Evaluation of the $\mathcal{P}, \mathcal{T}$-odd Faraday effect in Xe and Hg atoms

Accurate evaluation of the $\mathcal{P},\mathcal{T}$-odd Faraday effect (rotation of the polarization plane for the light propagating through a medium in presence of an external electric field) is presented. This effect can arise only due to the $\mathcal{P},\mathcal{T}$-odd ($\mathcal{P}$—space parity, $\mathcal{T}$—time reflection) interactions and is different from the ordinary Faraday effect, i.e., the light polarization plane rotation in an external magnetic field. The rotation angle is evaluated for the intracavity absorption spectroscopy- type experiments with Xe and Hg atoms. The results show that the Hg atom may become a good candidate for a search for the $\mathcal{P},\mathcal{T}$-odd effects in atomic physics.

Figure 1

Behavior of the functions $g(u,v), f(u,v)$, and $h(u,v)$ with $v\ll 1$ in the vicinity of the resonance. Figure 1 represents the optical rotation angle (natural or $\mathcal{P}$-odd), Fig. 1 represents the inverse absorption length, Fig. 1 represents the rotation angle for the Faraday effect (ordinary or $\mathcal{P},\mathcal{T}$-odd).

Figure 2

The scheme of the hyperfine and the linear Stark splitting for the E1 transition in Xe atom.

Figure 3

Dependence of the $\mathcal{P},\mathcal{T}$-odd Faraday signal $R$ (in rad) on dimensionless detuning $u$ and on vapor density $\rho$ (in ${\mathrm{cm}}^{-3}$) for the E1 transition $\left({}^{2}P_{3/2}^0\right)6s{[3/2]}_2^0\to \left({}^{2}P_{3/2}^0\right)6p{[1/2]}_1$ in Xe atom. The optical path length $l$ is assumed to be equal to 100 km.

Figure 4

The scheme of the hyperfine and the linear Stark splitting for the $6s6p\left({}^{3}P_1\right)\to 6s7s\left({}^{3}S_1\right)$ E1 transition in ${}^{199}\mathrm{Hg}$ atom.

Figure 5

Dependence of the $\mathcal{P},\mathcal{T}$-odd Faraday signal $R$ (in rad) on dimensionless detuning $u$ and on vapor density $\rho$ (in ${\mathrm{cm}}^{-3}$) for the $6s6p\left({}^{3}P_1\right)\to 6s7s\left({}^{3}S_1\right)$ E1 transition in Hg atom. The optical path length $l$ is assumed to be equal to 100 km

Figure 6

(a) Behavior of the $R(u,{\rho }_{\text{opt}})$ projection of Fig. 5 (in rad), assuming fixed number density ${\rho }_{\text{opt}}=4\times {10}^7{\mathrm{cm}}^{-3}$, and (b) behavior of the $R(u_{\text{opt}},\rho )$ projection of Fig. 5 (in rad), assuming fixed dimensionless detuning $u_{\text{opt}}=5$ ($\rho$ in ${\mathrm{cm}}^{-3}$).

Figure 7

The scheme of the hyperfine and the linear Stark splitting for the $6s^2\left({}^{1}S_0\right)\to 6s6p\left({}^{3}P_1\right)$ E1 transition in ${}^{199}\mathrm{Hg}$ atom.

Figure 8

Dependence of the $\mathcal{P},\mathcal{T}$-odd Faraday signal $R$ (in rad) on dimensionless detuning $u$ and on vapor density $\rho$ (in ${\mathrm{cm}}^{-3}$) for the $6s^2\left({}^{1}S_0\right)\to 6s6p\left({}^{3}P_1\right)$ E1 transition in Hg atom. The optical path length $l$ is assumed to be equal to 100 km.