Quantum non-demolition measurements in light-atom ensembles

The interaction of light with an atomic vapor can be configured to be one of the most sensitive magnetic field measurement techniques. Recently, the measurement precision of such atomic magnetometers has been improved by generating spin squeezing via quantum non-demolition measurements based on paramagnetic Faraday rotation. Initially, a continuous measurement of the precessing collective spin introduces a back-action noise (BAN) which limits the knowledge acquired by the measurement. Previous results have addressed how to mitigate the BAN for an ensemble of atoms in the presence of a constant magnetic field by pulsing the probe beam at half the Larmor period [1], or by performing a continuous measurement while pulsing the magnetic field [2]. In this work, we focus on deriving analytical expressions and present numerical results of the quantum noise of a pulsed parametric Faraday rotation measurement when the magnetic field is allowed to vary in time in a non-periodic fashion.

[1] G. Vasilakis and H. Shen, et. al., Nature Physics 11, 389–392 (2015).

[2] G-Y. Zhang and K-F Zhao, Phys. Rev. A 93, 033841 (2016).