Edge burst is a phenomenon in non-Hermitian quantum dynamics discovered by a recent numerical study [Phys. Rev. Lett. 128, 120401 (2022)]. It finds that a large proportion of particle loss occurs at the system boundary in a class of non-Hermitian quantum walk. In this paper, we investigate the evolution of real-space wave functions for this lattice system. We find the wave function of the edge site is distinct from the bulk sites. Using time-dependent perturbation theory, we derive the analytical expression of the real-space wave functions and find that the different evolution behaviors between the edge and bulk sites are due to their different nearest-neighbor site configurations. We also find the edge wave function primarily results from the transition of the two nearest-neighbor nondecay sites. Besides, the numerical diagonalization shows the edge wave function is mainly propagated by a group of eigenmodes with a relatively large imaginary part. Our work provides an analytical method for studying non-Hermitian quantum dynamical problems.
Edge burst is a phenomenon in non-Hermitian quantum dynamics discovered by a recent numerical study [Phys. Rev. Lett. 128, 120401 (2022)]. It finds that a large proportion of particle loss occurs at the system boundary in a class of non-Hermitian quantum walk. In this paper, we investigate the evolution of real-space wave functions for this lattice system. We find the wave function of the edge site is distinct from the bulk sites. Using time-dependent perturbation theory, we derive the analytical expression of the real-space wave functions and find that the different evolution behaviors between the edge and bulk sites are due to their different nearest-neighbor site configurations. We also find the edge wave function primarily results from the transition of the two nearest-neighbor nondecay sites. Besides, the numerical diagonalization shows the edge wave function is mainly propagated by a group of eigenmodes with a relatively large imaginary part. Our work provides an analytical method for studying non-Hermitian quantum dynamical problems.
We unveil an unexpected non-Hermitian phenomenon, dubbed edge burst, in non-Hermitian quantum dynamics. Specifically, in a class of non-Hermitian quantum walk in periodic lattices with open boundary condition, an exceptionally large portion of loss occurs at the system boundary. The physical origin of this edge burst is found to be an interplay between two unique non-Hermitian phenomena: non-Hermitian skin effect and imaginary gap closing. Furthermore, we establish a universal bulk-edge scaling relation underlying the non-Hermitian edge burst. Our predictions are experimentally accessible in various non-Hermitian systems including quantum-optical and cold-atom platforms.
The non-Hermitian skin effect, by which the eigenstates of the Hamiltonian are predominantly localized at the boundary, has revealed a strong sensitivity of non-Hermitian systems to the boundary condition. Here we experimentally observe a striking boundary-induced dynamical phenomenon known as the non-Hermitian edge burst, which is characterized by a sharp boundary accumulation of loss in non-Hermitian time evolutions. In contrast to the eigenstate localization, the edge burst represents a generic non-Hermitian dynamical phenomenon that occurs in real time. Our experiment, based on photonic quantum walks, not only confirms the prediction of the phenomenon, but also unveils its complete space-time dynamics. Our observation of edge burst paves the way for studying the rich real-time dynamics in non-Hermitian topological systems.
In a class of non-Hermitian quantum walk in lossy lattices with open boundary conditions, an unexpected peak in the distribution of the decay probabilities appears at the edge, referred to as an edge burst. It is proposed that the edge burst originates jointly from the non-Hermitian skin effect (NHSE) and the imaginary gaplessness of the spectrum [W.-T. Xue et al., Phys. Rev. Lett. 128, 120401 (2022)]. Using a particular one-dimensional lossy lattice with a nonuniform loss rate, we show that the edge burst can occur even in the absence of skin localizations. Furthermore, we discuss that the edge burst may not appear if the spectrum satisfies the imaginary gapless condition. Aside from its fundamental importance, by removing the restrictions on observing the edge burst effect, our results open the door to broader design space for future applications of the edge burst effect.
In quantum mechanics, the Hermitian Hamiltonian is generally used to describe the ideal closed quantum system, but in reality, the physical system is closely related to the environment, and the open quantum system coupled to the environment can be described by the equivalent non-Hermitian Hamiltonian to a certain extent. Among them, the dissipation intensity is closely related to the dynamic properties of non-Hermitian quantum systems. Therefore, it is of great practical significance to study how dissipation affects particle loss. In this paper, the dynamic law related to dissipation intensity in a one-dimensional non-Hermitian system under open boundary condition is studied, and it is found that dissipation can induce the recurrence of edge burst. After the time-dependent evolution of the particles in the one-dimensional non-Hermitian dissipative lattice system with open boundary condition, there is an edge burst in the system, that is, there is a large probability of particle loss at the edge, and the edge burst disappears after increasing the intracell hopping. It is found that if the dissipation intensity increases or decreases, the edge burst will reappear. This kind of reappearance is different from the original edge burst, which is mainly manifested in the loss probability distribution of particles from the edge distribution to the bulk distribution, which is due to the difference in probability of particle motion direction between the two cases. Under the re-induced edge burst, the particles move leftward and rightward from their initial positions, and rebound from the left after having reached the boundary, forming a more obvious loss probability at the edge and gradually decreasing to the body area. In the original edge burst, the particles only move to the left with a greater probability, and are ‘trapped’ at the edge to completely dissipated, forming a distribution with an independent loss peak at the edge. The movement to the left is due to the non-Hermitian skin effect. The deeper reason for different movement directions is related to parity-time symmetry. Under the parameter near the parity-time symmetry breaking point, the loss probability of the particle is of unilateral distribution, and the loss probability of the particle moving to both sides is of bilateral distribution when it is far away. This is the description of the dissipation-induced edge burst recurrence phenomenon and its characteristics. In addition, this paper also studies the influence of impurity barrier on the probability distribution of particle loss in non-Hermitian dynamics. The results show that placing a small barrier on the non-dissipative A-site can obviously hinder the particle motion, and when the barrier increases to a certain height, its influence on the particle motion tends to be unchanged. And the barrier at the dissipative B lattice has little effect on the dynamics.
Non-Hermitian quantum walks on lossy lattices with open boundaries can exhibit an anomalous peak of the loss probability at the boundary, known as the non-Hermitian edge burst (NHEB). This phenomenon has been attributed to the combined effect of the non-Hermitian skin effect (NHSE) and a gapless imaginary spectrum. Here we investigate a class of models in which the NHSE is induced by magnetic flux while the loss is spatially nonuniform. We show that the spatial distribution of loss plays a crucial role in determining the emergence and strength of the NHEB. Notably, even in the absence of the NHSE, a weak boundary accumulation of the loss probability persists. We term this effect a quasi-non-Hermitian edge burst (quasi-NHEB). By analyzing the dependence of the loss probability on the initial position, we further demonstrate that the quasi-NHEB obeys a bulk-edge scaling relation distinct from that of conventional NHEB. Our results show that spatially nonuniform loss alone can generate boundary-localized loss anomalies even without the NHSE, providing new insight into non-Hermitian boundary phenomena and a broader platform for their exploration and potential applications.