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arXiv:2507.12971

Approximate universality and large measurement gain of Rabi model in a linear potential under strong Doppler broadening

Dongyang Yu, Zheng, Zhan

Published Jul 17, 2025• 0 citations
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Abstract

Harnessing quantum resources in the atomic external degrees of freedom, particularly matter-wave states with large momentum broadening, holds significant potential for enhancing the sensitivity of Kasevich-Chu atom gravimeters at the standard quantum limit. However, a fully quantum-mechanical investigation of the critical Doppler effect inherent to this approach remains lacking. Employing SU(2) Lie group theory, we derive a generic scalar Riccati equation governing the unitary dynamics of the Rabi model within a linear potential and analyze the Doppler effect's impact on Rabi oscillations because of the strong coupling between the internal and external states. Furthermore, by integrating Fisher information theory, we demonstrate the approximate universality and high metrological gain of phase-rotation measurement protocols under strong Doppler broadening induced by large-momentum width. This theoretical work provides insightful implications for broader generalization, such as extensions to finite-temperature scenarios or multi-pulse sequences, exemplified by the $π/2-π-π/2$ pulse sequence characteristic of Kasevich-Chu atom gravimeters. Thus this study lays a theoretical foundation for developing high-sensitivity, noise-resistant atom gravimeters that leverage external-state quantum resources.

