Frequency Light Shifts Caused by the Effects of Quantization of Atomic Motion in an Optical Lattice

TL;DR

This paper investigates how quantization of atomic motion in optical lattices causes frequency light shifts, affecting the precision of atomic clocks, with a focus on forbidden transitions and the influence of lattice configurations.

Contribution

It provides a detailed analysis of frequency light shifts due to atomic motion quantization, including effects of magneto-dipole and quadrupole transitions, and highlights their impact on optical lattice clock accuracy.

Findings

Shift proportional to square root of lattice intensity in Lamb-Dicke regime

Shift persists at magic wavelength due to higher-order transitions

Magic frequency varies with lattice field configuration by 1-100 MHz

Abstract

Frequency light shifts resulting from the localization effects and effects of the quantization of translational atomic motion in an optical lattice is studied for a forbidden optical transition $J$=0$\to$$J$=0. In the Lamb-Dicke regime this shift is proportional to the square root from the lattice field intensity. With allowance made for magneto-dipole and quadrupole transitions, the shift does not vanish at the magic wavelength, at which the linear in intensity shift is absent. Preliminary estimates show that this shift can have a principal significance for the lattice-based atomic clocks with accuracy of order of 10$^{-16}-10^{-18}$. Apart from this, we find that the numerical value of the magic frequency depends on the concrete configuration of the lattice field and it can vary within the limits 1-100 MHz (depending on element) as one passes from one field configuration to another. Thus, theoretical and experimental investigations of contributions originated from magneto-dipole and quadrupole transitions are of principal self-dependent interest.