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arXiv:2506.03379 · Physical Review A

Globalized nonlinear critical quantum metrology using the two-photon Rabi-Stark model

Zu‐Jian Ying

Published Nov 24, 2025• 3 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/wnvk-lq8x

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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.
Quantum Rabi model (QRM) is a fundamental model for light-matter interactions, the finite-component quantum phase transition (QPT) in the QRM has established a paradigmatic application for critical quantum metrology (CQM). However, such a paradigmatic application is restricted to a local regime of the QPT which has only a single critical point. In this work we propose a globalized CQM in the QRM by introducing an auxiliary nonlinear term which is realizable and can extend the critical point to a continuous critical regime. As a consequence, a high measurement precision is globally available over the entire coupling regime from the original critical point of the QRM down to the weak-coupling limit, as demonstrated by the globally accessible diverging quantum Fisher information in dynamics. We illustrate a measurement scheme by quadrature dynamics, with globally criticality-enhanced inverted variance as well as the scaling relation with respect to finite frequencies. In particular, we find that the globally high measurement precisions still survive in the presence of decoherence. Our proposal paves a way to break the local limitation of QPT of the QRM in CQM and enables a broader application, with implications of applicability in realistic situation.
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.
Because quantum critical systems are very sensitive to the variation of parameters around the quantum phase transition (QPT), quantum criticality has been presented as an efficient resource for metrology. In this paper, we address the issue whether the divergent feature of the inverted variance is realizable in the presence of noise when approaching the QPT. Taking the quantum Rabi model (QRM) as an example, we obtain the analytical result for the inverted variance with single-photon relaxation. We show that the inverted variance may be convergent in time due to the noise. Since the precision of the metrology is very sensitive to the noise, as a remedy, we propose squeezing the initial state to improve the precision under decoherence. In addition, we also investigate the criticality-based metrology under the influence of the two-photon relaxation. Strikingly, although the maximum inverted variance still manifests a power-law dependence on the energy gap, the exponent is positive and depends on the dimensionless coupling strength. This observation implies that the criticality may not enhance but weaken the precision in the presence of two-photon relaxation, due to the non-linearity introduced by the two-photon relaxation.
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.
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.
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.