Non-Hermitian systems exhibit unique phenomena beyond conventional Hermitian physics, such as the non-Hermitian skin effect (NHSE) and exceptional points (EPs). In this work we introduce a one-dimensional double-chain model with nonreciprocal coupling to investigate the interplay between the NHSE and Anderson localization induced by quasiperiodic modulation. In the clean limit, the system exhibits a complex spectrum featuring EPs, tunable parity-time-symmetry breaking, and band splitting. When a quasiperiodic potential is added, a rich phase diagram emerges, including extended, localized, and critical phases, as well as mobility edges. Remarkably, we observe reentrant localization nonmonotonic transitions between extended and localized states driven by the competition between the NHSE and disorder scattering. Furthermore, we propose a concrete circuit implementation using negative-impedance converters, offering an experimentally accessible platform to simulate these non-Hermitian topological and localization effects at the classical level. Our results deepen the understanding of phase transitions in non-Hermitian quasicrystals and provide a direct route toward controllable simulators for observing and manipulating such phenomena in classical and future quantum settings.

Non-Hermitian effects and reentrant localization have attracted significant attention due to their unique physical properties and potential applications. Despite recent experimental advancements, achieving precise control and gaining a deeper theoretical understanding of these phenomena remain challenging. Here, we propose a one-dimensional doubly coupled lattice model, where two sublattices are interconnected via both horizontal and vertical hoppings, to investigate non-Hermitian phase transitions and localization behavior. Asymmetric hopping drives a transition from the Hermitian to the non-Hermitian regime, leading to the emergence of complex energy spectra. Moreover, when a quasiperiodic potential is introduced, the system exhibits a range of localization phases, including extended, localized, and intermediate phases characterized by mobility edges. Notably, under strong quasiperiodic modulation, we observe reentrant localization, where the system undergoes a nonmonotonic transition from localization to delocalization and back to localization as system parameters are varied. Our findings bridge theoretical insight into non-Hermitian phase transitions and localization with a practical circuit-based platform, enabling direct experimental exploration in quantum simulators.

Non-Hermitian topological phases and the non-Hermitian skin effect (NHSE) have attracted significant attention in recent years, yet effectively controlling these phenomena remains challenging. Here, we propose a one-dimensional non-Hermitian Su–Schrieffer–Heeger model implemented on a circuit platform, incorporating a tunable next-nearest-neighbor (NNN) hopping element. We systematically investigate the influence of NNN hopping on both topological properties and the NHSE. By mapping the circuit Laplacian to the Hamiltonian, we analyze the effects of NNN hopping on the admittance spectrum, eigenfrequency spectrum, and spatial impedance distribution. Our results demonstrate that increasing the NNN hopping strength suppresses the NHSE, driving boundary-localized eigenstates to extend into the bulk, a transition quantitatively characterized by the inverse participation ratio. Further analysis using non-Bloch band theory reveals that while NNN hopping does not alter the quantized values of topological invariants, it shifts the critical parameters of topological phase transitions. This work provides a theoretical platform for simulating and controlling non-Hermitian topological states in circuits and establishes a quantitative foundation, through generalized Brillouin zone deformation and non-Bloch invariants, for designing novel non-Hermitian topological devices based on coupling engineering.

Fractal energy spectra arise from the interplay between two periodic parameters at different scales. Artificial lattices with nontrivial topological features in synthetic dimensions can emulate such interplay, exhibiting topological boundary correspondence and fractal structures resembling the Hofstadter butterfly. However, the realization of Hofstadter butterfly spectra in cavity magnonic lattices has received limited attention. In this work, we propose a one-dimensional cavity magnonic lattice in which each unit cell couples a cavity photon with a magnon. By tuning the system parameters to implement a synthetic magnetic flux, we demonstrate the emergence of a Hofstadter butterflylike energy spectrum and the formation of distinct edge-state modes. These edge states exhibit flipping behavior, enabling controlled storage and transmission of quantum information. We further analyze the spectral structure and compute thetopological invariants to characterize the system's phase diagram. The influence of random defects is also investigated. While small imperfections have minimal impact on topological properties, larger defects may disrupt the edge modes, highlighting the need for defect suppression to preserve topological robustness in practical implementations.

