Precision lifetime measurements of a single trapped ion with ultrafast laser pulses

We report precision measurements of the excited state lifetime of the $5p$ ${}^{2}P_{1∕2}$ and $5p$ ${}^{2}P_{3∕2}$ levels of a single trapped ${\mathrm{Cd}}^{+}$ ion. Combining ion trap and ultrafast laser technologies, the ion is excited with picosecond laser pulses from a mode-locked laser and the distribution of arrival times of spontaneously emitted photons is recorded. The resulting lifetimes are $3.148\pm 0.011\mathrm{ns}$ and $2.647\pm 0.010\mathrm{ns}$ for ${}^{2}P_{1∕2}$ and ${}^{2}P_{3∕2}$ respectively. With a total uncertainty of under 0.4%, these are among the most precise measurements of any atomic state lifetimes to date.

Figure 1

The experimental apparatus. (a) A picosecond mode-locked Ti:sapphire laser is tuned to four times the resonant wavelength for either the $5p$ ${}^{2}P_{1∕2}$ or the $5p$ ${}^{2}P_{3∕2}$ level of ${\mathrm{Cd}}^{+}$. Each pulse is then frequency-quadrupled through nonlinear crystals, filtered from the fundamental and second harmonics, and directed to the ion. An amplified cw diode laser is also frequency quadrupled and tuned just red of the ${}^{2}P_{3∕2}$ transition for Doppler cooling of the ion within the trap. Acousto-optic modulators (AOM) are used to switch on and off the lasers as described in the text. Photons emitted from the ion are collected by an $f∕2.1$ imaging lens and directed toward a photon-counting photomultiplier tube (PMT). The output of the PMT provides the start pulse for the time to digital converter (TDC), whereas the stop pulse is provided by the reference clock of the mode-locked laser. (b) The relevant energy levels of ${\mathrm{Cd}}^{+}$. (c) An asymmetric quadrupole trap. (d) A linear trap.

Figure 2

(a) The response function of the instrument when viewing light scattered off an electrode surface (no atomic physics). The main peak asymmetry is due to the response time of the PMT of $\approx 0.5\mathrm{ns}$, whereas the secondary peaks are due to noise in the TDC triggering electronics ($\sim 0.6\%$ of the main peak amplitude). While laser light scattered off an electrode is not a single photon source, this curve was taken at a sufficiently low photon collection rate so that pulse pileup effects were negligible. (b) Data for the $5p$ ${}^{2}P_{1∕2}$ state taken in the quadrupole trap. The open circles show the data used to extract the excited state lifetime (see text). (c) The deviations from the fit function (residuals). Due to the difficulty in accurately defining a prompt peak background, the fit is not performed around the time of the excitation pulse. This has a small effect on the residuals, but as discussed in the text, is virtually independent of the resulting extracted lifetime.

Figure 3

Published results of theoretical (open circles) and experimental (filled circles) lifetimes, including this work (filled diamonds), for the $5p$ ${}^{2}P_{1∕2}$ and $5p$ ${}^{2}P_{3∕2}$ states of ${\mathrm{Cd}}^{+}$. (a) Hanle theory (1974) [23], (b) theory (1975) [24], (c) many body perturbation theory (1997) [25], (d) and (e) pseudorelativistic Hartree-Fock theory (2004) [9], (f) phaseshift (1970), ${}^{2}P_{1∕2}$ value is $4.8\mathrm{ns}$ [26], (g) beam-foil (1973) [27], (h) Hanle (1974) [23], (i) Electron-photon (1975) [13], (j) Hanle (1976) [28], (k) Hanle (1976) [29], (l) delayed coincidence (1980) [30], (m) beam-laser (1994) [5], (n) beam-foil (1994) [5], (o) laser-induced fluorescence (2004) [9], and (p) this experiment.