Hyperfine spectroscopy and laser cooling of the fermionic isotopes $^{47}$Ti and $^{49}$Ti

Abstract

We report on magneto-optical trapping of the two fermionic isotopes of atomic titanium, $^{47}$Ti and $^{49}$Ti. Unlike the even mass-number isotopes, which were recently laser cooled, $^{47}$Ti and $^{49}$Ti have nonzero nuclear spins and, consequently, their atomic levels are split by hyperfine structure. Combining and comparing theoretical calculations and atomic beam-spectroscopy measurements, we determine the hyperfine structures and isotope shifts of the $\mathrm{3d^24s^2}$ $\mathrm{a^3F_4\rightarrow 3d^2(^3P)4s4p(^3P^o)}$ $\mathrm{y^5D_4^o}$ optical-pumping transition at optical wavelength 391nm and the $\mathrm{3d^3(^4F)4s}$ $\mathrm{a^5F_5\rightarrow 3d^3(^4F)4p}$ $\mathrm{y^5G_6^o}$ laser-cooling transition at wavelength 498nm. With this information, we produce magneto-optical traps of both $^{47}$Ti and $^{49}$Ti by applying two additional tones of light to repump atoms to the maximum-spin states on the laser-cooling transition. Directly loading from the atomic flux of a titanium sublimation pump, we produce $^{47}$Ti and $^{49}$Ti traps with 731(190) and 1142(240) atoms, and with lifetimes of 330(15)ms and 310(8)ms, respectively.

Figures (7)