The squeezed state of a magnon has garnered widespread attention due to its distinct properties and potential applications. Although preliminary experimental verification has been achieved, numerous technical and theoretical challenges persist. Here, we investigate the nonlinear coupling within the magnon-cavity-qubit system and propose an innovative method for achieving magnon squeezing. By employing virtual photons as a mediator for magnon-qubit interactions and optimizing system parameters, we induce nonlinear coupling. This approach not only enhances the interaction strength between magnons and qubits but also opens up an alternative pathway for achieving magnon squeezing. Our findings significantly enrich the fields of quantum physics and magnetism by providing a method for magnon squeezing, thereby laying a solid foundation for future advancements and applications in quantum technology.

Artificial quantum systems have emerged as a crucial experimental platform for investigating topological states, thanks to their customizable structures and tunable parameters. Nevertheless, the exploration of topological photonic states within cavity magnonics systems has been somewhat limited, with only a handful of reports available on this topic. Here, we propose a novel scheme to trigger and detect topological photonic states in a one-dimensional (1D) cavity magnonics chain model, wherein a series of split-ring resonator (SRR) modes are interleaved with yttrium iron garnet (YIG) spheres, and the coupling between the SRR modes and the magnon modes is induced by electromagnetic interactions. By adjusting the system parameters, we found that not only can different topological properties and topological quantum channels be triggered, but topological invariants can also undergo phase transition processes. Furthermore, we study the average photon number and the winding number of the reflection coefficient phase (WNRCP) to detect the topological photonic states and determine the topological invariants of the system. Additionally, considering the impact of defects on topological characteristics, we found that the system is protected by topology, making the edge states robust against defects. This work provides a breakthrough method for studying topological photonic states, paves the way for developing advanced magnon-based quantum devices and information processing systems.

We propose a theoretical scheme for a one-dimensional superconducting circuit lattice system to achieve that topological phase transition and topological multi-channel transfer, which is adjusted by the asymmetric hopping modulations. The system consists of an array of coupled superconducting microwave cavities, the hopping between its can be modulated by the qubits. Here, we explore topological stages by introducing parameters to expand the hopping modulation range. We found that the energy bands in the system exhibit different structural characteristics, which can achieve topological phase switching. Meanwhile, the edge modes can undergo a flipping process, which can not only realize dual-channel topological quantum information transfer, but also can achieve four-channel. Furthermore, it is noted that the defect can induce new topological phases, which can be optimized by adjusting the hopping parameters, while disorder can only cause band fluctuations and inversions, but does not change the position and period of edge states, verifying that the edge state transport is robust. The results obtained in this work can be applied to the storage and transmission of quantum information, and have a guiding role in the future development of quantum technology.

We propose a theoretical scheme to study the topological properties of magnon-photon in a one-dimensional coupled cavity lattice. Each unit cell is composed of the cavity microwave photon and the magnon, where the magnon is placed inside the cavity. The coupling of cavity microwave photon and magnon is controlled by an external magnetic field, and multiple cavities are coupled with each other to form a one-dimensional coupled cavity lattice system. Here, we study the topological phase transition and topological quantum channels of magnon-photon in the system by adjusting the magnon-photon coupling. Firstly, considering odd and even number lattices, we analyze and discuss the energy spectrum and the edge state in one-dimensional coupled cavity lattices. It is found that the energy band of the system is symmetric, and the edge states in the energy gap have time reversal symmetry, which makes the system topologically protected. At the same time, it is also noted that the maximum value, flipping, and period of the energy spectrum have changed, and the region of the edge state has expanded and extended. In addition, the edge state distribution can undergo the flipping process, which can achieve multi-channel topological quantum state transmission. Besides, considering the presence of defects and disorder in the system, it is found that when the random defect potential is small, the edge state of the system is robust to it, but when the random defect potential is large, the fluctuation of the energy band will be enhanced, and the edge state will be submerged in the energy band. However, when the disorder is very small, it can cause band fluctuations and flipping phenomena, and the edge state is robust to it, indicating the topological protection of the edge state. This work offers an effective way to study topological magnon-photon, which will have promising applications in quantum information processing.

