AI 中文总结
研究悬浮铁磁陀螺仪的量子动力学，建立量子模型，分析其进动等现象及量子极限，表明射频场可驱动跃迁，实现多种功能，为其应用建立框架，相关技术可用于寻找多种物理现象。
AI 中文摘要
我们为自由悬浮的铁磁陀螺仪（LFG）的旋转动力学建立了一个量子模型，着重研究固有自旋\(\boldsymbol{S}\)、机械角动量\(\boldsymbol{L}\)和磁转矩之间的相互作用。沿\(z\)方向磁场\(\boldsymbol{B}\)的守恒总角动量投影\(J_z = S_z + L_z\)是量子化的，在小振动幅度极限下导致离散的进动状态\(|m\rangle\)和振动谐振子状态\(|n\rangle\)。能量和动力学变量的离散性由量子进动尺度\(\Omega_Q=\hbar/I\)决定。我们发现LFG进动现象在高场区域持续存在，此时进动相关的旋转角动量大小超过总固有自旋。我们分析了局部半经典LFG取向波包和精确\(J_z\)本征态\(|m\rangle\)的互补量子极限，阐明了经典进动信号与潜在的量子化自旋 - 转子动力学之间关系。还表明射频场可驱动\(\Delta m = \pm 1\)和\(\Delta n = \pm 1\)跃迁，实现阶梯光谱学、倾斜角控制以及进动和振动之间的类似边带耦合。耦合动力学还表现出分支点磁共振，进动和振动运动强烈耦合。这些结果为将LFG用作超灵敏转矩和磁场传感器以及可控介观量子系统建立了框架，相关技术可用于寻找奇异的、超出标准模型的自旋相关相互作用、超轻暗物质和自旋 - 引力耦合。
英文摘要
We develop a quantum model for the rotational dynamics of a freely floating levitated ferromagnetic gyroscope (LFG), emphasizing the interplay between intrinsic spin $\boldsymbol{S}$, mechanical angular momentum $\boldsymbol{L}$, and magnetic torque. The conserved total angular momentum projection along the $z$-directed magnetic field $\boldsymbol{B}$, $J_z=S_z+L_z$, is quantized, leading in the small-libration-amplitude limit to discrete precessional states $|m\rangle$ (eigenstates of $J_z$ with eigenvalues $J_z = m\hbar$) and librational harmonic oscillator states $|n\rangle$ ($n=0,1,2,\ldots$). The discreteness of the energies and dynamical variables is governed by the quantum precession scale $Ω_Q=\hbar/I$, where $I$ is the moment of inertia of the LFG. We find that the phenomenon of LFG precession persists into high-field regimes where the magnitude of the rotational angular momentum associated with precession exceeds the total intrinsic spin. We analyze the complementary quantum limits of localized semiclassical LFG orientation wave packets and exact $J_z$-eigenstates $|m\rangle$, clarifying the relation between classical precession signals and the underlying quantized spin-rotor dynamics. We further show that radio-frequency fields can drive $Δm = \pm 1$ and $Δn = \pm 1$ transitions, enabling ladder spectroscopy, tilt-angle control, and sideband-like coupling between precession and libration. The coupled dynamics also exhibit branch-point magnetic resonances where precession and librational motion become strongly coupled. These results establish a framework for using LFGs not only as ultrasensitive torque and magnetic-field sensors, but also as controllable mesoscopic quantum systems. The techniques developed here may be applied to searches for exotic, beyond-the-standard model spin-dependent interactions, ultralight dark matter, and spin-gravity couplings.
Comments26 pages, 10 figures
