Possible experiment on the observation of the $\mathcal{P},\mathcal{T}$-odd Faraday effect in intracavity absorption spectroscopy: Statistics and systematic errors

A recently proposed experiment on the observation of the $\mathcal{P},\mathcal{T}$-odd ($\mathcal{P}$ is space parity and $\mathcal{T}$ is time reflection) Faraday effect (optical rotation in an external electric field) (PTFE) in intracavity absorption spectroscopy is discussed. Two versions of this experiment are considered: the propagation of a continuous laser beam through an optical cavity filled with molecular gas (ThO vapor) and propagation of a continuous laser beam through an optical cavity crossed by the molecular beam (ThO molecules). With the use of optical cavities of high fineness, the accuracy of the experiment may reach a level exceeding the recently attained one by several orders of magnitude. The statistics of both types of experiment are analyzed. Ways to avoid experimentally the dangerous systematic errors, which can mimic the PTFE, are discussed.

Figure 1

Schematic of the possible experimental setup for the PTFE-ICAS experiment of type I.

Figure 2

Schematic of the possible experimental setup for the PTFE-ICAS experiment of type II.

Figure 3

False eEDM effect arising from the motional magnetic field in the case of the external electric field tilted with respect to the laser beam propagation direction $\mathit{\nu }$. Here ${\mathcal{E}}_{\perp }$ is electric-field component orthogonal to $\mathit{\nu }$ in the $yz$ plane, $\mathit{v}$ denotes the molecular beam velocity, and ${\left({\mathcal{H}}_M\right)}_{\parallel }$ is the component of motional magnetic field parallel to $\mathit{\nu }$.