Quantum Hall insulators in artificial systems have become a rapidly developing research field in recent years, and have made significant breakthroughs in observing many novel topological phenomena. However, there are few reports about quantum magnon-photon Hall insulators. Here, a scheme is proposed for implementing a 1D cavity magnonics lattice that exhibits quantum magnon-photon Hall insulator behaviors, where each unit cell comprises cavity photons and magnons. By adjusting the system parameters, it is found that not only different energy spectrum structures can be triggered, but also the distribution of the edge states can show the flipping process, which allows the achievement of the multi-channel topological quantum state transmission. In addition, considering the presence of defects, dissipation, and disorder, it is found that appropriate defects can trigger new topological phases, while dissipation only causes shifts in energy levels without changing the position and period of edge states, and disorder leads to shifts in band structures and edge states, thus demonstrating the robustness of edge states. This work offers an effective way to study topological magnon-photon Hall insulators, which will have promising applications in magnon-based quantum information processing. This work proposes a scheme for implementing a 1D cavity magnonics lattice that exhibits quantum magnon-photon Hall insulator behavior. By adjusting the parameters, the system can trigger different energy spectrum structures and observe a flipping of edge states, enabling multi-channel topological quantum state transmission. Remarkably, the edge state remains robust despite internal factors, indicating its significant potential for future applications. image

Anomalous transport of topological semimetals has generated significant interest for applications in optoelectronics, nanoscale devices, and interconnects. Understanding the origin of novel transport is crucial to engineering the desired material properties, yet their orders of magnitude higher transport than single-particle mobilities remain unexplained. This work demonstrates the dramatic mobility enhancements result from phonons primarily returning momentum to electrons due to phonon-electron dominating over phonon-phonon scattering. Proving this idea, proposed by Peierls in 1932, requires tuning electron and phonon dispersions without changing symmetry, topology, or disorder. This is achieved by combining de Haas - van Alphen (dHvA), electron transport, Raman scattering, and first-principles calculations in the topological semimetals MX_2 (M=Nb, Ta and X=Ge, Si). Replacing Ge with Si brings the transport mobilities from an order magnitude larger than single particle ones to nearly balanced. This occurs without changing the crystal structure or topology and with small differences in disorder or Fermi surface. Simultaneously, Raman scattering and first-principles calculations establish phonon-electron dominated scattering only in the MGe_2 compounds. Thus, this study proves that phonon-drag is crucial to the transport properties of topological semimetals and provides insight to further engineer these materials.

We introduce a novel technique for enhancing the robustness of light-pulse atom interferometers against the pulse infidelities that typically limit their sensitivities. The technique uses quantum optimal control to favorably harness the multipath interference of the stray trajectories produced by imperfect atom-optics operations. We apply this method to a resonant atom interferometer and achieve thousandfold phase amplification, representing a 50-fold improvement over the performance observed without optimized control. Moreover, we find that spurious interference can arise from the interplay of spontaneous emission and many-pulse sequences and demonstrate optimization strategies to mitigate this effect. Given the ubiquity of spontaneous emission in quantum systems, these results may be valuable for improving the performance of a diverse array of quantum sensors. We anticipate our findings will significantly benefit the performance of matter-wave interferometers for a variety of applications, including dark matter, dark energy, and gravitational wave detection.

