Progress toward the $\mathcal{P},\mathcal{T}$-odd Faraday effect: Light absorption by atoms briefly interacting with a laser beam

We investigate the process of photon absorption by atoms or molecules shortly interacting with a laser beam in the dipole approximation. Assuming that the interaction time $\tau$ is much smaller than the lifetime of the corresponding excited state, we examine the absorption probability as a function of $\tau$. In addition, we incorporate Doppler broadening due to nonzero temperature of the atoms (molecules). It is demonstrated that in the case of a zero detuning and without Doppler broadening the absorption probability is quadratic in $\tau$. Once Doppler broadening is taken into account or the laser beam is off from the resonant frequency, the absorption probability becomes linear in $\tau$. Our findings are expected to be important for experimental studies in optical cells or cavities where atoms or molecules traverse continuous laser beams. The experimental prospects of searching for the electric dipole moment of the electron are discussed in detail.

Figure 1

Principle scheme of the experimental setup for measuring the $\mathcal{P}$, $\mathcal{T}$-odd Faraday rotation. A beam of atoms or molecules (blue) traverses a high-finesse optical cavity between two mirrors and interacts with a linearly polarized laser beam (green). The interaction region is located in a background electric field (yellow) directed along the laser beam axis. The laser radiation transmitted through the mirrors is detected by means of a polarimeter.

Figure 2

Leading-order Feynman diagram describing absorption and emission of a photon by an atom interacting with a classical external field.