Abstract Quantum walks hold enormous potential applications in various areas such as quantum computing and quantum simulation. Discrete-time quantum walks on a ladder offer greater prospects compared to traditional quantum walks, especially in addressing physical problems in higher-dimension coupled systems. Here we give an experimental proposal of quantum walks on a two-leg ladder using linear optics, and further apply it to non-Hermitian systems by introducing loss-based non-unitary evolutions. Non-Hermitian systems under nonreciprocity-induced evolution present an exotic phenomenon, known as the non-Hermitian skin effect (NHSE). In a two-leg non-Hermitian system with the same preferred direction of NHSE, the direction has recently been found to reverse when interchain couplings are introduced. Based on quantum walks on a ladder, we also propose an experimentally feasible scheme to demonstrate the direction reversal of NHSE. Through the simulated results we show that particles on each chain accumulate to the preferred boundary driven by nonreciprocal hopping, while particles are transported in the opposite direction when interchain hopping is allowed, clearly demonstrating the existence of reversed NHSE. Our work further expands the application of the quantum walk platform and opens a door for the experimental investigation of reversed NHSE.
Abstract Quantum walks hold enormous potential applications in various areas such as quantum computing and quantum simulation. Discrete-time quantum walks on a ladder offer greater prospects compared to traditional quantum walks, especially in addressing physical problems in higher-dimension coupled systems. Here we give an experimental proposal of quantum walks on a two-leg ladder using linear optics, and further apply it to non-Hermitian systems by introducing loss-based non-unitary evolutions. Non-Hermitian systems under nonreciprocity-induced evolution present an exotic phenomenon, known as the non-Hermitian skin effect (NHSE). In a two-leg non-Hermitian system with the same preferred direction of NHSE, the direction has recently been found to reverse when interchain couplings are introduced. Based on quantum walks on a ladder, we also propose an experimentally feasible scheme to demonstrate the direction reversal of NHSE. Through the simulated results we show that particles on each chain accumulate to the preferred boundary driven by nonreciprocal hopping, while particles are transported in the opposite direction when interchain hopping is allowed, clearly demonstrating the existence of reversed NHSE. Our work further expands the application of the quantum walk platform and opens a door for the experimental investigation of reversed NHSE.
The non-Hermitian skin effect (NHSE), referring to the anomalous localization of eigenstates, has been widely discussed in single-particle systems. However, the interplay between the interacting NHSE and the quantum optical phenomena remains elusive. Here, We present the non-Hermitian quantum walks of strongly correlated photon pairs. Through studying the dynamic behavior of the photon pairs in the nonreciprocal Bose-Hubbard chain, we theoretically demonstrate the interplay between interactions and the NHSE. When launching two non-entangled photons, the photons exhibit the nonreciprocal bunching effect, which can be suppressed by the interactions. When launching two path-entangled photons, the interactions can not only suppress but reverse the nonreciprocal bunching. In stark contrast to the common wisdom that the NHSE suppresses the entanglement of the quantum many-body system, the entanglement of the photons here can be significantly enhanced. Our results reveal that many-body interactions and entanglement significantly restrain the non-Hermitian nonreciprocal quantum dynamics, offering insights into the interplay between many-body quantum entanglement and non-Hermitian physics. The non-Hermitian skin effect, which nonreciprocally accumulates particles at the boundary, generally suppresses entanglement by constraining global correlations. Here, the authors demonstrate that interactions can suppress nonreciprocal bunching, while entangled photons can reverse bunching direction, leading to enhanced entanglement.
