Improved Measurement of the Differential Polarizability Using Co-Trapped Ions

We present a novel approach for measuring the differential static scalar polarizability of a target ion utilizing a "polarizability scale" scheme with a reference ion co-trapped in a linear Paul trap. The differential static scalar polarizability of the target ion can be precisely extracted by measuring the ratio of the ac Stark shifts induced by an add-on infrared laser shed on both ions. This method circumvents the need for the calibration of the intensity of the add-on laser, which is usually the bottleneck for measurements of the polarizability of trapped ions. As a demonstration, ^{27}Al^{+} (the target ion) and ^{40}Ca^{+} (the reference ion) are used in this work, with an add-on laser at 1068 nm injected into the ion trap along the trap axis. The differential static scalar polarizability of ^{27}Al^{+} is extracted to be 0.416(14) a.u. by measuring the ratio of the ac Stark shifts of both ions. Compared to the most recent result [Phys. Rev. Lett. 123, 033201 (2019)PRLTAO0031-900710.1103/PhysRevLett.123.033201], the relative uncertainty of the differential static scalar polarizability of ^{27}Al^{+} is reduced by approximately a factor of 4, to 3.4%. This improvement is expected to be further enhanced by using an add-on laser with a longer wavelength.