Measurement of infrared magic wavelength for an all-optical trapping of $^{40}$Ca$^{+}$ ion clock

TL;DR

This study experimentally determines the infrared magic wavelength for $^{40}$Ca$^{+}$ ion optical clock transition, achieving high precision measurement that enables all-optical trapping and improves understanding of blackbody radiation effects.

Contribution

First experimental measurement of the magic wavelength for $^{40}$Ca$^{+}$ ion transition with unprecedented precision, facilitating all-optical trapping of the ion clock.

Findings

Magic wavelength determined as 1056.37(9) nm.

Measured differential static polarizability as -44.32(32) a.u.

Results agree with theoretical predictions and improve precision by a factor of 300.

Abstract

For the first time, we experimentally determine the infrared magic wavelength for the $^{40}$Ca$^{+}$ $4s\, ^{2}\!S_{1/2} \rightarrow 3d\,^{2}\!D_{5/2}$ electric quadrupole transition by observation of the light shift canceling in $^{40}$Ca$^{+}$ optical clock. A "magic" magnetic field direction is chosen to make the magic wavelength insensitive to both the linear polarization purity and the polarization direction of the laser. The determined magic wavelength for this transition is 1056.37(9)~nm, which is not only in good agreement with theoretical predictions but also more precise by a factor of about 300. Using this measured magic wavelength we also derive the differential static polarizability to be $-44.32(32)$~a.u., which will be an important input for the evaluation of the blackbody radiation shift at room temperatures. Our work paves a way for all-optical-trapping of $^{40}$Ca$^{+}$ optical clock.