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arXiv:2411.10734 · Advanced Quantum Technologies

Combining Squeezing and Transition Sensitivity Resources for Quantum Metrology by Asymmetric Non‐Linear Rabi Model

Zu‐Jian Ying

Published Mar 31, 2025• 6 citations
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Abstract

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.

DOI
10.1002/qute.202400630

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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.
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.
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 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 Applications of quantum systems with non‐linear light–matter interaction have to deal with a peculiar instability in the ultra‐ and deep strong coupling regime, the so‐called “spectral collapse.” To solve this problem, the present work investigates a generalized quantum Rabi model (QRM) with two‐ and four‐photon terms in view of applications for critical quantum metrology. In the introduced model, the spectral collapse occurring in the standard two‐photon QRM is stabilized by the presence of the quartic potential. The collapse is then transformed into a quantum phase transition, which occurs in the low‐frequency limit of the light mode, whose remnant at finite ratio between qubit and mode frequencies can be applied to critically enhanced quantum metrology. It is found that the four‐photon term entails a much higher measurement precision compared to the standard two‐photon QRM. The mechanism behind the higher precision can be traced to the different behavior of the ground state wave function as the system is tuned through the transition. As the standard two‐photon QRM, despite the absence of the spectral collapse, the proposed model allows for a finite preparation time for the probe state (PTPS).
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.