Exceptional points define branch-exchange state transfers through holomorphic continuation of non-Hermitian eigenmodes, but realizing these transfers dynamically remains difficult. Slow encircling does not generally transport the full set of instantaneous eigenstates, while shortcuts to adiabaticity can require controls outside the native experimental manifold. Here, we introduce a constrained shortcut-to-adiabaticity principle for exceptional-point braiding using native controls. In a dressed instantaneous-eigenstate frame, the available controls cancel the accessible transition channels locally, while the residual channels remain active during the evolution but are constrained to have no net accumulated effect over the closed loop. The protocol therefore targets the endpoint state transfer selected by ideal adiabatic branch exchange, rather than enforcing complete local cancellation or adiabatic following throughout the trajectory. We demonstrate the construction in a minimal two-mode non-Hermitian model equivalent, up to a trace shift and a basis convention, to the effective Hamiltonian used in dissipative-transmon exceptional-point experiments, where detuning and drive amplitude provide real controls and the relative loss imbalance fixes the non-Hermitian scale. Smooth real waveforms reshape only these controls, reproduce the branch-exchange transfer, and remain accurate under calibration errors, exceptional-point uncertainty and finite-bandwidth filtering with modest overhead.
Comments
13 pages, 5 figures. Includes supplementary information (additional 12 pages, 1 figure)
Exceptional points define branch-exchange state transfers through holomorphic continuation of non-Hermitian eigenmodes, but realizing these transfers dynamically remains difficult. Slow encircling does not generally transport the full set of instantaneous eigenstates, while shortcuts to adiabaticity can require controls outside the native experimental manifold. Here, we introduce a constrained shortcut-to-adiabaticity principle for exceptional-point braiding using native controls. In a dressed instantaneous-eigenstate frame, the available controls cancel the accessible transition channels locally, while the residual channels remain active during the evolution but are constrained to have no net accumulated effect over the closed loop. The protocol therefore targets the endpoint state transfer selected by ideal adiabatic branch exchange, rather than enforcing complete local cancellation or adiabatic following throughout the trajectory. We demonstrate the construction in a minimal two-mode non-Hermitian model equivalent, up to a trace shift and a basis convention, to the effective Hamiltonian used in dissipative-transmon exceptional-point experiments, where detuning and drive amplitude provide real controls and the relative loss imbalance fixes the non-Hermitian scale. Smooth real waveforms reshape only these controls, reproduce the branch-exchange transfer, and remain accurate under calibration errors, exceptional-point uncertainty and finite-bandwidth filtering with modest overhead.
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.
The existence of exceptional points (EPs) in the spectrum of non-Hermitian Hamiltonians leads to a nontrivial spectral topology that can be exploited to generate topological operations. However, their implementation has remained elusive due to the difficulty of generating a true adiabatic evolution. Here, we develop fast, robust control protocols that generate a desired topological operation. Our strategy relies on shortcuts to adiabaticity, but is not a trivial extension. The presence of EPs renders the strategy developed for Hermitian Hamiltonians impractical as it will lead to faulty control protocols. Moreover, due to the dynamics sensitivity to parameter uncertainties, not all shortcuts to adiabaticity can be used in a realistic setting. We illustrate our method in the context of a two-mode non-Hermitian Hamiltonian and discuss why in general celebrated shortcuts to adiabaticity like transitionless driving and superadiabatic transitionless are not appropriate control protocols for non-Hermitian systems.
Cooling a mechanical mode in finite time is a routing problem: excitation must reach a lossy mode before thermal noise rebuilds the population. Exceptional points are non-Hermitian degeneracies at which two hybrid modes and their eigenvectors merge, so a loop around them can exchange connected spectral branches. The main obstacle in testing whether this topology improves cooling is causal. Independently optimized enclosing and non-enclosing protocols normally have different waveforms, so topology and waveform geometry change together. We remove this ambiguity in a three-mode optomechanical system with a strongly damped main cavity and an exactly lossless auxiliary cavity. We keep one power modulation and one detuning shape fixed and change only their relative phase. The shift preserves the matched local control resources but changes the loop from non-enclosing to a braid around both exceptional points. Certified dynamics show that the two-exceptional-point protocol lowers the final mechanical occupation by more than 55 percent. The advantage survives the complete admissible phase family, deliberate waveform changes, a finite neighborhood of nearby smooth controls, and the restoration of counter-rotating heating processes. The auxiliary cavity acts as a coherent buffer, while the main cavity remains the only optical loss channel.
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.
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.