Two-photon $E1$-$M1$ optical clock

An allowed $E1$-$M1$ excitation scheme creates optical access to the ${}^1{S}_0\to {}^3{P}_0$ clock transition in group-II-type atoms. This method does not require the hyperfine mixing or application of an external magnetic field of other optical clock systems. The advantages of this technique include a Doppler-free excitation scheme and increased portability with the use of vapor cells. We will discuss technical mechanisms of a monochromatic excitation scheme for a hot $E1$-$M1$ clock and briefly discuss a bichromatic scheme to eliminate light shifts. We determine the optimal experimental parameters for Hg, Yb, Ra, Sr, Ba, Ca, Mg, and Be and calculate that neutral Hg has ideal properties for a hot, portable frequency standard.

Figure 1

Two-photon clock level structure. This is the prototypical, optical clock-level structure with a ${}^3{P}_0$ clock state. The electric field of one photon and the magnetic field of a second degenerate photon directly couple the ${}^1{S}_0$ ground state to the clock state by coupling to the intermediate ${}^3{P}_1$ level with some detuning $\Delta$. A sample detection channel for a hot clock is the ${}^3{P}_0\genfrac{}{}{0pt}{}{E1}{⟺}{}^3{S}_1$, $E1$ allowed transition.

Figure 2

Hot optical clock. This diagram of a monochromatic laser in a vapor cell depicts the experimental system. The detection length $L_o$ is the detection optics aperture, and the laser beam radius is ${\omega }_0$. The Rayleigh range $z_R$ that limits the interrogation region is shown in this graphic. The area enclosed by a box is the Rayleigh-limited interrogation region of the atoms.

Figure 3

Vapor cell density. Number density of group-II-type atoms with respect to vapor cell temperature. The high number density of Hg gives it a statistical advantage for optical stability.

Figure 4

Optimal laser beam size. Plot of effective excitation rate ${\dot{N}}_{{}^3{P}_0}$ with respect to beam waist size, Eq. (3), for neutral Hg at 448 K. The asymptotic behavior in Rayleigh-limited and detection-limited regimes where the peak rates are found when the Rayleigh range $z_R$ is set to match the detection length $L_o$ is displayed. In Hg this happens at 41 $\mu$m.

Figure 5

Asymptotic behavior of $\Delta \nu$ in Ra. Calculation results for laser beam radius ${\omega }_0$ dependence of the transit broadening $\Delta {\nu }_{TT}$, first-order Doppler broadening $\Delta {\nu }_{D1}$, and total broadening $\Delta \nu$ for Ra at vapor cell temperature 800 K are shown.

Figure 6

Experimental parameters for Hg stability. The stability $\mathcal{S}$[Eq. (25)] of a hot Hg $E1$-$M1$ clock is plotted for laser beam radius ${\omega }_0$ and vapor cell temperature $T$. $\mathcal{S}$${}_{\text{min}}$= $1.6\times {10}^{-15}$ $\left(\sqrt{{\mathrm{Hz}}^{-1}}\right)$ is found at ${\omega }_0=0.6$ mm and $T=380$ K.