We investigate quantum dynamics of a quantum walker on a finite bipartite non-Hermitian lattice, in which the particle can leak out with certain rate whenever it visits one of the two sublattices. Quantum walker initially located on one of the non-leaky sites will finally totally disappear after a length of evolution time and the distribution of decay probability on each unit cell is obtained. In one regime, the resultant distribution shows an expected decreasing behavior as the distance from the initial site increases. However, in the other regime, we find that the resultant distribution of local decay probability is very counterintuitive, in which a relatively high population of decay probability appears on the edge unit cell which is the farthest from the starting point of the quantum walker. We then analyze the energy spectrum of the non-Hermitian lattice with pure loss, and find that the intriguing behavior of the resultant decay probability distribution is intimately related to the existence and specific property of the edge states, which are topologically protected and can be well predicted by the non-Bloch winding number. The exotic dynamics may be observed experimentally with arrays of coupled resonator optical waveguides.
We investigate quantum dynamics of a quantum walker on a finite bipartite non-Hermitian lattice, in which the particle can leak out with certain rate whenever it visits one of the two sublattices. Quantum walker initially located on one of the non-leaky sites will finally totally disappear after a length of evolution time and the distribution of decay probability on each unit cell is obtained. In one regime, the resultant distribution shows an expected decreasing behavior as the distance from the initial site increases. However, in the other regime, we find that the resultant distribution of local decay probability is very counterintuitive, in which a relatively high population of decay probability appears on the edge unit cell which is the farthest from the starting point of the quantum walker. We then analyze the energy spectrum of the non-Hermitian lattice with pure loss, and find that the intriguing behavior of the resultant decay probability distribution is intimately related to the existence and specific property of the edge states, which are topologically protected and can be well predicted by the non-Bloch winding number. The exotic dynamics may be observed experimentally with arrays of coupled resonator optical waveguides.
We analyze a quantum walk on a bipartite one-dimensional lattice, in which the particle can decay whenever it visits one of the two sublattices. The corresponding non-Hermitian tight-binding problem with a complex potential for the decaying sites exhibits two different phases, distinguished by a winding number defined in terms of the Bloch eigenstates in the Brillouin zone. We find that the mean displacement of a particle initially localized on one of the nondecaying sites can be expressed in terms of the winding number, and is therefore quantized as an integer, changing from zero to one at the critical point. We show that the topological transition is relevant for a variety of experimental settings. The quantized behavior can be used to distinguish coherent from incoherent dynamics.
Abstract The non-Hermitian skin effect and edge burst reflect the vital role of spatial boundaries in non-Hermitian systems from both static and dynamic perspectives. In this study, we investigate a non-Hermitian dissipative lattice with nonlocal coupling and demonstrate many interesting static and dynamic phenomena. In the case of global coupling with all sites coupled with each other, we observe anomalous hopping resonance, where a quantum walker initially placed at a single site almost completely escapes from the boundary of the system regardless of its initial position. In the case of non-global coupling, which is infinite-range coupling, the interplay between nonlocal hopping and the non-Hermitian skin effect results in the emergence of local bulk modes exhibiting a multipartite density distribution. The presence of local bulk modes induces the nontrivial dynamics of a quantum walker, which features multiple peaks of lost probability in spatially separated domains. Our findings demonstrate unique properties induced by nonlocal coupling in non-Hermitian systems.
The phenomenon of localization usually happens due to the existence of disorder in a medium. Nevertheless, certain quantum systems allow dynamical localization solely due to the nature of internal interactions. We study a discrete time quantum walker which exhibits disorder-free localization. The quantum walker moves on a one-dimensional lattice and interacts with on-site spins by coherently rotating them around a given axis at each step. Since the spins do not have dynamics of their own, the system poses the local spin components along the rotation axis as an extensive number of conserved moments. When the interaction is weak, the spread of the walker shows subdiffusive behavior having downscaled ballistic tails in the evolving probability distribution at intermediate timescales. However, as the interaction gets stronger the walker gets completely localized in total absence of disorder in both lattice and initial state. Using a matrix-product-state ansatz, we investigate the relaxation and entanglement dynamics of the on-site spins due to their coupling with the quantum walker. Surprisingly, we find that, even in the delocalized regime, entanglement growth and relaxation occur slowly, unlike majority of the other models displaying a localization transition.
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.
One-dimensional topological insulators are characterized by edge states with exponentially small energies. According to one generalization of topological phase to non-Hermitian systems, a finite system in a nontrivial topological phase displays surface states with exponentially long lifetimes. In this work we explore the possibility of exploiting such non-Hermitian topological phases to enhance the quantum coherence of a fiducial qubit embedded in a dissipative environment. We first show that a network of qubits interacting with lossy cavities can be represented, in a suitable super-one-particle sector, by a non-Hermitian ``Hamiltonian'' of the desired form. We then study, both analytically and numerically, one-dimensional geometries with up to three sites per unit cell and up to a topological winding number W=2. For finite-size systems the number of edge modes is a complicated function of W and the system size N. However, we find that there are precisely W modes localized at one end of the chain. In such topological phases the qubit's coherence lifetime is exponentially large in the system size. We verify that for W>1, at large times, the Lindbladian evolution is approximately a nontrivial unitary. For W=2 this results in Rabi-like oscillations of the qubit's coherence measure.
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.