Angle-dependent magic wavelengths for the $4s_{1/2}\to3d_{5/2,3/2}$ transitions of Ca$^{+}$ ions

TL;DR

This paper investigates how the magic wavelengths for specific calcium ion transitions depend on the angle between the quantization axis and polarization, revealing angle-sensitive and insensitive magic wavelengths near key transition points.

Contribution

It identifies angle-dependent magic wavelengths for Ca+ ion transitions, highlighting the anisotropic effects on dynamic polarizabilities and Stark shift nullification.

Findings

Magic wavelengths near 395.79 nm are angle-insensitive.

Longer magic wavelengths beyond 854.21 nm are highly angle-sensitive.

The study enhances understanding of polarization effects on atomic transition control.

Abstract

The dynamic polarizabilities of the atomic states with angular momentum $j> \frac12$ are sensitive to the angle between the quantization axis $\hat{e}_z$ and the polarization vector $\hat{\mathbf{\epsilon}}$ owing to the contribution of anisotropic tensor polarizabilities. The magic wavelength, at which the differential Stark shift of an atomic transition nullifies, depends on this angle. We identified the magic wavelengths for the $4s_{\frac12}\to3d_{\frac32,\frac52}$ transitions of Ca$^{+}$ ions at different angles between $\hat{e}_z$ and $\hat{\mathbf{\epsilon}}$ in the case of linearly polarized light. We found that the magic wavelengths near 395.79 nm, which lie between the $4s_{\frac12}\to4p_{\frac12}$ and $4s_{\frac12}\to 4p_{\frac32}$ transition wavelengths, remain unsensitive to the angle, while the magic wavelengths, which are longer than the $3d_{\frac52}\to 4p_{\frac32}$ resonant transition wavelength (854.21 nm), are very sensitive to the angle.