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arXiv:2502.04466 · Physical Review A

Upgrading quantum metrology by combined sensitivity resources in mixed linear-nonlinear light-matter interactions with bias field

Zu‐Jian Ying

Published Aug 25, 2025• 3 citations
arXivHTMLPDF

Abstract

The major goal of quantum metrology (QM) is to exploit the quantum resources to raise the measurement precision (MP) as high as possible. When the quantum resources such as squeezing has been widely explored, light-mater interaction systems set up a highly controllable platform applicable for QM in novel pursuit of high MP. However, critical QM by the conventional linear interaction is confronted with the restriction of low-frequency-limit condition and the detrimental problem of diverging preparation time of the probe state (PTPS). This work shows that mixed interactions by linear and nonlinear light-matter couplings in the presence of bias field can provide various quantum resources, including squeezing, degeneracy lifting, displacement and quantum phase transition. These resources manifest high sensitivity for QM as demonstrated by analytically obtained critical components or exponential behavior of quantum Fisher information. We find that these sensitivity resources can be combined to upgrade the upper bound of MP by many orders over the widely-applied squeezing resource. As further advantages, such an upgraded metrology protocol not only breaks the frequency-limit restrictions but also avoids the detrimental problem of diverging PTPS which were both encountered in linear interaction. Our work paves a way to exploit and combine all the resources in momentum, position and spin spaces to maximize the MP and expand the applicable conditions simultaneously.

DOI
10.1103/rtd9-z7cl

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The major goal of quantum metrology (QM) is to exploit the quantum resources to raise the measurement precision (MP) as high as possible. When the quantum resources such as squeezing has been widely explored, light-mater interaction systems set up a highly controllable platform applicable for QM in novel pursuit of high MP. However, critical QM by the conventional linear interaction is confronted with the restriction of low-frequency-limit condition and the detrimental problem of diverging preparation time of the probe state (PTPS). This work shows that mixed interactions by linear and nonlinear light-matter couplings in the presence of bias field can provide various quantum resources, including squeezing, degeneracy lifting, displacement and quantum phase transition. These resources manifest high sensitivity for QM as demonstrated by analytically obtained critical components or exponential behavior of quantum Fisher information. We find that these sensitivity resources can be combined to upgrade the upper bound of MP by many orders over the widely-applied squeezing resource. As further advantages, such an upgraded metrology protocol not only breaks the frequency-limit restrictions but also avoids the detrimental problem of diverging PTPS which were both encountered in linear interaction. Our work paves a way to exploit and combine all the resources in momentum, position and spin spaces to maximize the MP and expand the applicable conditions simultaneously.
Squeezing and transition criticality are two major sensitivity resources for quantum metrology (QM), combination of them may yield an upgraded QM protocol. In article number 2400630, Zu-Jian Ying proposes that such a combination is feasible in asymmetric non-linear light-matter interaction. The protocol not only enhances measurement precision (MP) by several orders but also has advantages of globally high MP and dramatically reduced preparation time of probe state. This work establishes a paradigmatic case of combining different sensitivity resources to manipulate QM and maximize MP.
Abstract Squeezing and transition criticality are two main sensitivity resources for quantum metrology (QM), combination of them may yield an upgraded metrology protocol for higher upper bound of measurement precision (MP). The present work shows that such a combination is feasible in light–matter interactions by a realizable asymmetric non‐linear quantum Rabi model (QRM). Indeed, the non‐linear coupling possesses a squeezing resource for diverging MP while the non‐monotonous degeneracy lifting by the asymmetries induces an additional tunable transition which further enhances the MP by several orders, as demonstrated by the quantum Fisher information (QFI). The resource combination not only leads to cooperative boosts to the divergence of QFI but also brings divergence compensation with the merit of globally high MP. Moreover, the protocol is immune from the problem of diverging preparation time of probe state that may hinder the conventional linear QRM in application of QM. This work establishes a paradigmatic case of combining different sensitivity resources to manipulate QM and maximize MP.
Quantum metrology employs quantum resources to achieve measurement precision beyond classical limits. This work investigates a Mach--Zehnder interferometer incorporating a Kerr nonlinear phase shifter, with photon-added two-mode squeezed coherent states generated via four-wave mixing as input. We demonstrate that increasing both the photon-addition order and the input resource strength systematically enhances phase sensitivity, quantum Fisher information, and the corresponding quantum Cramér--Rao bound. The proposed system not only surpasses the standard quantum limit but also approaches or exceeds the Heisenberg limit for linear phase shifts, while Kerr nonlinearity enables surpassing the super-Heisenberg limit. Furthermore, the scheme exhibits enhanced robustness against photon loss, providing a promising pathway toward practical high-precision quantum metrology applications.
Squeezing as a quantum resource for quantum metrology is robust against decoherence and dissipation, while the conventional nonlinear two-photon quantum Rabi model (QRM) provides a squeezing resource immune to the divergence problem of the preparation time of the probe state (PTPS). However, the critical point of the two-photon QRM is locally restricted to one single point, which hinders a wider application. In the present work we propose to combine the Stark coupling with the two-photon QRM to realize a tunable critical point so that the nonlinear critical quantum metrology can be globalized. As demonstrated by the diverging quantum Fisher information (QFI) the protocol enables us to acquire a high measurement precision in a wide range of coupling parameters rather than locally at a single critical point. Moreover, we find that the QFI not only manifests criticality but also exhibits universality. As a particular merit of our protocol, a strong squeezing can be globally retained as the leading quantum resource, while at the same time the PTPS remains in a finite order.
Virtual excitations, inherent to ultrastrongly coupled light-matter systems, induce measurable modifications in system properties, offering a novel resource for quantum technologies. In this Letter, we demonstrate how these virtual excitations and their correlations can be harnessed to enhance precision measurements, without the need to extract them. Building on the paradigmatic Dicke model, which describes the interaction between an ensemble of two-level atoms and a single radiation mode, we propose a method to harness hybridized light-matter modes whose renormalized frequencies encode the effects of virtual excitations for quantum metrology. Remarkably, we find that, for a fixed squeezing parameter ξ, exploiting virtual squeezing through oscillator frequency shifts yields a quadratic enhancement in estimation precision-scaling as exp(4ξ)-compared to the conventional exp(2ξ) scaling of real squeezed states. These results show that virtual excitations, though unobservable, can drive metrological performance beyond the standard quantum limit. Our approach establishes a broadly applicable framework for high-precision measurements across a wide class of ultrastrongly coupled quantum systems.
The quantum Rabi model (QRM) with linear coupling between light mode and qubit exhibits the analog of a second-order phase transition for vanishing mode frequency which allows for criticality-enhanced quantum metrology in a few-body system. We show that the QRM including a nonlinear coupling term exhibits much higher measurement precisions due to its first-order-like phase transition at finite frequency, avoiding the detrimental slowing-down effect close to the critical point of the linear QRM. When a bias term is added to the Hamiltonian, the system can be used as a fluxmeter or magnetometer if implemented in circuit QED platforms.