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Non-Hermitian skin effect (NHSE) and nonlinearity can each delocalize topological zero modes (TZMs) from the boundary. To overcome the challenge of precise parameter tuning imposed by the NHSE-induced delocalization and to enhance the capacity of TZMs limited by nonlinearity-induced partial delocalization in Hermitian systems, we develop non-Hermitian nonlinear topological interface models. This model consists of both Hermitian and non-Hermitian Su-Schrieffer-Heeger (SSH) chains, incorporating nonreciprocal hopping and nonlinearity. When the nonlinearity is applied to both chains, the TZM becomes fully delocalized, extending across the entire lattice of two chains without the need for precise parameter tuning. By adjusting nonlinear coefficients in both chains, the wavefunction profile and plateaus across the entire lattice can be effectively controlled and customized through inherent configuration and intensity of the nonlinearity. Furthermore, the spectral localizer is utilized to demonstrate the topological protection of these extended non-Hermitian TZMs, confirming their robustness against disorder. Their dynamical stability under external pumping is also validated. Our findings provide a deeper insight into how nonlinearity and NHSE affect the behavior of topological modes, opening new possibilities for enhancing their capacity and performance in compact devices., Comment: 5 figures in the main text

Non-Hermitian skin effects (NHSEs) have recently been investigated extensively at the single-particle level. When many-body interactions become dominant, novel non-Hermitian physical phenomena can emerge. In this work, we theoretically study NHSEs controlled by dissipation and interaction. We consider a 1D zigzag Bose-Hubbard lattice, subject to magnetic flux, staggered onsite single-particle loss, and uniform onsite two-particle loss. When the two-particle loss is small, two-body bound eigenstates (i.e., doublons) are all localized at the same boundary due to the interplay of the magnetic flux and staggered single-particle loss. While, for strong two-particle loss, the localization direction of doublons is unexpectedly reversed. This is attributed to the effective strong nonreciprocal hopping of doublons contributing from the virtual second-order and third-order hopping processes of particle pairs in combination with the magnetic flux, the strong two-particle loss, and the many-body interaction. Moreover, a two-particle gain can induce the same skin-localization of doublons, which can be utilized to dynamically observe the NHSE and its reversal of doublons controlled by interactions. Our results open up a new avenue for exploring novel non-Hermitian phenomena in many-body systems., Comment: 16 pages, 9 figures; Comments are welcome

The interplay of quantum emitters and non-Hermitian structured baths has received increasing attention in recent years. Here, we predict unconventional quantum optical behaviors of quantum emitters coupled to a non-Hermitian topological bath, which is realized in a 1D Su-Schrieffer-Heeger photonic chain subjected to nonlocal dissipation. In addition to the Hermitian-like chiral bound states in the middle line gap and skin-mode-like hidden bound states inside the point gap, we identify peculiar in-gap chiral and extended photon-emitter dressed states. This is due to the competition of topological-edge localization and non-Hermitian skin-mode localization in combination with the non-Bloch bulk-boundary correspondence. Furthermore, when two emitters are coupled to the same bath, such in-gap dressed states can mediate the nonreciprocal long-range emitter-emitter interactions, with the interaction range limited only by the dissipation of the bath. Our work opens the door to further study rich quantum optical phenomena and exotic many-body physics utilizing quantum emitters coupled to non-Hermitian topological baths., Comment: 22 pages, 10 figures; Comments are welcome

The non-Hermitian skin effect (NHSE), featured by the collapse of bulk-band eigenstates into the localized boundary modes of the systems, is one of most striking properties in the fields of non-Hermitian physics. Unique physical phenomena related to the NHSE have attracted a lot of interest, however, their experimental realizations usually require nonreciprocal hopping, which faces a great challenge in ultracold-atom systems. In this work, we propose to realize the NHSE in a 1D optical lattice by periodically-driven ultracold atoms in the presence of staggered atomic loss. By studying the effective Floquet Hamiltonian in the high-frequency approximation, we reveal the underlying mechanism for the periodic-driving-induced the NHSE. We found that the robust NHSE can be tuned by driving phase, which is manifested by the dynamical localization. Most remarkably, we uncover the periodic-driving-induced critical skin effect for two coupled chains with different driving phases, accompanied by the appearance of size-dependent topological in-gap modes. Our studies provide a feasible way for observing the NHSE and exploring corresponding unique physical phenomena due to the interplay of non-Hermiticity and many-body statistics in ultracold-atom systems., Comment: 10 pages, 9 figures