The eigenvalue susceptibility divergence at the exceptional point (EP) stimulates the idea of high sensitivity metrology. Parameter estimation around the EPs is theoretically studied. We find that the EP bears no enhancement of the sensitivity.
Abstract The exceptional points (EPs) of non-Hermitian systems, where n different energy eigenstates merge into an identical one, have many intriguing properties that have no counterparts in Hermitian systems. In particular, the ϵ 1 / n dependence of the energy level splitting on a perturbative parameter ϵ near an n th order EP stimulates the idea of metrology with arbitrarily high sensitivity, since the susceptibility d ϵ 1/ n /d ϵ diverges at the EP. Here we theoretically study the sensitivity of parameter estimation near the EPs, using the exact formalism of quantum Fisher information (QFI). The QFI formalism allows the highest sensitivity to be determined without specifying a specific measurement approach. We find that the EP bears no dramatic enhancement of the sensitivity. Instead, the coalescence of the eigenstates exactly counteracts the eigenvalue susceptibility divergence and makes the sensitivity a smooth function of the perturbative parameter.
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.
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.
Rydberg atoms, with their large transition dipole moments and extreme sensitivity to electric fields, have attracted widespread attention as promising candidates for next-generation quantum precision electrometry. Meanwhile, exceptional points (EPs) in non-Hermitian systems have opened new avenues for ultrasensitive metrology. Despite increasing interest in non-Hermitian physics, EP-enhanced sensitivity has rarely been explored in Rydberg atomic platforms. Here, we provide a new theoretical understanding of Autler-Townes effect-based Rydberg electrometry under non-Hermitian conditions, showing that dissipation fundamentally modifies the spectral response and enables sensitivity enhancement via EP-induced nonlinearity. Experimentally, we realize a second-order EP in a passive thermal Rydberg system without requiring gain media or cryogenics, and demonstrate the first EP-enhanced atomic electrometer. The EP can be tuned in real time by adjusting laser and microwave parameters, forming a flexible and scalable platform. Near the EP, the system exhibits a square-root response, yielding a nearly 20-fold enhancement in responsivity. Using amplitude-based detection, we achieve a sensitivity of 22.68(3) nV cm^{-1} Hz^{-1/2} under realistic conditions. Our Letter establishes a practical, tunable platform for EP-enhanced sensing and real-time control, with broad implications for quantum metrology in open systems.
High-order exceptional points (EPs) emerging in non-Hermitian systems have attracted broad interest for their significantly enhanced sensitivity to perturbations. However, quantum sensing schemes based on high-order EPs remain scarce, due to the experimental challenge of fine-tuning the system to such an extremely sensitive isolated point. Here we propose a four-channel dissipative coupling model that supports both fourth-order exceptional surfaces and second-order exceptional volumes. This non-Hermitian model can be realized in a thermal atomic system, and its complex energy spectra can be determined via electromagnetically induced transparency spectroscopy. The proposed model exhibits a characteristic fourth-order response to multiple physical quantities such as the laser detuning and the distance between optical channels, significantly surpassing the response of second-order EPs. We further reveal the sensitivity-robustness trade-off under experimental noise. Our work opens a route toward high-performance sensing leveraging higher-order EPs.
Exceptional points (EPs), which arose early from non-Hermitian physics, significantly amplify the system's response to minor perturbations, and they act as a useful concept to enhance measurement in metrology. In particular, such a metrological enhancement grows dramatically with the EP's order. However, the Langevin noises intrinsically existing in the non-Hermitian systems diminish this enhancement. In this study, we propose a protocol for quantum metrology with the construction of higher-order EPs (HOEPs) in an atom-cavity system through Hermitian magnon-photon interaction. The construction of HOEPs utilizes the atom-cavity non-Hermitian-like dynamical behavior but avoids the external Langevin noises via the Hermitian interaction. A general analysis is exhibited for the construction of arbitrary n th -order EP (EPn). As a demonstration of the superiority of these HOEPs in quantum metrology, we work out an EP3/4-based atomic sensor with sensitivity being orders of magnitude higher than that achievable in an EP2-based atomic sensor. We further unveil the mechanism behind the sensitivity enhancement from HOEPs. The experimental establishment for this proposal is suggested with potential candidates. This EP-based atomic sensor, taking advantage of the atom-light interface, offers new insight into quantum metrology with HOEPs.