Frequency metrology on the $4s{}^{2}S_{1∕2}–4p{}^{2}P_{1∕2}$ transition in ${}^{40}\mathrm{Ca}^{+}$ for a comparison with quasar data

High accuracy frequency metrology on the $4s{}^{2}S_{1∕2}–4p{}^{2}P_{1∕2}$ transition in calcium ions is performed using laser cooled and crystallized ions in a linear Paul trap. Calibration is performed with a frequency comb laser, resulting in a transition frequency of $f=755222766.2\left(1.7\right)\mathrm{MHz}$. The accuracy presents an improvement of more than one order of magnitude, and will facilitate a comparison with quasar data in a search for a possible change of the fine structure constant on a cosmological time scale.

Figure 1

(Color online) Electrode configuration for the linear trap. The trap consists of four linear electrodes (labeled 1–4) for radial confinement: A radio frequency voltage is put on two diagonally facing rods (1,4), while the other two rods are grounded (2,3). A dc voltage is applied to the ring electrodes for axial confinement.

Figure 2

(Color online) Schematic design of the laser system and linear Paul trap. The lens used for focusing the light onto the single mode fiber is a 40 times microscope objective. DL, diode laser; PMT, photomultiplier tube; $2\omega$, frequency-doubling setup; $3\omega$, frequency-tripling setup; PBC, polarizing beamsplitter cube; CEM, channel electron multiplier.

Figure 3

Partial energy level diagram of ${\mathrm{Ca}}^{+}$.

Figure 4

(Color online) Observed fluorescence vs frequency detuning $\Delta f$, on scanning the cooling laser over the $4s{}^{2}S_{1∕2}–4p{}^{2}P_{1∕2}$ transition in ${\mathrm{Ca}}^{+}$. Red thin trace, $T_{\text{ions}}\approx 40\mathrm{K}$; blue thick trace, $T_{\text{ions}}\approx 4\mathrm{K}$. The sudden decrease in fluorescence in the blue thick curve is the typical signature for crystallization of the ion cloud (see text).

Figure 5

Schematic view of the setup for heterodyning the cw diode laser with the frequency comb. The cw laser is overlapped with the comb on a beam splitter (BC). A grating-based spectral filter is used to reduce the number of comb modes on the detector. For clarity a lens is drawn; in practice a curved mirror is used. APD, avalanche photodiode; ph, pinhole; $\lambda ∕2$, half-wave plate.

Figure 6

(Color online) An example of the measured fluorescence spectrum for the $4s{}^{2}S_{1∕2}–4p{}^{2}P_{1∕2}$ transition in ${\mathrm{Ca}}^{+}$ (black dots) and the corresponding Voigt fit (red line), corrected for the trap loss during the scan.

Figure 7

(Color online) Absolute calibration of the $4s{}^{2}S_{1∕2}–4p{}^{2}P_{1∕2}$ transition in ${\mathrm{Ca}}^{+}$ is performed by finding the coincidence of measurements with two different frequency comb repetition rates of $189\mathrm{MHz}$ (circles) and $207\mathrm{MHz}$ (triangles). The depicted transition frequency $f=2f_l$, since the laser frequency is measured in the infrared, after which the laser is frequency doubled for the spectroscopy. Consequently the spacing between adjacent points in the picture is $2f_{\mathrm{rep}}$. The upper graph shows the frequency dependence on the choice of mode number. The lower graph shows the frequency difference between the points in the upper graph, with $\Delta f=f-755222766\mathrm{MHz}-2n^{\prime }\times 198\mathrm{MHz}$, where $n^{\prime }$ is the relative mode number (error bars are smaller than the point size).

Figure 8

(Color online) Transition frequency for the $4s{}^{2}S_{1∕2}–4p{}^{2}P_{1∕2}$ transition in ${\mathrm{Ca}}^{+}$ with respect to an applied magnetic field $B_{\text{applied}}$. Three different polarizations were used (see text): Right-circular (${\sigma }^{+}$, green triangles), left-circular (${\sigma }^{-}$, red circles), and linearly polarized light (${\sigma }^{+}+{\sigma }^{-}$, black squares). The dotted line indicates the value of the applied field where $B_{\text{applied}}=-B_{\text{earth}}$.