We propose a one-dimensional lattice theory scheme based on superconducting microwave cavities, which includes two different types of microwave cavity unit cells. The coupling between unit cells is controlled by flux qubits to simulate and study their topological insulator characteristics. Specifically, a one-dimensional superconducting microwave cavity lattice scheme with a p-wave superconducting pairing term is achieved by mapping the counter-rotating wave terms to the p-wave superconducting pairing term. We found that the p-wave superconducting pairing term can modulate the topological quantum state of the system, allowing for the creation of topological quantum information transmission channels with four edge states. In addition, when the p-wave superconducting pairing term and the nearest-neighbor interaction exist, we find that the energy band undergoes fluctuations, inducing the generation of new energy bands, but the degeneracy of the edge states remains stable, which can achieve multiple topological quantum state transmission paths. However, when its regulatory value exceeds the threshold, the energy gap of the system will close, causing the edge states to annihilate in new energy bands. Furthermore, when considering the existence of defects in the system, we found that when the strength of the defects are small, the edge state produces small fluctuations, but it can be clearly distinguished, indicating its robustness. When the strength of the defect exceeds the threshold, the edge state and energy band cause irregular fluctuations, allowing the edge state to integrate into the energy band. Our research results have important theoretical value and practical significance, and can be applied in quantum optics and quantum information processing in the future.

We propose a theoretical method to study the topological properties of spin-phonon coupled modes (SPCMs) in a one-dimensional superconducting resonator lattice, where each unit cell is composed of superconducting resonators and nitrogen-vacancy (NV) spins. By diagonalization and dimensionality reduction methods, a quantum spin-phonon Hall insulator system can be obtained. Here, the coupling strength is extended to explore the topological stage by controlling the number of photons and the NV spin ensemble. Therefore, the different topological structures can be displayed by adjusting the coupling parameters. We find that the distribution of edge states can undergo an inversion process, realizing topological quantum channel transmission. In addition, we also discuss the topological index of the topological phase, in which the different topological phases of this system can be distinguished. Furthermore, when considering the impact of dissipation and disorder, we find that the edge states are still very stable, which indicates that the edge states are topologically protected. This work provides an effective way to study the topological insulators of the spin and the phonon, which will promote the development of quantum simulation and quantum computing.

We theoretically study the topological properties in a one-dimensional superconducting circuit lattice, where each unit cell is composed of a superconducting microwave cavity, a nanomechanical resonator (NAMR) and a superconducting qubit. By using diagonalization and dimensional reduction methods, the quantum spin Hall system of the photon-phonon coupled modes can be achieved. We analyze the energy spectrum and edge states of different lattice sizes. It is found that the number of lattices affects the topological characteristics of the system, and the inversion of the edge state distribution can be realized. In addition, considering the effects of defects, dissipation and disorder on the system, we find that they will respectively expand the region of the edge state, change the maximum value of the energy spectrum and cause small fluctuation of the energy spectrum. But the edge state is still very stable, which is due to the topological protection of the edge state. This scheme opens up a new way to study the application of topological matter in quantum information processing, meanwhile, the research results can be used to design novel quantum devices.

We propose a theoretical scheme for a one-dimensional lattice based on a superconducting quantum circuit system consisting of two types of superconducting microwave cavities, the interaction between nearest-neighbor and next-nearest-neighbor unit cells that can be adjusted by the magnetic flux, the system can obtain the collective dynamic evolution and study the topological properties of the system.First, we investigate the energy spectrum and edge states of the odd-even lattice size and find that the odd-even lattice number affects the topological properties of the system. Furthermore, considering the next-nearest interactions, it is found that there are constraints on the next-nearest interactions, which can be tuned to study the topological phase transitions of the system and the transfer of topological quantum states.In addition, considering the influence of defects on topological properties, it is found that the defect potential energy is small, the system energy band is stable, the edge states remain unchanged, and the energy spectrum fluctuation is small and distinguishable. Conversely, the energy band distribution is destroyed, it will become disordered and chaotic. The research results can design some new quantum devices for quantum optics and quantum information processing.

