Nontrivial spectral properties of non-Hermitian systems can give rise to intriguing effects that lack counterparts in Hermitian systems. For instance, when dynamically varying system parameters along a path enclosing an exceptional point (EP), chiral mode conversion occurs. A recent study [Phys. Rev. Lett. 133, 113802 (2024)] demonstrates the achievability of pure adiabatic state transfer by specifically selecting a trajectory in the system parameter space where the corresponding evolution operator exhibits a real spectrum while winding around an EP. However, the intended adiabatic state transfer becomes fragile when taking into account the effect of the nonadiabatic transition. In this work, we propose a scheme for achieving robust and rapid adiabatic state transfer in time-modulated two-level non-Hermitian systems by appropriately modulating the system Hamiltonian and time-evolution trajectory. Numerical simulations confirm that a complete adiabatic transfer can always be achieved even under nonadiabatic conditions after one period for different initialized adiabatic states, and the scheme remains insensitive to moderate fluctuations in control parameters. Therefore, this scheme offers alternative approaches for quantum-state engineering in non-Hermitian systems.
Nontrivial spectral properties of non-Hermitian systems can give rise to intriguing effects that lack counterparts in Hermitian systems. For instance, when dynamically varying system parameters along a path enclosing an exceptional point (EP), chiral mode conversion occurs. A recent study [Phys. Rev. Lett. 133, 113802 (2024)] demonstrates the achievability of pure adiabatic state transfer by specifically selecting a trajectory in the system parameter space where the corresponding evolution operator exhibits a real spectrum while winding around an EP. However, the intended adiabatic state transfer becomes fragile when taking into account the effect of the nonadiabatic transition. In this work, we propose a scheme for achieving robust and rapid adiabatic state transfer in time-modulated two-level non-Hermitian systems by appropriately modulating the system Hamiltonian and time-evolution trajectory. Numerical simulations confirm that a complete adiabatic transfer can always be achieved even under nonadiabatic conditions after one period for different initialized adiabatic states, and the scheme remains insensitive to moderate fluctuations in control parameters. Therefore, this scheme offers alternative approaches for quantum-state engineering in non-Hermitian systems.
Exceptional points (EPs) have attracted extensive research interest due to their intriguing properties. One of the hallmarks of EP physics is that dynamically encircling the EPs induces chiral mode switching, arising from the breakdown of adiabaticity due to the presence of a complex spectrum in the system's Hamiltonian. While such chiral mode behavior has been widely observed experimentally, achieving truly adiabatic, and thus symmetric, state transfer, regardless of the winding direction, in time-modulated non-Hermitian systems has remained elusive. In this work, we demonstrate that this long-sought adiabatic state dynamics can indeed be restored. By steering a two-mode photonic setup along specifically designed trajectories in parameter space, we realize conditions where the associated non-Hermitian evolution operator acquires a purely real spectrum. Moreover, our experimental platform enables controlled switching between symmetric (adiabatic) and chiral (non-adiabatic) state-transfer regimes for the same set of initial modes, thus effectively implementing a universal symmetric-asymmetric two-mode switch. Our results therefore open new avenues for harnessing unique topological spectral properties of non-Hermitian systems, paving the way for the practical design of versatile optical wave-manipulation devices and for advancing both classical and quantum information technologies.
Non-Hermitian systems have attracted much interest in recent decades, driven partly by the existence of exotic spectral singularities, known as exceptional points (EPs), where the dimensionality of the system evolution operator is reduced. Among various intriguing applications, the discovery of EPs has suggested the potential for implementing a symmetric mode switch, when encircling them in a system parameter space. However, subsequent theoretical and experimental works have revealed that dynamical encirclement of EPs invariably results in asymmetric mode conversion; namely, the mode switching depends only on the winding direction but not on the initial state. This chirality arises from the failure of adiabaticity due to the complex spectrum of non-Hermitian systems. Although the chirality revealed has undoubtedly made a significant impact in the field, a realization of the originally sought symmetric adiabatic passage in non-Hermitian systems with EPs has since been elusive. In this work, we bridge this gap and theoretically demonstrate that adiabaticity, and therefore a symmetric state transfer, is achievable when dynamically winding around an EP. This becomes feasible by specifically choosing a trajectory in the system parameter space along which the corresponding evolution operator attains a real spectrum. Our findings, thus, offer a promise for advancing various wave manipulation protocols in both quantum and classical domains.
