non-Hermitian Aharonov-Bohm cages and to extend non-Bloch band theory. Previous studies in non-Hermitian physics have largely concentrated on classical systems. The influence of non-Hermitian properties on quantum effects remains a key issue awaiting exploration and has evolved into a research direction at the interface of non-Hermitian and quantum physics.
The well-established non-Bloch band theory predicts exponential localization of skin-mode eigenstates in one-dimensional (1D) non-Hermitian systems. Recent studies, however, have uncovered anomalous algebraic localization in higher dimensions. Here, we extend these ideas to Hermitian bosonic quadratic Hamiltonians incorporating quantum squeezing, offering a genuine quantum framework to explore non-Hermitian phenomena without external reservoirs. We construct a two-dimensional (2D) bosonic lattice model with two-mode squeezing and study its spectral properties of bosonic excitation within the Bogoliubov-de Gennes (BdG) formalism. We demonstrate an algebraic non-Hermitian skin effect (NHSE), characterized by quasi-long-range power-law localization of complex eigenstates. The system shows ultra spectral sensitivity to double infinitesimal on-site and long-range hopping impurities, while remaining insensitive to single impurities. Analytical treatment via the Green's function reveals that this sensitivity originates from the divergence of the nonlocal Green's function associated with the formation of nonlocal bound states between impurities. Our study establishes a framework for realizing novel higher-dimensional non-Hermitian physics in Hermitian bosonic platforms such as superconducting circuits, photonic lattices, and optomechanical arrays, with the demonstrated ultraspectral sensitivity enabling quantum sensing and amplification via bosonic squeezing.
We propose a novel type of skin effects in non-Hermitian quantum many-body systems that we dub a "non-Hermitian Mott skin effect." This phenomenon is induced by the interplay between strong correlations and the non-Hermitian point-gap topology. The Mott skin effect induces extreme sensitivity to the boundary conditions only in the spin degree of freedom (i.e., the charge distribution is not sensitive to boundary conditions), which is in sharp contrast to the ordinary non-Hermitian skin effect in noninteracting systems. Concretely, we elucidate that a bosonic non-Hermitian chain exhibits the Mott skin effect in the strongly correlated regime by closely examining an effective Hamiltonian. The emergence of the Mott skin effect is also supported by numerical diagonalization of the bosonic chain. The difference between the ordinary non-Hermitian skin effect and the Mott skin effect is also reflected in the time evolution of physical quantities; under the time evolution spin accumulation is observed while the charge distribution remains spatially uniform.
The non-Hermitian skin effect (NHSE), which drives bulk states toward system boundaries, modifies bulk-boundary correspondence and complicates the identification of topological edge modes. Although breaking translational symmetry is known to influence this behavior, a systematic comparison of different structural classes remains limited. Here we investigate periodic, random, and quasiperiodic (Fibonacci) systems using a one-dimensional non-Hermitian quantum walk model. By matching the local scattering parameters in a topologically nontrivial regime, we isolate the role of spatial structure in the presence of the NHSE. We find that periodic systems exhibit pronounced boundary accumulation of bulk states. Random systems suppress this accumulation through Anderson localization, but the topological gap becomes partially filled with localized in-gap states. In contrast, the Fibonacci quasiperiodic system suppresses large-scale boundary accumulation while maintaining a well-defined topological gap. Analysis of the wave functions suggests that the hierarchical quasiperiodic structure fragments bulk states across multiple length scales, thereby mitigating the NHSE. These results identify deterministic quasiperiodicity as a distinct structural regime for controlling non-Hermitian skin dynamics and isolating topological boundary modes.
The interplay between the non-Hermitian skin effect and the imaginary gap of lossy lattices results in the edge burst, a boundary-induced dynamical phenomenon in which an exceptionally large portion of particle loss occurs at the edge. Here, we find that this intriguing non-Hermitian dynamical phenomenon can be exactly mapped into the steady-state density distribution of a corresponding open quantum system. Consequently, the bulk-edge scaling relation of loss probability in the edge burst maps to that of steady-state density. Furthermore, we introduce a many-body open-system model in which the two-body loss generates an interaction-induced non-Hermitian skin effect. Using the positive-PPP method, we demonstrate the validity of the scaling relation for steady-state correlators. These results provide a unique perspective on the interaction-induced many-body non-Hermitian skin effect. Our predictions are testable in state-of-the-art experimental platforms.