Abstract Non-Hermitian (NH) systems and the Lindblad form master equation have always been regarded as reliable tools in dissipative modeling. Intriguingly, existing literature often obtains an equivalent NH Hamiltonian by neglecting the quantum jumping terms in the master equation. However, there lacks investigation into the effects of discarded terms as well as the unified connection between these two approaches. In this study, we study the Su–Schrieffer–Heeger model with collective loss and gain from a topological perspective. When the system undergoes no quantum jump events, the corresponding shape matrix exhibits the same topological properties in contrast to the traditional NH theory. Conversely, the occurrence of quantum jumps can result in a shift in the positions of the phase transition. Our study provides a qualitative analysis of the impact of quantum jumping terms and reveals their unique role in quantum systems.
Abstract Non-Hermitian (NH) systems and the Lindblad form master equation have always been regarded as reliable tools in dissipative modeling. Intriguingly, existing literature often obtains an equivalent NH Hamiltonian by neglecting the quantum jumping terms in the master equation. However, there lacks investigation into the effects of discarded terms as well as the unified connection between these two approaches. In this study, we study the Su–Schrieffer–Heeger model with collective loss and gain from a topological perspective. When the system undergoes no quantum jump events, the corresponding shape matrix exhibits the same topological properties in contrast to the traditional NH theory. Conversely, the occurrence of quantum jumps can result in a shift in the positions of the phase transition. Our study provides a qualitative analysis of the impact of quantum jumping terms and reveals their unique role in quantum systems.
Open quantum systems far from thermal equilibrium can exhibit remarkable physical phenomena including topological properties without a direct equilibrium counterpart. Along these lines, in periodically driven-dissipative systems within the effective non-Hermitian (NH) Hamiltonian approximation spectral winding numbers have been linked to intriguing nonreciprocal transport properties. Here, going beyond an NH Hamiltonian description, we introduce and study a microscopic lattice model of a driven open quantum system described by a Markovian quantum master equation, which exhibits the mentioned spectral winding within an NH approximation. By encompassing quantum jump processes in the topological analysis, we uncover a distinct \emph{jump-induced} topological phase, which qualitatively corresponds to the richer nonreciprocal transport properties of the fully quantum model. In addition, we find that the NH skin effect, i.e., the accumulation of a macroscopic number of eigenstates at one end of the system, is already visible in the transient dynamics even for systems with periodic boundary conditions. Our results exemplify the subtle correspondence between NH topological properties and physical manifestations of Liouvillian topological properties in open quantum systems, thus providing a theoretical framework towards understanding unidirectional transport in quantum dissipative Floquet dynamics.
One possible realization of non-Hermitian systems is based on open quantum systems by omitting quantum jumping terms in the master equation. This is a good approximation at short times where the effects of quantum jumps can be ignored. However, the jumps can affect the long-time dynamics of the system, motivating us to take the jumps into account in these studies. In this paper, by treating the quantum jumps as perturbations, we examine the effect of the quantum jumps on the non-Hermitian system. For this purpose, we first derive an effective Hamiltonian to describe the dynamics of the open quantum system based on the master equation, then expand the eigenstates and eigenenergies up to the first and second order in the quantum jumps. Finally, we apply our theory to a dissipative two-level system and dissipative fermionic superfluids. The effect of the quantum jump on the dynamics and the nonequilibrium phase transition is demonstrated and discussed.
ABSTRACT Recent studies demonstrate that the anharmonicity caused by losses, encoded in the imaginary parts of the eigenvalues of the non‐Hermitian Hamiltonian, can lead to strong photon antibunching, known as the non‐Hermitian photon blockade (NHPB). The non‐Hermiticity of the system might originate from the effective non‐Hermitian Hamiltonian derived from the Lindblad master equation by neglecting the quantum jumping terms. However, neglecting these terms means the system‐environment interactions are not fully considered, leading to features missed in the blockade effect. This motivates us to study the effects of these jumps on NHPB. In this work, we employ the effective Hamiltonian approach to the master equation to investigate the blockade effect. This approach treats the jumping terms as perturbations, making the analysis clear. We show that jumps can increase the relative second‐order correlation () and weaken the blockade. This highlights that quantum jumps can degrade the strong photon antibunching. Furthermore, we demonstrate that this feature can be attributed to the joint effect of the reduction in both the second‐order correlation () and the intensity (), which can be interpreted as jump‐induced changes in the mean photon numbers in the steady state.
We investigate a non-Hermitian quantum battery based on the Su-Schrieffer-Heeger (SSH) lattice, charged through a parity-time (PT)-symmetric protocol that alternates gain and loss between the two sublattices. The interplay between lattice topology and non-Hermiticity gives rise to both bulk and edge exceptional points (EPs), which govern the charging dynamics. In the topological regime, an edge-state EP appears at a smaller gain-loss strength than the bulk thresholds and gives rise to an additional edge-broken regime absent in the trivial configuration. This topology-specific spectral structure is reflected in the charging dynamics, where the topological phase exhibits more favorable transient and long-time performance in the representative non-Hermitian regimes considered here. We further examine the corresponding Lindblad dynamics, identifying the non-Hermitian model as the conditional no-jump description of the same gain-loss processes. The Lindblad results show that the topological advantage remains visible at the level of stored energy, extractable work, and extractable fraction under unconditional open-system evolution. These findings demonstrate that topology constitutes a genuine physical resource for enhancing the performance of quantum batteries.
The Lindblad master equation (LME) describing the Markovian dynamics of the quantum open system can be understood as the evolution of the effective non-Hermitian Hamiltonian balanced with random quantum jumps. Here we investigate the balance-breaking dynamics by partly eliminating jumps from postselection experiments. To describe this dynamics, a nonlinear Lindblad master equation (NLME) is derived from the quantum trajectory method. However, the NLME shows significant advantages in analytical analysis over the quantum trajectory method. Using the NLME, we classify the dynamics into two classes. In the trivial class, the process of reducing jumps is completely equivalent to weakening the coupling from the environment. In contrast, the nontrivial class presents more complex dynamics. We study a prototypical model within this class and demonstrate the existence of the postselected skin effect whose steady state is characterized by the accumulation of particles on one side. The steady-state distribution can be fitted by a scale-invariant tanh function which is different from the uniform distribution of LME. Furthermore, the NLME can give a reasonable framework for studying the interplay and competition between the non-Hermitian Hamiltonians and dissipative terms. We show this by capturing the characteristics of the trajectory-averaged entanglement entropy influenced by non-Hermitian skin effect and Zeno effect in the model of postselected skin effect.
We investigate quantum correlations and entanglement in a non-Hermitian quantum system modeled by a 2D stacked Su–Schrieffer–Heeger (SSH) lattice incorporating nonreciprocal hopping amplitudes and balanced on-site gain and loss. Focusing on the interplay between non-Hermiticity, topology, and open-boundary conditions, we analyze how these factors shape bipartite entanglement properties, characterized through the entanglement spectrum and entanglement negativity ( E N ). By examining the complex energy spectrum under open boundary conditions, we identify critical points associated with the closing of complex energy gaps, which significantly influence entanglement structure and signal topological phase transitions. Our findings reveal that boundary-localized non-Bloch modes and nonreciprocal couplings can induce highly tunable and unconventional entanglement features, absent under periodic boundary conditions. These results highlight the breakdown of conventional bulk-boundary correspondence and underscore the utility of entanglement measures in diagnosing non-Hermitian topological phases. Beyond advancing the fundamental understanding of quantum correlations in open systems, our study suggests potential pathways to engineer quantum devices and topological materials where gain, loss, and nonreciprocity are intrinsic elements.