• Figure 1: (a) Atomic structure of Ti, including all levels below 31000. Even (odd) parity levels are shown in black (red), and the levels relevant to laser cooling are bolded and labeled. The 391 optical pumping and 498 laser cooling transitions are shown with purple and blue arrows. A dashed arrow indicates branching from the $\mathrm{y^5D_4^o}$ level to the $\mathrm{a^5F_5}$ level. (b,c) show the hyperfine structure of the four levels studied in this work for $\mathrm{^{47}Ti}$ and $\mathrm{^{49}Ti}$. The $\mathrm{a^3F_4}$ and $\mathrm{a^5F_5}$ hyperfine splittings are derived from the hyperfine constants given in channappa_hyperfine_structure_measurements_lowlying_multiplets_47ti_49ti_59co_105pd_1965aydin_sternheimer_free_determination_the47ti_nuclear_quadrupole_moment_hyperfine_structure_measurements_1990, while the $\mathrm{y^5D_4^o}$ and $\mathrm{y^5G_6^o}$ splittings were determined in this work.
• Figure 2: (a) Optical pumping on the $F=13/2\rightarrow F'=13/2$ transition in $^{47}$Ti produces population in the $F=11/2,13/2,15/2$ levels of the $\mathrm{a^5F_5}$ state. Because of the large degeneracy of the $F=13/2$ level of the $\mathrm{a^3F_4}$ state, approximately $1/4$ of the atoms in the $\mathrm{a^3F_4}$ state are addressed by this light. (b) Laser cooling light is detuned to the red of the $F=15/2\rightarrow F'=17/2$ transition. Off-resonant Raman scattering on the $F\rightarrow F$ and $F\rightarrow F-1$ transitions out of the $F=15/2$ state leads to depumping of population into the $F=13/2,\ 11/2$ states (long curvy arrows). Repump tones resonantly drive the $F=13/2\rightarrow F'=15/2$ and $F=11/2\rightarrow F'=13/2$ transitions and return population to the $F=15/2$ level of the $\mathrm{a^5F_5}$ state.
• Figure 3: (a) Diagram of the atomic beam spectroscopy setup. Sublimated Ti atoms are collimated by two slits to form an atomic beam traveling along the $z$ direction. The atomic beam first passes through a pair of counter-propagating 391 wavelength optical pumping laser beams before entering the 498 wavelength probe laser beam, at which point the atomic fluorescence is imaged onto a photomultiplier tube (PMT). An optical chopper in the path of the 391 wavelength light enables lock-in amplification of the fluorescence signal. In a second configuration, indicated by the dotted outline, an additional 498 wavelength depumping beam is introduced before the probe beam in order to measure splittings between $F$ levels in the $\mathrm{y^5G_6^o}$ term. (b) Spectra observed through one-color fluorescence spectroscopy. The frequencies of the 391nm wavelength optical pumping (top) or the 498nm wavelength laser cooling transition (bottom) are scanned broadly across the resonances of the 5 different isotopes. Frequencies, $\delta\nu^\lambda$, are given relative to the corresponding resonance frequency in $^{48}$Ti. The probe light is frequency modulated at frequency $f_\mathrm{mod}$, and then the PMT signal is demodulated at $2 f_\mathrm{mod}$ to observe resonance lines with reduced noise. These spectra are dominated by strong signals from each of the three bosonic Ti isotopes. A few additional features (indicated with arrows) are identified, arising from the fermionic isotopes. However, these additional features are insufficient to determine the full hyperfine structure of the relevant transitions, necessitating a two-color spectroscopic method.
• Figure 4: (a,b) Simultaneous determination of optical pumping and laser cooling resonances using the "X marks the spot" scheme. When tuned near a line in the optical pumping multiplet, the double-passed 391 wavelength light pumps atoms with opposite transverse velocities into the $\mathrm{a^5F_5}$ manifold, causing two peaks to be observed for a given line in the 498 wavelength fluorescence signal. By stepping the optical pumping light frequency and scanning the 498 wavelength light, the spectra shown in (a) are obtained, with the optical-pumping light frequency indicated by the vertical offset. Data and fits are shown in light and dark pink respectively. The fit locations of the peaks are shown in (b), with the crossing point indicating the zero-velocity frequency of both the optical pumping and laser cooling resonances. (c) By repeating this procedure for a variety of optical pumping and laser cooling transitions on each isotope, more of the overall structure is measured. Each "X" on the plot is a dataset like the one shown in part (a). The frequencies of the optical pumping resonances ($\delta\nu^\mathrm{391nm}$) and the laser cooling resonances ($\delta\nu^\mathrm{498nm}$) are again given relative to the resonances in $^{48}$Ti. At top (right), the theoretical one-color fluorescence spectra for the laser cooling (optical pumping) transition multiplet is plotted, demonstrating the strength of the two-color scheme for resolving obscured lines. The strong lines from the bosonic isotopes are above the vertical scale of the plot. (d) Three-color spectroscopy. Weak $F\rightarrow F$ laser cooling resonances (shown as squares in (c)) were observed by tuning the optical pumping and laser cooling light to the center of an "X" and adding an additional 498nm wavelength beam that depumps atoms from the hyperfine level addressed by the fluorescence beam. The figure shows the depletion of fluorescence on the $F\rightarrow F+1$ transitions as the $F\rightarrow F$ depumping beam is scanned through resonance. (e) Additional optical pumping resonances were observed by tuning the probe beam to a laser cooling resonance and broadly scanning the optical pumping light frequency. Multiple optical pumping lines can optically pump into a given $\mathrm{a^5F_5}$ level. When the optical pumping light is scanned through one of these lines, a peak is observed in the probe fluorescence. Each trace is labeled by the laser-cooling line addressed by the probe beam, and the horizontal offset of each trace shows the probe frequency. The resonances observed this way are indicated by triangles in (c).
• Figure 5: (a) Apparatus used to produce magneto-optical traps of $^{47}$Ti and $^{49}$Ti. The direct flux of Ti atoms from a Ti sublimation pump is sent through several passes of OP light before encountering a standard six-beam magneto-optical trap. Fluorescence and absorption images are taken through a 4-$f$ imaging system as depicted (not to scale). (b) Fluorescence images of trapped clouds of $^{47}$Ti and $^{49}$Ti atoms.