Direct Frequency Comb Spectroscopy of Trapped Ions

Direct frequency comb spectroscopy of trapped ions is demonstrated for the first time. It is shown that the $4s{}^{2}S_{1/2}–4p{}^{2}P_{3/2}$ transition in calcium ions can be excited directly with a frequency comb laser that is up-converted to 393 nm. Detection of the transition is performed using a shelving scheme to suppress the background signal from nonresonant comb modes. The measured transition frequency of $f=761905012.7(0.5)\mathrm{MHz}$ presents an improvement in accuracy of more than 2 orders of magnitude.

Figure 1

Schematic layout of the laser system and linear Paul trap. $\mathrm{DL}=\mathrm{\text{diode laser}}$, $\mathrm{PMT}=\mathrm{\text{photo-multiplier tube}}$, $2\omega =\mathrm{\text{frequency-doubling setup}}$, $\mathrm{CEM}=\mathrm{\text{channel electron multiplier}}$. Inset: Setup for chirped doubling of the frequency comb. Lenses are drawn for clarity; in practice only reflective optics are used. The comb spectrum is dispersed on a $600\mathrm{l}/\mathrm{mm}$ grating before being doubled in a beta-barium borate (BBO) crystal. The colors in the doubled spectrum are overlapped using a $1200\mathrm{l}/\mathrm{mm}$ grating. $f_1=20\mathrm{cm}$; $f_2=10\mathrm{cm}$.

Figure 2

Schematic view of the energy levels and the shelving principle. Arrows indicate laser beams; the wavy lines spontaneous fluorescence. The second repumper at 854 nm is periodically blocked using a chopper. If this repumper is present [situation (a)], all ions stay in the cooling cycle. A blocked repumper leads to transfer of the ions into the dark state, and the fluorescence from the cooling laser decreases [situation (b)].

Figure 3

Top: Measured fluorescence signal for the periods where the second repumper at 854 nm is on [gray (red) trace] and the periods where the repumper is off (black trace). The comb repetition frequency $f_{\mathrm{rep}}$ is scanned against time (upper axis) and frequency (lower axis). Bottom: Normalized fluorescence signal (corrected for decay, thin black trace) and the corresponding fit [thick gray (red) trace].

Figure 4

Mode number determination: The upper part of the graph shows the fits to the scans at different frequency comb repetition frequencies ($f_{\mathrm{rep}}$), multiplied with a mode number $n_0$ to the approximate optical transition frequency (see text). Three different $f_{\mathrm{rep}}$ are shown (frequency uncertainty margins are smaller than the shown data points): $178$ MHz (thin green trace), $183$ MHz (thick blue trace), and $189$ MHz (circles, red trace). The lower part shows the possible transition frequencies corresponding to the upper graph. The overlap of the traces at $f_{\mathrm{trans}}=761905012.7$ MHz can clearly be seen, and was checked for five different repetition frequencies (only 3 are shown for clarity).

Figure 5

(a) Measured data for light shifts induced by the cooling laser at $P_{\mathrm{comb}}=1.9(0.2)\mathrm{mW}$ (circles). (b) Measured data for light shifts induced by the frequency comb laser at $P_{\mathrm{cooling}\mathrm{laser}}=200(10)\mu \mathrm{W}$. The weighted fits to the data are also shown [gray (red) lines].