Abstract Exceptional points (EPs) occur in non-Hermitian systems where eigenvalues and eigenvectors coalesce. In open quantum systems, EPs are typically studied via non-Hermitian effective Hamiltonians or Liouvillians, but these omit the full generality of quantum dynamics, which requires description using quantum channels. Here, we introduce a general strategy for generating quantum-channel EPs in the single-qubit setting. We show that quantum channels naturally fall into two distinct phases, purely real or complex-conjugate eigenvalues, without the need of enforcing additional symmetries, and interpolating between different phases induces a phase transition where EPs can emerge. We experimentally simulate such channels on a nuclear magnetic resonance quantum computer, observing second-order quantum-channel EPs with 93% fidelity, and extend the approach to three channels to uncover exceptional lines and a third-order quantum-channel EP. Our results promise potential applications from enhanced quantum sensing to quantum control, such as Jordan-chain mediated asymmetric conversion.
Abstract Exceptional points (EPs) occur in non-Hermitian systems where eigenvalues and eigenvectors coalesce. In open quantum systems, EPs are typically studied via non-Hermitian effective Hamiltonians or Liouvillians, but these omit the full generality of quantum dynamics, which requires description using quantum channels. Here, we introduce a general strategy for generating quantum-channel EPs in the single-qubit setting. We show that quantum channels naturally fall into two distinct phases, purely real or complex-conjugate eigenvalues, without the need of enforcing additional symmetries, and interpolating between different phases induces a phase transition where EPs can emerge. We experimentally simulate such channels on a nuclear magnetic resonance quantum computer, observing second-order quantum-channel EPs with 93% fidelity, and extend the approach to three channels to uncover exceptional lines and a third-order quantum-channel EP. Our results promise potential applications from enhanced quantum sensing to quantum control, such as Jordan-chain mediated asymmetric conversion.
Exceptional points (EPs) occur in non-Hermitian systems where eigenvalues and eigenvectors coalesce. In open quantum systems, EPs are typically studied via non-Hermitian effective Hamiltonians or Liouvillians, but these omit the full generality of quantum dynamics, which requires description using quantum channels. Here, we introduce a general strategy for generating quantum-channel EPs in the single-qubit setting. We show that quantum channels naturally fall into two distinct phases, purely real or complex-conjugate eigenvalues, without the need of enforcing additional symmetries, and interpolating between different phases induces a phase transition where EPs can emerge. We experimentally simulate such channels on a nuclear magnetic resonance quantum computer, observing second-order quantum-channel EPs with 93% fidelity, and extend the approach to three channels to uncover exceptional lines and a third-order quantum-channel EP. Our results promise potential applications from enhanced quantum sensing to quantum control, such as Jordan-chain mediated asymmetric conversion.
One of the most remarkable features that distinguish open systems from closed ones is the presence of exceptional points (EPs), where two or more eigenvectors of a non-Hermitian operator coalesce, accompanying the convergence of the corresponding eigenvalues. So far, EPs have been demonstrated on a number of platforms, ranging from classical optical systems to fully quantum-mechanical spin-boson models. In these demonstrations, the reservoir that induced the non-Hermiticity was treated as a Markovian one, without considering its memory effect. We here present the first experimental demonstration of non-Markovian quantum EPs, engineered by coupling a Josephson-junction-based qubit to a leaky electromagnetic resonator, which acts as a non-Markovian reservoir. We map out the spectrum of the extended Liouvillian superoperator by observing the quantum state evolution of the qubit and the pseudomode, in which the memory of the reservoir is encoded. We identify a twofold second-order EP and a third-order EP in the Liouvillian spectrum, which cannot be realized with a Markovian reservoir. Our results pave the way for experimental exploration of exotic phenomena associated with non-Markovian quantum EPs.
Exceptional points (EPs), the degeneracy points of non-Hermitian systems, have recently attracted great attention because of their potential of enhancing the sensitivity of quantum sensors. Unlike the usual degeneracies in Hermitian systems, at EPs, both the eigenenergies and eigenvectors coalesce. Although EPs have been widely explored, the range of EPs studied is largely limited by the underlying systems, for instance, higher-order EPs are hard to achieve. Here we propose an extendable method to simulate non-Hermitian systems and study EPs with quantum circuits. The system is inherently parity-time (PT) broken due to the non-symmetric controlling effects of the circuit. Inspired by the quantum Zeno effect, the circuit structure guarantees the success rate of the post-selection. A sample circuit is implemented in a quantum programming framework, and the phase transition at EP is demonstrated. Considering the scalable and flexible nature of quantum circuits, our model is capable of simulating large-scale systems with higher-order EPs.
Exceptional points (EPs) are singularities in the spectra of non-Hermitian operators where eigenvalues and eigenvectors coalesce. Open quantum systems have recently been explored as EP testbeds due to their non-Hermitian nature. However, most studies focus on the Markovian limit, leaving a gap in understanding EPs in the non-Markovian regime. This work addresses this gap by proposing a general framework based on two numerically exact descriptions of non-Markovian dynamics: the pseudomode equation of motion (PMEOM) and the hierarchical equations of motion (HEOM). The PMEOM is particularly useful due to its Lindblad-type structure, aligning with previous studies in the Markovian regime while offering deeper insights into EP identification. This framework incorporates non-Markovian effects through auxiliary degrees of freedom, enabling the discovery of additional or higher-order EPs that are inaccessible in the Markovian regime. We demonstrate the utility of this approach using the spin-boson model and linear bosonic systems. The full description of exceptional points in the non-Markovian regime is complicated by the unclear applicability of standard techniques such as spectral analysis. Here, the authors fill this gap by proposing a general framework that combines the pseudomode equation of motion and the hierarchical equations of motion.
Open photonic systems provide a versatile platform for non-Hermitian physics, enabling control over complex spectra, transport, and light-matter interactions. Exceptional points (EPs), at which eigenvalues and eigenvectors coalesce and the governing operator becomes defective, play a central role because they combine branch-point spectral topology, nonanalytic perturbative response, and controllable eigenstate conversion. This Review provides a unified framework for EP photonics by systematically distinguishing exceptional degeneracies according to the underlying operator, spectral variable, boundary conditions, and experimentally accessible observables. We discuss Hamiltonian EPs, absorbing EPs associated with scattering zeros, real-frequency scattering-matrix and Jones-matrix EPs, Bloch and Floquet EPs, and Liouvillian EPs in open quantum systems. We review their spectral topology, static and dynamical encircling, higher-order exceptional structures, and coexistence with bound states in the continuum, together with applications in sensing, lasing, coherent absorption, directional scattering, polarization and wavefront control, nonlinear optics, optical storage, nonreciprocal photonics, and quantum photonics. We also critically assess the current limitations, practical challenges, and future perspectives of EP-based photonic technologies, with particular attention to robustness, noise, scalability, and experimentally measurable performance.
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.