Precision measurement of the light shift of ${}^{25}\mathrm{Mg}^{+}$ ions

We calculate the polarizabilities of the Zeeman sublevels of ${}^{25}\mathrm{Mg}^{+}$ ion hyperfine ground states. To verify the calculation result, a single ${}^{25}\mathrm{Mg}^{+}$ ion is trapped in a Paul trap and a microwave resonance measurement is carried out on the ground states with and without the light shift. A good agreement between the experimental result and the calculation result is obtained.

Figure 1

The relevant energy levels of the ${}^{25}\mathrm{Mg}^{+}$ ion. The cooling and detection laser is near resonant with the ${}^{2}S_{1/2}|3,3\rangle \to {}^{2}P_{3/2}|4,4\rangle$ cycling transition, the $\pi$ laser has the same frequency as that of the cooling laser, ${\sigma }^{+}$ is the laser for inducing the light shift, and $\mathrm{\Delta }$ is the detuning of the ${\sigma }^{+}$ laser. The frequency of the microwave is about 1.79 GHz.

Figure 2

Schematic of the experimental setup. The detection laser beam counterpropagates with the ${\sigma }^{+}$ laser which generates the light shift. A linearly polarized $\pi$ beam propagates perpendicularly for state preparation. CCD and PMT are used to detect the fluorescence signal of the ions.

Figure 3

Fluorescence per 0.1 second vs laser power at different frequency detunings ${\mathrm{\Delta }}_D$ of the detection laser. For the reference fluorescence curve, the frequency detuning ${\mathrm{\Delta }}_D$ is 8(1) MHz. For the other three plotted curves, they have additional 4-, 8-, and 12-MHz red detuning compared to the reference.

Figure 4

Typical microwave resonance spectrum of the $|2,2\rangle$ to $|3,3\rangle$ transition with and without the light shift.

Figure 5

The light shifts for the seven microwave transitions. Black squares, theoretical results; red circles, experimental results; blue triangles, the ratio of theoretical and experimental results. The purple line corresponds to a ratio of one.

Figure 6

The black curves are the theoretical light shifts under saturated intensity $I_S$ at different dutuning frequencies of the ${\sigma }^{+}$ light. The relative frequency is relative to the transition of $|F=3\rangle$ to the excited state $|F=4\rangle$. The red data points are our experimental results.