Spectroscopy and isotope shifts of the $4s3d$ ${}^1{D}_2$–$4s5p$ ${}^1{P}_1$ repumping transition in magneto-optically trapped calcium atoms

We investigate a repumping scheme for magneto-optically trapped calcium atoms. It is based on excitation of the $4s3d^1{D}_2$–$4s5p^1{P}_1$ transition at $672$ nm with an extended cavity diode laser. The effect of the repumping is approximately a factor of three increase in trap lifetime and a doubling of the trapping efficiency from a Zeeman slowed thermal beam. Added to this, the 672-nm laser repumps atoms from an otherwise dark state to yield an overall increase in detected fluorescence signal from the magneto-optic trap (MOT) of more than an order of magnitude. Furthermore, we report isotope shift measurements of the $672$-nm transition, for the first time, for four naturally occurring even isotopes. Using available charge radii data, the observed shifts, extending up to $4.3$ GHz, display the expected linear dependence in a King plot analysis. The measured shifts are used to determine the isotope shifts of the remaining ${}^{41,43,46}\mathrm{Ca}$ isotopes. These might be of interest where less abundant isotopes are used enabling isotope selective repumping, resulting in enhanced trapping and detection efficiencies.

Figure 1

Low energy level diagram of the calcium atom with wavelengths and lifetimes of the states relevant for the current work. The transition rates along with their wavelengths of other contributing transitions are given in Table . The solid arrows correspond to the ${}^1{S}_0$–${}^1{P}_1$ $423$-nm transition and to the 672-nm repump transition. The dashed arrows show the decays from the $4s4p$ ${}^1{P}_1$ state of the 423-nm MOT and various decay paths of the atoms from the $4s5p$ ${}^1{P}_1$ state to the low-lying states.

Figure 2

Experimental setup of the magneto-optical trapped calcium atoms used for the spectroscopy of the $4s3d$ ${}^1{D}_2$–$4s5p$ ${}^1{P}_1$ $672$-nm transition. A thermal beam of atoms is slowed down using a Zeeman slower. The slowed atoms are transversely cooled and deflected using deflection laser beams to magneto-optic trap. The magnetic coils are shown in the figure. The fluorescence from the trapped atoms is detected with a photodiode (PD). The $672$-nm laser beam is also shown.

Figure 3

The schematic layout of the $672$-nm laser frequency stabilization scheme. A $300$-MHz free spectral range Fabry-Perot (FP) cavity of finesse 300 is used as a transfer cavity for frequency stabilization of the $672$-nm laser. Details of the frequency stabilization method are given in the text.

Figure 4

(A) Loading of the 423-nm ${}^1{S}_0$–${}^1{P}_1$ MOT with (upper) and without (lower) the resonant frequency stabilized 672-nm laser. The smooth curves are exponential fits to the data. (B) 423-nm MOT fluorescence in the absence and subsequent presence of the 672-nm repumper. (a) The MOT (lifetime 16 ms) is loaded for 400 ms after which filling is terminated by extinguishing the deflection laser beams after the Zeeman slower. (b) Decay of the 423-nm MOT (lifetime 16 ms) is allowed for 20 ms, which is larger than the transit time from the deflection region to the MOT. This ensures no further atoms are being loaded. (c) The 672-nm laser is switched on for 400 ms. The initial rise (with a time constant of 400 ms) is due to the atoms previously shelved in the ${}^1{D}_2$ state. The subsequent decay shows the increased lifetime of 43 ms for the repumped MOT. Curves a and b [Eq. (1)], and curve c [Eq. (2)] are the fits to the data.

Figure 5

Histogram of the number of photons scattered by 6500 simulated deflected beam atoms until they are captured by the MOT (i.e., until they reach the MOT radius $r=0.5$ mm). Experimental parameters were used for the three-dimensional classical trajectory simulation. Total photon scatter is estimated via the integral of the average local scattering rate over time. A fraction of $47\%$ of the atoms never leave the cooling cycle.

Figure 6

Lifetime ($•$) of the ${}^1{S}_0$–${}^1{P}_1$ MOT measured at different intensities of the $672$-nm laser beam intensities. Increase in the $423$-nm steady-state MOT fluorescence ($\square$) as a function of the $672$-nm laser beam intensity. In both cases the $423$-nm MOT beams intensity is fixed. The solid curve is obtained from the rate equation model.

Figure 7

Enhancement of MOT parameters with increasing $672$-nm laser beam diameter. MOT lifetime ($•$) and ratio of steady-state fluorescence to lifetime ($▴$). The intensity of the $672$-nm laser is 14 mW$/$${\mathrm{cm}}^2$.

Figure 8

The ${}^{42,44}\mathrm{Ca}$ isotope spectra with respect to the $672$-nm laser frequency detuning of the ${}^{40}\mathrm{Ca}$ isotope. The ${}^{48}\mathrm{Ca}$ isotope spectrum is not shown. All the isotopes are detected as an increase in the ${}^1{S}_0$–${}^1{P}_1$ MOT fluorescence when the $423$-nm laser is tuned to the resonance of the respective isotope. The black curves are Lorentzian fits. The measured linewidths are 80–90 MHz. A typical mode spectrum of the high-finesse Fabry-Perot cavity used for calibration of the frequency axis is also shown. Offsets to the isotope data are added to distinguish the isotope positions for clarity.

Figure 9

King plot for the $672$-nm repump transition. The modified isotope shifts ($\Delta {\nu }_M^{A_1{A}_2}$) are plotted against the modified difference in root mean square (RMS) nuclear charge radii ($\frac{A_1{A}_2}{A_1-A_2}$$\delta \langle r^2\rangle {}^{A_1{A}_2}$) of the calcium isotopes. The specific mass shift $M_{\mathrm{SMS}}$ and the field shift $F_{\mathrm{FS}}$ of the $4s3d$ ${}^1{D}_2$–$4s5p$ ${}^1{P}_1$ transition at $672$ nm are determined from a linear regression analysis, which is shown as a solid line. The points relating to the 42, 44, and 48 are the experimental data while those relating to isotopes 41, 43, and 46 are the estimated center of gravities.