Frequency Metrology on Single Trapped Ions in the Weak Binding Limit: The $3s_{1/2}-3p_{3/2}$ Transition in ${}^{24}\mathrm{Mg}^{+}$

We demonstrate a method for precision spectroscopy on trapped ions in the limit of unresolved motional sidebands. By sympathetic cooling of a chain of crystallized ions, we suppress adverse temperature variations induced by the spectroscopy laser that usually lead to a distorted line profile and obtain a Voigt profile with negligible distortions. We applied the method to measure the absolute frequency of the astrophysically relevant $D2$ transition in single ${}^{24}\mathrm{Mg}^{+}$ ions and find $1072082934.33(16)\mathrm{MHz}$, a nearly 400-fold improvement over previous results. Further, we find the excited state lifetime to be 3.84(10) ns.

Figure 1

Calculated temperature of the spectroscopy ion in a chain of two ions. The intensity of the cooling laser is set to a saturation parameter of $s=0.5$ and tuned 64 MHz below resonance. The spectroscopy beam is set to $s=0.004$. The dashed line shows for comparison the temperature profile if the cooling laser is turned off.

Figure 2

Schematic of the optical setup. The dye laser is phase locked to a fiber laser frequency comb using a diode laser as transfer oscillator (phase-locked loops PLL #1 and #2). The output of the dye laser is converted to 280 nm in a second harmonic generation (SHG) stage. Spectroscopy and cooling beams with separately adjustable frequency and stabilized intensity are obtained by splitting the UV output and passing them through two double-pass AOM (DP-AOM) setups. The inset shows the geometry of the cooling and spectroscopy beam relative to the ion chain (to scale).

Figure 3

Typical recorded resonance. The solid line is a Voigt fit to the data; the error bars represent Poissonian noise as derived from the counts.

Figure 4

Compensation of magnetic field shifts. We measured the line center versus polarization. The polarization is given in terms of the rotation angle of the quarter wave plate used; before the retarder, the beam is linearly polarized. For each polarization, three ions were evaluated.

Figure 5

Measured line centers. We determined the line center as in Fig. 4 on 11 days within four weeks. The error bars represent the statistical uncertainty only. The last data point was measured with a different laser system (fiber laser).