DOI
10.48550/arxiv.2507.12971

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Harnessing quantum resources in the atomic external degrees of freedom, particularly matter-wave states with large momentum broadening, holds significant potential for enhancing the sensitivity of Kasevich-Chu atom gravimeters at the standard quantum limit. However, a fully quantum-mechanical investigation of the critical Doppler effect inherent to this approach remains lacking. Employing SU(2) Lie group theory, we derive a generic scalar Riccati equation governing the unitary dynamics of the Rabi model within a linear potential and analyze the Doppler effect's impact on Rabi oscillations because of the strong coupling between the internal and external states. Furthermore, by integrating Fisher information theory, we demonstrate the approximate universality and high metrological gain of phase-rotation measurement protocols under strong Doppler broadening induced by large-momentum width. This theoretical work provides insightful implications for broader generalization, such as extensions to finite-temperature scenarios or multi-pulse sequences, exemplified by the π/2−π−π/2π/2-π-π/2π/2−π−π/2 pulse sequence characteristic of Kasevich-Chu atom gravimeters. Thus this study lays a theoretical foundation for developing high-sensitivity, noise-resistant atom gravimeters that leverage external-state quantum resources.
Abstract Strong spin-squeezing is unavoidably followed by large momentum broadening for a cloud of expanding two-component Bose-Einstein condensate, where the associated Doppler effects may be crucial and not yet clarified from a perspective of full quantum mechanics. Employing SU(2) Lie group theory, we derive a generic Riccati equation governing the unitary dynamics of the Rabi model within a linear potential and analyze the Doppler effect's impact on Rabi oscillations. Furthermore, by integrating Fisher information theory, we demonstrate the approximate universality and high metrological gain of phase-rotation measurement protocols even though under strong Doppler broadening. For a Kasevich-Chu atom gravimeter based on a cloud of expanding two-component Bose-Einstein condensate with strong interatomic interactions, our work provides a theoretical foundation for clarifying the role of Doppler suppression on the high sensitivity from large momentum broadening, and strongly indicates that the phase-rotation operation can be still applied to get large measurement gain even under strong Doppler broadening.
Hybridization of internal and external atomic degrees of freedom in a Kasevich-Chu interferometer enables the possibility to enhance the sensitivity significantly even under quantum-standard limit. By introducing motional squeezing state as an input, we systematically derive the computational framework of quantum and classical Fisher information of two measurement protocols for arbitrary strength of Doppler effects. Through maximizing the corresponding classical Fisher information, we obtain the optimal control parameters and the corresponding quantum Fisher information. For population measurement, the largest sensitivity can be as large as four times than the semi-classical limit through enlarging the atom coherence length. For joint measurement of population and position, the competition between quantum enhancement and Doppler suppression induces two three behaviors, in one regime, the quantum enhancement dominates even in presence of strong Doppler broadening effects where the sensitivity is significantly enhanced; while in another regime, an optimal squeezing parameter is observed where the classical Fisher information reaches the maximum. Our results clearly demonstrate the robustness of external quantum enhancement against Doppler suppression. Our proposal can be readily applied to gravimeter of mobile platform where decoherence from noise will damage the many-body entanglement of internal spin squeezing.
Abstract The intrinsic hybridization of internal and external atomic degrees of freedom in a Kasevich--Chu interferometer enables engineered motional fluctuations to serve as an independent metrological resource while preserving standard-quantum-limit scaling. We develop a unified computational framework, based on quantum and classical Fisher information, for arbitrary uncorrelated motional inputs under both ideal and Doppler-modified atom--light interactions; a hybrid numerical integration scheme makes the highly oscillatory joint population--position calculation tractable. Applied to single-mode motional squeezed states, the framework predicts up to a twofold sensitivity gain over the semiclassical limit for population measurement through an enlarged atomic coherence length. Joint population--position measurement additionally exploits squeezing-induced reshaping of the spatial interference fringes, yielding substantial gains over a broader parameter regime and exceeding threefold in the quantum-enhancement-dominated regime. This enhancement remains robust to Doppler-induced pulse imperfections under strong momentum broadening and finite spatial resolution, while an optimal squeezing strength emerges from the competition between quantum enhancement and Doppler-induced suppression. Our results establish external motional fluctuations as a robust and underexplored single-particle resource for quantum-enhanced atom interferometry and provide a basis for extensions to correlated many-body systems.
Large momentum transfer (LMT) enhances the gravitational phase of a light-pulse atom interferometer by a factor nnn, while mirrorless operation with momentum-resolved detection can quadruple the phase-carrying quantum Fisher information. These gains compete in practice because the momentum-space fringe period scales as 1/n1/n1/n, making the fringe signal increasingly vulnerable to finite detector resolution. We analyze this trade-off in a solvable model with instantaneous lossless nnn-photon pulses, a Gaussian source, and Gaussian detection blur, allowing continuous interpolation between Kasevich--Chu and mirrorless geometries. Closed-form expressions for the blurred output distributions and classical Fisher information are obtained, with a fringe-phase averaging approximation whose error is exponentially suppressed and agrees with numerical simulations at the 10−810^{-8}10−8 level. We find that mirrorless operation surpasses a conventional interferometer with the same momentum transfer only when σp<0.91 m/(nk0T)σ_p < 0.91\,m/(n k_0 T)σp​<0.91m/(nk0​T). Fringe-based readout exhibits an optimal momentum transfer n∗≃0.93 m/(σpk0T)n^* \simeq 0.93\,m/(σ_p k_0 T)n∗≃0.93m/(σp​k0​T) and a resolution-limited sensitivity floor Δg≃4.4 σp/(mTN)Δg \simeq 4.4\,σ_p/(mT\sqrt{N})Δg≃4.4σp​/(mTN​), independent of photon momentum. When this criterion is not satisfied, partial mirror asymmetry can recover part of the enhancement, whereas population-based readout remains insensitive to detector blur and ultimately favors the conventional sequence at sufficiently large nnn. Estimates for 87^{87}87Rb sensors show that the mirrorless advantage is primarily restricted to short-baseline instruments.
A point source interferometer (PSI) is a device where atoms are split and recombined by applying a temporal sequence of Raman pulses. During the pulse sequence, an initially trapped cloud of cold atoms is released and allowed to expand, behaving approximately as a point source. The PSI can work as a sensitive multi-axes gyroscope that can automatically filter out the signal from accelerations. The phase shift arising from rotations is proportional to the momentum transferred to each atom from the Raman pulses. Therefore, by increasing the momentum transfer, it should be possibly to enhance the sensitivity of the PSI. Here, we investigate the degree of enhancement in sensitivity that could be achieved by augmenting the PSI with large momentum transfer (LMT) employing a sequence of many Raman pulses with alternating directions. Contrary to typical approaches used for describing a PSI, we employ a model under which the motion of the center of mass of each atom is described quantum mechanically. We show how increasing Doppler shifts lead to imperfections, thereby limiting the visibility of the signal fringes, and identify ways to suppress this effect by increasing the effective, two-photon Rabi frequencies of the Raman pulses. Considering the effect of spontaneous emission, we show that for a given value of the one-photon Rabi frequency, there is an optimum value for the number of pulses employed, beyond which the net enhancement in sensitivity begins to decrease. For a one-photon Rabi frequency of 200 MHz, for example, the peak value of the factor of enhancement in sensitivity is ~39, for a momentum transfer that is ~69 times as large as that for a conventional PSI. We also find that this peak value scales as the one-photon Rabi frequency to the power of 4/5.
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.