We suggest to employ the dissipative nature of open quantum systems for the purpose of parameter estimation: the dynamics of open quantum systems is typically described by a quantum dynamical semigroup generator The eigenvalues of are complex, reflecting unitary as well as dissipative dynamics. For certain values of parameters defining non-Hermitian degeneracies emerge, i.e. exceptional points (EP). The dynamical signature of these EPs corresponds to a unique time evolution. This unique feature can be employed experimentally to locate the EPs and thereby to determine the intrinsic system parameters with a high accuracy. This way we turn the disadvantage of the dissipation into an advantage. We demonstrate this method in the open system dynamics of a two-level system described by the Bloch equation, which has become the paradigm of diverse fields in physics, from NMR to quantum information and elementary particles.
We suggest to employ the dissipative nature of open quantum systems for the purpose of parameter estimation: the dynamics of open quantum systems is typically described by a quantum dynamical semigroup generator The eigenvalues of are complex, reflecting unitary as well as dissipative dynamics. For certain values of parameters defining non-Hermitian degeneracies emerge, i.e. exceptional points (EP). The dynamical signature of these EPs corresponds to a unique time evolution. This unique feature can be employed experimentally to locate the EPs and thereby to determine the intrinsic system parameters with a high accuracy. This way we turn the disadvantage of the dissipation into an advantage. We demonstrate this method in the open system dynamics of a two-level system described by the Bloch equation, which has become the paradigm of diverse fields in physics, from NMR to quantum information and elementary particles.
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.
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.
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) are non-Hermitian degeneracies at which two or more eigenvalues and their corresponding eigenvectors coalesce. In open quantum systems, exceptional points can arise in the Lindbladian governing the dissipative dynamics. Their signatures have so far been mainly identified in finite-time observables, such as transient currents, while steady-state average currents generally provide no direct evidence of the underlying exceptional-point structure. In this work, we demonstrate that signatures of Lindbladian EPs can nevertheless be accessed in the steady-state regime through current noise. We derive general expressions for current correlation functions within a Lindblad master-equation framework and show, in particular, how exceptional points affect their behaviour as a function of the time delay. We illustrate these results with the paradigmatic example of two interacting qubits coupled to two reservoirs, where the steady-state noise clearly distinguishes overdamped, underdamped, and critical regimes. Our results establish current correlation functions as a steady-state probe of Lindbladian EPs in open quantum systems.
The open quantum system can be described by either a Lindblad master equation or a non-Hermitian Hamiltonian (NHH). However, these two descriptions usually have different exceptional points (EPs), associated with the degeneracies in the open quantum system. Here, considering a dissipative quantum Rabi model, we study the spectral features of EPs in these two descriptions and explore their connections. We find that, although the EPs in these two descriptions are usually different, the EPs of NHH will be consistent with the EPs of master equation in the weak coupling regime. Further, we find that the quantum Fisher information (QFI), which measures the statistical distance between quantum states, can be used as a signature for the appearance of EPs. Our study may give a theoretical guidance for exploring the properties of EPs in open quantum systems.
We suggest a method for accurate parameter estimation of atomic systems, employing the special properties of the exceptional points. The non-Hermitian degeneracies at the exceptional points emerge from the description of the spontaneous emission of the atomic system in the framework of an open quantum system, resulting in a non-Hermitian quantum master equation. The method is demonstrated for the atomic spectrum of $S\ensuremath{\rightarrow}P$ transitions of 85Rb and 40Ca+.