The exploration of the effect of non-Hermitian (NH) in quantum systems is gaining renewed momentum as a result of the recent progress in experiments. It has been indicated that the ability to engineer the orders of exceptional points (EPs) can be fundamental to its applications in quantum control, such as accelerating entanglement generation; however, an initial survey of the interactions between different orders of EPs is still missing. In this work, we try to partially address this issue by employing a non-reciprocally coupled cavity system which can be experimentally realizable with a two-dimensional reconfigurable NH gauged laser array. With deliberate design, our systems display both second and third orders of EPs. The sign of a novel, purely quantum continuous entanglement phase transition is observed, which reveals how multi-EP interactions alter entanglement dynamics across different regimes while maintaining accelerated generation. Our findings reveil the genuinely quantum NH physics of higher-order EPs, which has opened up a new avenue for future investigations of the higher-order degeneracy application and the dynamic phase transitions of quantum systems.
The exploration of the effect of non-Hermitian (NH) in quantum systems is gaining renewed momentum as a result of the recent progress in experiments. It has been indicated that the ability to engineer the orders of exceptional points (EPs) can be fundamental to its applications in quantum control, such as accelerating entanglement generation; however, an initial survey of the interactions between different orders of EPs is still missing. In this work, we try to partially address this issue by employing a non-reciprocally coupled cavity system which can be experimentally realizable with a two-dimensional reconfigurable NH gauged laser array. With deliberate design, our systems display both second and third orders of EPs. The sign of a novel, purely quantum continuous entanglement phase transition is observed, which reveals how multi-EP interactions alter entanglement dynamics across different regimes while maintaining accelerated generation. Our findings reveil the genuinely quantum NH physics of higher-order EPs, which has opened up a new avenue for future investigations of the higher-order degeneracy application and the dynamic phase transitions of quantum systems.
Non-Hermitian systems have attracted significant interest because of their intriguing properties, including exceptional points (EPs), where eigenvalues and the corresponding eigenstates coalesce. In particular, quantum systems with EPs exhibit an enhanced sensitivity to external perturbations, which increases with the order of the EP. Therefore, higher-order EPs hold significant potential for advanced sensing applications, but they are challenging to achieve due to stringent symmetry requirements. In this work, we study the dynamics of a generalized lossy waveguide beam splitter with asymmetric coupling by introducing non-reciprocity as a tunable parameter to achieve higher-order EPs even without dissipation. Moreover, we analyze the evolution of NOON-states under activated non-reciprocity, highlighting its impact on quantum systems. Our results open new pathways for realizing higher-order EPs in non-reciprocal open quantum systems.
As a most important feature of non-Hermitian systems, exceptional points (EPs) lead to a variety of unconventional phenomena and applications. Here, we study a generic model composed of two coupled non-Hermitian qubits; the EPs can be easily obtained in this system by adjusting the driving amplitude applied to the qubits. The diverse entanglement dynamics on the two sides of the original fourth-order EP ($\mathrm{EP}{4}^{\ensuremath{'}}$) and second-order EP (EP2) can be observed simultaneously in the weak coupling regime. With the increase of the coupling strength, the $\mathrm{EP}{4}^{\ensuremath{'}}$ is replaced by an additional EP2, leading to the disappearance of the entanglement dynamics change induced by $\mathrm{EP}{4}^{\ensuremath{'}}$ in the strong coupling regime. Considering the case of Ising-type interaction, we also realize EP-induced entanglement dynamics changing without the driving field. Our study paves the way for the investigation of EP-induced quantum effects and applications of EP-related quantum technologies.
Exceptional points (EPs), arising in non-Hermitian systems, have garnered significant attention in recent years, enabling advancements in sensing, wave manipulation, and mode selectivity. However, their role in quantum systems, particularly in influencing quantum correlations, remains underexplored. In this work, we investigate how EPs control multimode entanglement in bosonic chains. Using a Bogoliubov-de Gennes (BdG) framework to describe the Heisenberg equations, we identify EPs of varying orders and uncover spectral transitions between purely real, purely imaginary, and mixed eigenvalue spectra. These spectral regions, divided by EPs, correspond to three distinct entanglement dynamics: oscillatory, exponential, and hybrid. Remarkably, we demonstrate that higher-order EPs, realized by non-integer-pi hopping phases or nonuniform interaction strengths, significantly enhance the degree of multimode entanglement compared to second-order EPs. Our findings provide a pathway to leveraging EPs for entanglement control and exhibit the potential of non-Hermitian physics in advancing quantum technologies.
The appearance of topological singularities, namely exceptional points (EPs) is an intriguing feature of parameter-dependent open quantum or wave systems. EPs are the special type of nonHermitian degeneracies where two (or more) eigenstates of the underlying system coalesce. In this paper, we present a three level non-Hermitian Hamiltonian which hosts three interacting eigenstates. The matrix elements are optimized in such a way that the intermediate eigenstate interacts with both the other states and the underlying system hosts at least two different second order EPs. The impact of quasi-static parameter variation along a cyclic contour around the embedded EPs on the dynamics of interacting eigenvalues is well investigated in the context of cascaded state conversion. Such dynamics of the eigenvalues shows a clear signature of the third order EP with a combined effect of both the second order EPs. Moreover, we examine the accumulation of phases around the identified EPs and study the hallmark of phase exchange during cascaded state conversions accompanied by the parametric encirclement of the third order EP.
Exceptional points (EPs) are non-Hermitian spectral singularities exhibiting fractional-power responses, yet their implications for multipartite entanglement of interacting quantum many-body systems remain largely unexplored. Here we develop a general framework that links higher-order non-Hermitian degeneracies to the scaling behavior of genuine multipartite entanglement in interacting identical-qubit systems. Permutation symmetry of the identical qubits decomposes the exponentially large Hilbert space into independent irreducible-representation sectors, thereby constraining the maximal EP order of N qubits to N+1 rather than 2N. Near an nth-order EP, genuine multipartite entanglement inherits the spectral response and generically exhibits a fractional-power scaling under weak perturbations. Explicit examples show that conventional two-body interactions support third- and fourth-order EPs with the corresponding entanglement responses, whereas higher-order EPs with genuine multipartite-entangled coalesced states require additional independent interaction channels, such as three-body interactions. Our results establish a fundamental connection among non-Hermitian degeneracies, multipartite entanglement, and symmetry, extending higher-order EP physics from spectral singularities to genuine many-body quantum correlations.
Exceptional points (EPs), arising in non-Hermitian systems, have garnered significant attention in recent years, enabling advancements in sensing, wave manipulation, and mode selectivity. However, their role in quantum systems, particularly in influencing quantum correlations, remains underexplored. In this work, we investigate how EPs control multimode entanglement in bosonic chains. Using a Bogoliubov-de Gennes (BdG) framework to describe the Heisenberg equations, we identify EPs of varying orders and uncover spectral transitions between purely real, purely imaginary, and mixed eigenvalue spectra. These spectral regions, divided by EPs, correspond to three distinct entanglement dynamics: oscillatory, exponential, and hybrid. Remarkably, we demonstrate that higher-order EPs, realized by non-integer-pi hopping phases or nonuniform interaction strengths, significantly enhance the degree of multimode entanglement compared to second-order EPs. Our findings provide a pathway to leveraging EPs for entanglement control and exhibit the potential of non-Hermitian physics in advancing quantum technologies.