| Summary: | For the first time, we experimentally determine the infrared magic wavelength for the ^40 Ca ^+ $4s{\,^2}{S_{1/2}} \to 3d{\,^2}{D_{5/2}}$ 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 (‘Dirac–Fock plus core polarization’ method) 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.
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