论文标题
通过连续监测的原子集合估算波动的磁场
Estimating a fluctuating magnetic field with a continuously monitored atomic ensemble
论文作者
论文摘要
我们研究了通过对原子集合的连续光学探测来估计依赖时间的磁场的问题。假定磁场遵循随机的Ornstein-Uhlenbeck过程，并诱导原子基态旋转的Larmor进攻，这是通过激光场探头的Faraday极化旋转读取的。相互作用和测量方案与未知磁场的混合量子量子高斯的描述以及原子和场变量兼容。这将连接条件量子动力学和经典参数估计问题以更新公式的形式用于经典和量子自由度的第一矩和第二矩。我们的混合量子古典理论等于卡尔曼过滤的经典理论以及高斯国家的量子理论。通过参考平滑的经典理论以及过去量子状态的量子理论，我们展示了在时间$ t $上的光学探测$ t $之后如何改善我们对磁场值的估计，并提出了分析和解释对常规过滤方法的改进的数值模拟。
We study the problem of estimating a time dependent magnetic field by continuous optical probing of an atomic ensemble. The magnetic field is assumed to follow a stochastic Ornstein-Uhlenbeck process and it induces Larmor precession of the atomic ground state spin, which is read out by the Faraday polarization rotation of a laser field probe. The interactions and the measurement scheme are compatible with a hybrid quantum-classical Gaussian description of the unknown magnetic field, and the atomic and field variables. This casts the joint conditional quantum dynamics and classical parameter estimation problem in the form of update formulas for the first and second moments of the classical and quantum degrees of freedom. Our hybrid quantum-classical theory is equivalent with the classical theory of Kalman filtering and with the quantum theory of Gaussian states. By reference to the classical theory of smoothing and with the quantum theory of past quantum states, we show how optical probing after time $t$ improves our estimate of the value of the magnetic field at time $t$, and we present numerical simulations that analyze and explain the improvement over the conventional filtering approach.
