Relativistic full-configuration-interaction calculations of magic wavelengths for the $2\,^3S_1\rightarrow2\,^1S_0$ transition of helium isotopes

TL;DR

This paper performs high-precision relativistic calculations to identify magic wavelengths for helium isotopes' transition, aiding experimental optical trapping and nuclear radius measurements.

Contribution

It provides the first high-accuracy theoretical determination of magic wavelengths for helium isotopes including QED and hyperfine effects.

Findings

Magic wavelength for $^4$He: 319.8153(6) nm, matching experimental data.

Magic wavelength for $^3$He: 319.8302(7) nm, supporting future experiments.

High-accuracy energies and matrix elements up to n=13 obtained.

Abstract

A large-scale full-configuration-interaction calculation based on Dirac-Coulomb-Breit (DCB) Hamiltonian is performed for the $2\,^1S_0$ and $2\,^3S_1$ states of helium. The operators of the normal and specific mass shifts are directly included in the DCB framework to take the finite nuclear mass correction into account. High-accuracy energies and matrix elements involved n (the main quantum number) up to 13 are obtained from one diagonalization of Hamiltonian. The dynamic dipole polarizabilities are calculated by using the sum rule of intermediate states. And a series of magic wavelengths with QED and hyperfine effects included for the $2\,^3S_1\rightarrow2\,^1S_0$ transition of helium are identified. In addition, the high-order Ac Stark shift determined by the dynamic hyperpolarizabilities at the magic wavelengths are also evaluated. Since the most promising magic wavelength for application in experiment is 319.8 nm, the high-accuracy magic wavelength of 319.815 3(6) nm of $^4$He is in good agreement with recent measurement value of 319.815 92(15) nm [Nature Physics (2018)/arXiv:1804.06693], and present magic wavelength of 319.830 2(7) nm for $^3$He would provide theoretical support for experimental designing an optical dipole trap to precisely determine the nuclear charge radius of helium in future.