Quantum metrology employs quantum effects to attain a measurement precision surpassing the limit achievable in classical physics. However, it was previously found that the precision returns the shot-noise limit (SNL) from the ideal Zeno limit (ZL) due to the photon loss in quantum metrology based on Mech-Zehnder interferometer. Here, we find that not only the SNL can be beaten, but also the ZL can be asymptotically recovered in long-encoding-time condition when the photon dissipation is exactly studied in its inherent non-Markovian manner. Our analysis reveals that it is due to the formation of a bound state of the photonic system and its dissipative noise. Highlighting the microscopic mechanism of the dissipative noise on the quantum optical metrology, our result supplies a guideline to realize the ultrasensitive measurement in practice by forming the bound state in the setting of reservoir engineering.Introduction.-Pursuing high-precision measurement to physical quantities, metrology plays a significant role in advancing the innovation of science and technology. Restricted by the unavoidable errors, the metrology precision realized in classical physics is strongly bounded by the shot-noise limit (SNL) N −1/2 with N being the number of resource employed in the measurements. It was found that the SNL can be beaten by taking advantage of the quantum effects such as squeezing [1-3] and entanglement [4][5][6]. This inspires the birth of a newly emerged field, quantum metrology [7][8][9]. Many fascinating applications of quantum metrology have been proposed. The quantum effects of light can offer enhanced imaging resolution [10][11][12] in biological monitoring [13][14][15] and in optical lithography [16], and improved sensitivity in gravitational wave detection [17] and in radar [18]. The quantum characters of atoms or spins can provide an enhanced precision in sensing weak magnetic field [19][20][21][22][23][24] and ultimate accuracy for clocks [25][26][27].

Higher-order exceptional points (HOEPs) with extraordinary responsivity are expected to exhibit a vastly improved performance in detection-related applications. However, over the past few years, such an approach has been questioned due to several potential drawbacks, including the stringent parameter requirements, fundamental resolution limits, and noise. Here, exploring the consequence of nonlinear gain saturation in exceptional singularities of non-Hermitian systems, we offer a feasible scheme to overcome all the above difficulties. We provide a simple and intuitive example by demonstrating with both theory and circuit experiments an “exceptional nexus” (“EX”), a HOEP with an ultra-enhanced signal-to-noise ratio (SNR), in only two coupled resonators with the aid of nonlinear gain. The tedious parameter tuning in a 6D hyper-dimensional space is reduced to 2D. The feedback mechanism of nonlinear saturable gain can give a solution to the ongoing debate on the SNR of EPs in other linear systems. Our findings advance the fundamental understanding of the peculiar topology of nonlinear non-Hermitian systems, significantly reduce the practical difficulty in EP sensing, and possibly open new avenues for applications.

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Quantum metrology utilizes quantum effects to reach higher precision measurements of physical quantities compared with their classical counterparts. However the ubiquitous decoherence obstructs its application. Recently, non-Markovian effects are shown to be effective in performing quantum optical metrology under locally dissipative environments [PhysRevLett.123.040402 (2019)]. However, the mechanism is still rather hazy. Here, we uncover the reason why forming a bound state can protect the quantumness against a dissipative ambient via the quantum Fisher information of entangled coherent states. An exact analytical expression of the quantum Fisher information in the long-encoding-time condition is derived, which reveals that the dynamics of precision can asymptotically reach the ideal-case-promised one easily when the average photon number is small. Meanwhile, the scaling exhibits a transition from the weak Heisenberg limit to the subclassical limit with increasing of average photon number. Our work provides a recipe to realize ultrasensitive measurements in the presence of noise by utilizing non-Markovian effects.