Be optical lattice clocks with the fractional Stark shift up to the level of 10$^{-19}$

TL;DR

This paper calculates the properties of Be atom energy levels and identifies magic wavelengths for optical lattice clocks, demonstrating fractional Stark shifts below 10$^{-19}$, enhancing clock precision.

Contribution

The study provides detailed calculations of Be atom polarizabilities and identifies optimal conditions for optical lattice clocks with extremely low Stark shifts.

Findings

Identified two magic wavelengths at 300.03 nm and 252.28 nm.

Achieved fractional Stark shifts below 10$^{-19}$ under specific laser conditions.

Provided comprehensive polarizability data for Be atom states.

Abstract

The energy levels and electric dipole ($E1$) matrix elements of the ground state and low-lying excited states of Be atoms are calculated using the relativistic configuration interaction plus core polarization (RCICP) method. The static and dynamic $E1$, magnetic dipole ($M1$) and electric quadrupole ($E2$) polarizabilities as well as the hyperpolarizabilities of the $2s^2~^1S_0$ and $2s2p~^3P_0$ states are determined. Two magic wavelengths, 300.03 and 252.28 nm, of $2s^2~^1S_0 \rightarrow 2s2p~^3P_0$ clock transition are found. Then, the multipolar and nonlinear Stark shifts of the clock transition at the magic wavelength are discussed in detail. We find that when the laser intensity $I$ is in the range of 14.3 $\sim$ 15.9 kW/cm$^{2}$ and the detuning $\delta$ (the frequency detuning of the lattice laser frequency relative to the magic frequency) is in the range of 40.7 $\sim$ 40.9 MHz, the fractional Stark shifts of the clock transition are less than 1.0 $\times$ 10$^{-18}$. While, when $I$ is in the range of 15.01 $\sim$ 15.46 kW/cm$^{2}$ and $\delta$ is in the range of 40.73 $\sim$ 40.76 MHz, the fractional Stark shifts are lower than 1.0 $\times$ 10$^{-19}$.