Open quantum systems can have exceptional points (EPs), degeneracies where both eigenvalues and eigenvectors coalesce. Recently, it has been proposed and demonstrated that EPs can enhance the performance of sensors in terms of amplification of a detected signal. However, typically amplification of signals also increases the system noise, and it has not yet been shown that an EP sensor can have improved signal-to-noise performance. We develop a quantum noise theory to calculate the signal-to-noise performance of an EP sensor. We use the quantum Fisher information to extract a lower bound for the signal-to-noise ratio (SNR) and show that parametrically improved SNR is possible. Finally, we construct a specific experimental protocol for sensing using an EP amplifier near its lasing threshold and heterodyne signal detection that achieves the optimal scaling predicted by the Fisher bound. Our results can be generalized to higher order EPs for any bosonic non-Hermitian system with linear interactions.
Open quantum systems can have exceptional points (EPs), degeneracies where both eigenvalues and eigenvectors coalesce. Recently, it has been proposed and demonstrated that EPs can enhance the performance of sensors in terms of amplification of a detected signal. However, typically amplification of signals also increases the system noise, and it has not yet been shown that an EP sensor can have improved signal-to-noise performance. We develop a quantum noise theory to calculate the signal-to-noise performance of an EP sensor. We use the quantum Fisher information to extract a lower bound for the signal-to-noise ratio (SNR) and show that parametrically improved SNR is possible. Finally, we construct a specific experimental protocol for sensing using an EP amplifier near its lasing threshold and heterodyne signal detection that achieves the optimal scaling predicted by the Fisher bound. Our results can be generalized to higher order EPs for any bosonic non-Hermitian system with linear interactions.
Abstract Recently, multiple studies have suggested that exceptional points (EPs) in lossless nonlinear optical systems can minimize quantum noise arising from the material gain and loss in conventional non-Hermitian systems, offering the possibility of quantum EP sensing. Meanwhile, nonlinear SU(1,1) interferometers have been established as useful in sensing due to their reduced quantum noise. In this work, we demonstrate the existence of EPs in a dual-beam SU(1,1) interferometer with two nonlinear parametric amplifiers. Our analysis of the input-output matrix in terms of joint quadrature amplitudes shows that EPs can be linked to both high signal, through a zero matrix element, and low noise, through noise preservation, in sensing by selecting an appropriate operation gauge of the quadrature amplitudes. Additionally, for a multistage SU(1,1) interferometer, EPs of the overall input-output matrix form multiple bands of high signal-to-noise ratio (SNR) which further separate into two phases indicated by the EPs of the transfer matrix of a repeating unit. Our investigations demonstrate the significance of quantum EPs in quantum interferometer sensing and broaden the operating regimes from diabolical points in some of the conventional SU(1,1) interferometers to EPs while still maintaining a high SNR.
In recent years, significant progress has been made in utilizing the divergence of spectrum response rate at the exceptional point (EP) for sensing in classical systems, while the use and characterization of quantum EPs for sensing have been largely unexplored. For a quantum EP sensor, an important issue is the relation between the order of the quantum EP and the scaling of quantum Fisher information (QFI), an essential quantity for characterizing quantum sensors. Here we investigate multi-mode quadratic bosonic systems, which exhibit higher-order EP dynamics, but possess Hermitian Hamiltonians without Langevin noise, thus can be utilized for quantum sensing. We derive an exact analytic formula for the QFI, from which we establish a scaling relation between the QFI and the order of the EP. We apply the formula to study a three-mode EP sensor and a multi-mode bosonic Kitaev chain and show that the EP physics can significantly enhance the sensing sensitivity. Our work establishes the connection between two important fields: non-Hermitian EP dynamics and quantum sensing, and may find important applications in quantum information and quantum non-Hermitian physics.
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.
Exceptional points (EPs) exhibit strongly enhanced spectral responses and are therefore promising candidates for sensing applications. Whether these non-Hermitian degeneracies provide a genuine advantage in the quantum regime has been the subject of ongoing debate. Here, we address this issue within a scattering-matrix formalism for sensing with coherent light, which allows the quantum Fisher information (QFI) to be evaluated directly from experimentally accessible scattering data without introducing additional noise channels beyond those inherent to the scattering process. We analyze both nondegenerate and degenerate scattering-matrix poles, including EPs of arbitrary order, and show that the QFI per incoming photon flux is governed by three key factors: the decay rate of the resonant mode, the strength of the spectral response associated with non-normality, and the adjustment between the scattering states and the information source. For spatially localized perturbations, this implies that the Fisher information is fully determined by the local density of states at the perturbation site. Within this framework, we demonstrate that EPs can enhance the QFI compared to isolated modes or diabolic points with identical decay rates, and that the QFI can be further increased by moving away from the EP toward parameter regimes where non-Hermitian linewidth splitting reduces the decay rate of one mode. We further show that sufficiently small additional internal losses do not alter this overall picture, thereby providing a unified and experimentally relevant perspective on the design of quantum-limited non-Hermitian sensors.
There has been debate around applicability of exceptional points (EPs) for quantum sensing. To resolve this, we first explore how to experimentally implement the non-Hermitian non-diagonalizable Hamiltonians, which exhibit EPs, in quantum computers that run on unitary gates. We propose to use an ancilla-based method in this regard. Next, we show how such Hamiltonians can be used for parameter estimation using quantum computers and analyze its performance in terms of the quantum Fisher information (QFI) at EPs, both without noise and in the presence of noise. It is well known that QFI of a parameter to be estimated is inversely related to the variance of the parameter by the quantum Cramer–Rao bound. Therefore, the divergence of the QFI at EPs promises sensing advantages. We experimentally demonstrate in a cloud quantum architecture and theoretically show, using Puiseux series, that the QFI indeed diverges in such EP systems that were earlier considered to be non-divergent.
Exceptional points (EPs) represent non-Hermitian degeneracies where eigenvalues and eigenvectors coalesce, giving rise to enhanced sensitivity and critically damped dynamics. We demonstrate that when an EP coincides with a dissipative phase transition in an extended open Dicke model of two cavities coupled to a collective spin, the critical fluctuations are strongly amplified and governed by modified critical exponents. Numerical results reveal enhanced critical scaling in both the normal and superradiant phases, in agreement with an analytical theory based on the Jordan-block structure of the linearized dynamical matrix at the EP. Our results establish EPs as a mechanism to engineer critical scaling in open quantum systems, with potential applications to critical quantum sensing.