Non-Hermitian systems have been at the center of intense research for over a decade, partly due to their nontrivial energy topology formed by intersecting Riemann manifolds with branch points known as exceptional points (EPs). This spectral property can be exploited, e.g., to achieve topologically controlled state permutations that are necessary for implementing a wide class of classical and quantum information protocols. However, the complex-valued spectra of typical non-Hermitian systems lead to instabilities, losses, and breakdown of adiabaticity, which impedes the practical use of EP-induced energy topologies in quantum information protocols based on state permutation symmetries. Indeed, in a given non-Hermitian multiqubit system, the dynamical winding around EPs always results in a predetermined set of attenuated final eigenstates, due to the interplay of decoherence and nonadiabatic transitions, irrespective of the initial conditions. In this work, we address this long-standing problem by introducing a model of interacting qubits governed by an effective non-Hermitian Hamiltonian that hosts a special type of EPs while maintaining a completely real energy spectrum, ensuring the absence of losses in the system’s dynamics. We demonstrate that such non-Hermitian Hamiltonians enable the realization of genuine, in general, non-Abelian permutation groups in the multiqubit system’s eigenspace while dynamically encircling these EPs. Our findings indicate that, contrary to previous beliefs, non-Hermiticity can be utilized to achieve controlled topological state permutations in time-modulated multiqubit systems, thus paving the way for the advancement and development of quantum information protocols in real-world non-Hermitian quantum systems.
Exceptional points in non-Hermitian systems possess fascinating properties. We present an exactly solvable attractor dynamics for the first time from the two-level time-dependent non-Hermitian Hamiltonian. This allows the evolution from a pure or mixed initial state to the coalescence state by varying the imaginary parameter along a specific diabatic passage. In contrast to a chaotic attractor that is ultrasensitive to initial conditions, the designed attractor is insensitive to initial conditions. The attractor-like behavior is applicable to several adiabatic processes.
Exceptional points (EPs) in non-Hermitian systems give rise to enhanced sensitivity and chiral state transfer, which are important for quantum technologies. Although parameter trajectories encircling EPs can control symmetric and chiral state transfer, their robustness against practical perturbations and their role in quantum sensing remain largely unexplored. Here, we study three time-modulated parameter loops in a non-Hermitian two-level system to show how trajectory design governs state-transfer symmetry, robustness, and sensing performance. Trajectories avoiding the EP support robust symmetric transfer, while those encircling the EP yield chiral transfer governed by the topological winding number, whose robustness depends on the distance to the EP and the encircling direction. For quantum sensing, trajectory engineering enables tuning of sensitivity amplitude, time window, and parameter selectivity in both eigenvalue-based and eigenstate-based sensors. Notably, eigenstate-based sensing achieves full parameter selectivity that is unattainable with eigenvalue-based methods. Our results establish a quantitative connection between trajectory topology and system dynamics, providing a unified framework for robust state-transfer protocols and high-performance quantum sensors.
Exceptional points emerge in the complex eigenspectra of non-Hermitian systems, and give rise to rich critical behaviors. An outstanding example is the chiral state transfer, where states can swap under an adiabatic encircling around the exceptional point, but only along one direction. In dissipative quantum systems, such exceptional-point encirclings are often accompanied by decoherence, whose impact is beyond the description of non-Hermitian Hamiltonians. In this paper, we study in detail the effects of dephasing on the encircling dynamics, adopting the full Lindblad master equation. Introducing experimentally relevant quantum-jump processes that account for dephasing, we show that gaps emerge in the eigenspectra landscape of the corresponding Liouvillian superoperator. It follows that the chiral state transfer does not take place in the adiabatic limit, since the system always adiabatically follows the quasisteady state of the Liouvillian regardless of the encircling direction. Nevertheless, the chirality is restored at intermediate encircling times, where the dynamics is nonadiabatic in both encircling directions, distinct from the typical chiral state transfer in non-Hermitian systems. While our results are applicable to several recent experiments, we examine a recent cold-atom experiment in particular, and show that the observed long-time chirality is limited to the special encircling path therein. Our paper provides further insight into the chiral state transfer under experimental conditions, and is helpful for controlling open-system dynamics from the perspective of non-Hermitian physics.