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Spin squeezing characteristic time and quantum metrological precision in the two-axis twisting model
| 更新时间：2026-06-10
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Spin squeezing characteristic time and quantum metrological precision in the two-axis twisting model
- Acta Photonica Sinica Pages: 1-13(2026)
- 作者机构：
浙江理工大学 理学院 浙江 杭州310018
- 作者简介：
- 基金信息：Quantum Science and Technology-National Science and Technology Major Project(2023ZD0300904)
DOI：10.3788/gzxb20265507.0727002
CLC： O431.2- CSTR：32255.14.gzxb20265507.0727002
Received：22 January 2026，
Revised：2026-04-09，
Accepted：17 April 2026，
- 稿件说明：
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杨亚亚，李航，金光日. 双轴扭曲模型自旋压缩特征时间及量子度量精度［J］.光子学报，2026，55（7）：0727002
YANG Yaya， Li Hang， JIN Guangri. Spin squeezing characteristic time and quantum metrological precision in the two-axis twisting model［J］. Acta Photonica Sinica， 2026， 55（7）：0727002
杨亚亚，李航，金光日. 双轴扭曲模型自旋压缩特征时间及量子度量精度［J］.光子学报，2026，55（7）：0727002 DOI： 10.3788/gzxb20265507.0727002. CSTR： 32255.14.gzxb20265507.0727002.
YANG Yaya， Li Hang， JIN Guangri. Spin squeezing characteristic time and quantum metrological precision in the two-axis twisting model［J］. Acta Photonica Sinica， 2026， 55（7）：0727002 DOI： 10.3788/gzxb20265507.0727002. CSTR： 32255.14.gzxb20265507.0727002.
Spin squeezing characteristic time and quantum metrological precision in the two-axis twisting model
摘要
双轴扭曲模型描述
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个自旋
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粒子的非线性相互作用，用于制备原子自旋压缩态。过去的数值和近似解析解显示最优压缩态出现于特定时间，满足
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标度律。本文重新研究双轴扭曲模型并分析其宇称对称性，从而得到平均自旋方向，以及自旋态压缩、反压缩方向。对自旋算符运动方程中高阶项采用截断近似，得到最优压缩时间的
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标度律。分析有无噪声情况量子Fisher信息最大值，发现双轴扭曲自旋态可实现干涉仪相位测量精度突破标准量子极限，达到所谓的类海森堡标度率。
Abstract
The two-axis twisting model is used to describe the nonlinear interaction of
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spin particles and serves as an important means for generating atomic spin-squeezed states. As one of the core research subjects in the field of quantum precision measurement， multi-particle spin-squeezed states offer the potential to enhance measurement accuracy. The physical mechanisms for generating spin squeezing primarily involve nonlinear atom-atom interactions and atom-light interactions. KITAGAWA M and UEDA M proposed two nonlinear interaction models： the one-axis twisting model and the two-axis twisting model. The latter is specifically employed to define vacuum-squeezed states in multi-atom systems and can， in principle， be realized on existing one-axis twisting experimental platforms through multi-pulse techniques. Examples of such platforms include ultracold alkali metal atomic systems and nitrogen-vacancy centers in diamond. Recently， multi-pulse techniques have further been utilized to implement the so-called three-axis twisting model， as well as generalized versions of the two-axis twisting model.This work systematically investigates the dynamical behavior of the two-axis twisting model and the evolution of its associated quantum Fisher information under noisy environments by combining analytical analysis with numerical simulations. The study begins by examining the symmetry between the Hamiltonian and the parity operator of the model. This symmetry determines the mean spin direction of the system， allowing us to unambiguously identify the directions of spin squeezing and anti-squeezing. Systematically analyze the characteristics of the three squeezing parameters and focuson the characteristic times at which they reach their minimum values. For few-particle systems， we derive an explicit analytical form of the quantum state at the optimal squeezing time， which directly reveals the underlying quantum state structure and its squeezing characteristics. In systems with finite particle numbers， both numerical simulations and approximate analytical
studies consistently indicate that the optimal spin-squeezed state emerges at a specific time following a characteristic scaling law
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with respect to the particle number. Guided by this scaling law， we adopt an operator truncation approximation to obtain an explicit analytical expression linking the optimal squeezing time to the particle number. This result provides a crucial theoretical guideline for optimizing experimental parameters. Furthermore， we systematically analyze the impact of collective dephasing noise on the quantum Fisher information， aiming to assess the robustness of the metrological advantage offered by the prepared spin-squeezed states under realistic noisy conditions.For the two-axis twisting system， the mean spin of the collective ensemble is strictly aligned along the
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axis of the Bloch sphere， while the squeezing and anti
-squeezing directions are oriented along the
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axis and
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axis， respectively. Each of the three squeezing parameters attains its minimum at a specific time， and the dominant factor influencing all three criteria is whether the spin state is Gaussian. The optimal squeezing time is given analytically by the coefficient
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.Under the influence of noise， the squeezing parameter defined via the quantum Fisher information satisfies the relation
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.In summary， this study systematically investigates the dynamical characteristics of the two-axis twisting model and the application of quantum Fisher information in quantum metrology. The results indicate that the optimal squeezing time for two-axis twisting spin squeezing follows a scaling law of
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， and explicit analytical expressions for three squeezing coefficients are derived. Furthermore， by using the generated spin-squeezed state as a probe for interferometry， we show that under collective decoherence， the optimal squeezing coefficient defined via quantum Fisher information can reach
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， where the coefficient
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exhibits a weak dependence on the particle
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. The corresponding phase measurement precision surpasses the standard quantum limit and approaches a Heisenberg-like scaling， demonstrating that the two-axis twisting model not only facilitates quantum metrology under ideal conditions but also retains practical utility in the presence of realistic noise.
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