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

Dongyang Yu, Zhan Zheng

Published Mar 12, 2026• 0 citations
Publisher

Abstract

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.

DOI
10.21203/rs.3.rs-8197834/v1

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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.
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.
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.
We show that the inherently large interatomic interactions of a Bose-Einstein condensate (BEC) can enhance the sensitivity of a high precision cold-atom gravimeter beyond the shot-noise limit (SNL). Through detailed numerical simulation, we demonstrate that our scheme produces spin-squeezed states with variances up to 14 dB below the SNL, and that absolute gravimetry measurement sensitivities between two and five times below the SNL are achievable with BECs between 10^{4} and 10^{6} in atom number. Our scheme is robust to phase diffusion, imperfect atom counting, and shot-to-shot variations in atom number and laser intensity. Our proposal is immediately achievable in current laboratories, since it needs only a small modification to existing state-of-the-art experiments and does not require additional guiding potentials or optical cavities.
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.
The production of large-scale entangled states is one of the main goals of next-generation quantum technologies, with an immediate potential for applications in the context of entanglement-assisted quantum sensing. A very promising platform to achieve this goal is offered by ultracold spinor gases, made of atoms with a large internal spin sensitive to magnetic fields. Here we show that the native spin-changing collisions in a spinor Bose-Einstein condensate, combined with an arbitrary quadratic Zeeman shift, can generate scalable spin squeezing in the collective spin of the ensemble, following the universal paradigm of the celebrated one-axis-twisting model. Squeezing dynamics is driven by the quadratic Zeeman shift when this shift is small; and by the spin-changing collisions for large shifts, in the form of stroboscopic squeezing. Turning off the Zeeman shift freezes out the collective-spin dynamics, so that the ensuing collective spin dynamics can be uniquely governed by an external field to be sensed. Our theoretical results pave the way for the use of spinor Bose gases with a large spin in fundamental studies of entanglement, as well as in advanced metrological applications.