Non-Hermitian systems under nonreciprocity-induced evolution present an exotic phenomenon, known as the non-Hermitian skin effect. Yet, the control mechanisms and the generalized Brillouin zone in disordered systems have not been fully understood. Here, using Floquet quantum-walk models with disorder, we demonstrate effective control of the direction of the non-Hermitian skin effect in both one- and two-dimensional systems. Once the disorder strength exceeds a critical threshold, the direction of the skin effect is reversed. We develop a modified generalized Brillouin zone theory that correctly predicts skin effect reversal. Furthermore, we also investigate how the direction of the non-Hermitian skin effect depends on the disorder strength in each subsystem of the two-dimensional quantum walk. Our work paves the way for the design of quantum transport devices in quantum simulation platforms.
We investigate the non-Hermitian skin effect (NHSE) and topological phases in a ladder model with staggered nonreciprocal inter-leg hopping, consisting of an Su-Schrieffer-Heeger (SSH) chain coupled to a normal tight-binding chain. By tuning the system parameters, we show that the direction of the NHSE under open boundary conditions can be reversed and can even become energy dependent. The NHSE is further characterized by the spectral winding number under periodic boundary conditions. We further demonstrate that the inter-leg coupling significantly enlarges the topologically nontrivial parameter regime. Remarkably, the zero-energy topological edge modes reside on different legs of the ladder and are characterized by real-space winding numbers W=±1. Furthermore, increasing the nonreciprocity of the inter-leg hopping modifies the topological phase boundaries and eventually drives the system into a topologically trivial phase. Our results establish staggered nonreciprocal inter-leg hopping as an effective mechanism for engineering both the non-Hermitian skin effect and topological phases in ladder systems.
Decoherence and dissipation, arising from unavoidable interactions with the environment, can exert a dual influence on transport in physical systems, suppressing coherent propagation while inducing diffusion and mitigating localization in disordered systems. Non-Hermitian physics reveals a qualitatively different scenario, in which structured dissipation can induce directional bulk-to-boundary transport, known as the non-Hermitian skin effect (NHSE), that remains robust against disorder. Whether such transport can persist, be enhanced or hindered under decoherence, remains a largely open question. Here we experimentally address this question using photonic quantum walks with two tunable prototypical decoherence channels, dephasing and amplitude damping. Under dephasing, the NHSE survives up to the fully incoherent regime and is observed to even be enhanced by dephasing, yielding drift velocities that exceed those of coherent dynamics. By contrast, amplitude damping shows a pronounced order dependence: applied before the non-Hermitian loss operator, it suppresses and ultimately eliminates the NHSE in the fully incoherent limit; applied afterward, the NHSE persists and can be enhanced at sufficiently large loss strengths. Our work bridges quantum and classical non-Hermitian dynamics, demonstrates the resilience of the NHSE to decoherence, and opens avenues for harnessing decoherence to enhance directional transport in noisy, nonequilibrium systems.
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. It is shown that 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 laser-controlled trapped Ca+ ion. Our experimental proposal may be applicable to research of dissipative quantum walk systems and may be able to generalize to other platforms, such as superconducting circuits and atoms in cavity.
A distinctive feature of non-Hermitian systems is the skin effect, which has recently attracted widespread attention. Quantum walks provide a powerful platform for investigating the underlying mechanisms of the non-Hermitian skin effect. Additionally, hybrid entanglement generation in quantum walks is recognized as another crucial property. However, experimentally investigating the influence of skin effect on the evolution of entanglement dynamics in the non-Hermitian systems remains a challenge. In this paper, we present a flexible implementation of 20-step discrete-time quantum walks using an optimized time-multiplexed loop configuration. By optimizing the coin parameter, we achieve maximal coin-position entanglement after 20-step quantum walks. Moreover, we experimentally measure the polarization-averaged growth rates and the evolution of coin-position entanglement under specific coin and loss parameters. We observe the asymmetric Lyapunov exponent profiles and the entanglement suppression induced by the non-Hermitian skin effect. Interestingly, this entanglement suppression weakens with increasing coin parameters and enhances with increasing loss parameters and evolution steps. Our results demonstrate the potential of quantum walks as a powerful platform for investigating hybrid entanglement properties and skin effects in non-Hermitian systems.