We propose a one-dimensional lattice theory scheme based on a coupled optomechanical system consisting of multiple cavity field modes and mechanical modes, where their frequencies can be tuned. In this system, by manipulating parameters to obtain collective dynamical evolution of the system, we study topological properties and topological quantum channels in the system. Firstly, the topological insulator properties and topological quantum channels of the system are studied by modulating the periodic coupling parameters of the system and analyzing the characteristics of the energy spectrum and edge states of the system. It is found that edge state distributions can exhibit flipping processes, which can be applied to quantum information processing. Secondly, based on the scattering theory of topological insulators and the relationship between input and output, the variation characteristics of the steady-state average photon number of the cavity field and the winding number of the reflection coefficient phase are analyzed. It is found that the dissipation of the cavity field has a certain influence on the locality of the distribution of the average photon number in the lattice, and it also indirectly explains the locality of the edge states of the system, and the topological invariants are detected by the winding number. In addition, considering the effect of disordered defects on topological properties, we further analyze their effects on the energy spectrum of the system, the winding number of the reflection coefficient phase and the average photon number of the cavity field. It is found that two defects in the system cause different physical effects, and when their values are small, the edge states of the system are robust to it, which also shows that the system has the characteristics of topological protection. However, when disorder and perturbation are larger than the energy gap, the topological properties of the system will be annihilated, so that the edge states will be indistinguishable, and the topological invariants will change at the same time. The research results of this system can be generalized to other types of models and can be applied to quantum communication and quantum information processing, which will have certain constructive suggestions for the development of future quantum technology.

We propose a one-dimensional lattice theory scheme based on a coupled optomechanical system consisting of multiple cavity field modes and mechanical modes, where their frequencies can be tuned. In this system, by manipulating parameters to obtain collective dynamical evolution of the system, we study topological properties and topological quantum channels in the system. Firstly, the topological insulator properties and topological quantum channels of the system are studied by modulating the periodic coupling parameters of the system and analyzing the characteristics of the energy spectrum and edge states of the system. It is found that edge state distributions can exhibit flipping processes, which can be applied to quantum information processing. Secondly, based on the scattering theory of topological insulators and the relationship between input and output, the variation characteristics of the steady-state average photon number of the cavity field and the winding number of the reflection coefficient phase are analyzed. It is found that the dissipation of the cavity field has a certain influence on the locality of the distribution of the average photon number in the lattice, and it also indirectly explains the locality of the edge states of the system, and the topological invariants are detected by the winding number. In addition, considering the effect of disordered defects on topological properties, we further analyze their effects on the energy spectrum of the system, the winding number of the reflection coefficient phase and the average photon number of the cavity field. It is found that two defects in the system cause different physical effects, and when their values are small, the edge states of the system are robust to it, which also shows that the system has the characteristics of topological protection. However, when disorder and perturbation are larger than the energy gap, the topological properties of the system will be annihilated, so that the edge states will be indistinguishable, and the topological invariants will change at the same time. The research results of this system can be generalized to other types of models and can be applied to quantum communication and quantum information processing, which will have certain constructive suggestions for the development of future quantum technology.

In this paper, a novel fractional quantum logistic map (FQLM) based on fractional difference is proposed and image encryption algorithm based on it are exploited. First, the FQLM is proposed and its dynamical behaviors are observed with bifurcation diagram, phase portraits and largest Lyapunov exponent plots. After that, the ECC is utilized to cover up the encryption keys and the FQLM is used for the permutation and diffusion process of image encryption. Finally, the cryptosystem is used in image encryption and the algorithm is analyzed in four respects, showing a distinct advantage of the proposed cryptosystem over some of existing ones.

A new fractional two-dimensional triangle function combination discrete chaotic map (2DTFCDM) with the discrete fractional difference is proposed in this paper. The chaos behaviors are observed through the bifurcation diagrams, the largest Lyapunov exponent plot and the phase portraits. The proposed map is applied in color image encryption with the secret keys generated by Menezes–Vanstone Elliptic Curve Cryptosystem. The image encryption system is analyzed using six aspects indicating the superiority of the proposed algorithm compared to the other algorithms.