Lifetime determination of the $5d^2$ ${}^3{F}_2$ state in barium using trapped atoms

Magneto-optically trapped atoms enable the determination of lifetimes of metastable states and higher lying excited states like the $5d^2{}^3{F}_2$ state in barium. The state is efficiently populated by driving strong transitions from metastable states within the cooling cycle of the barium magneto-optical trap (MOT). The lifetime is inferred from the increase of MOT fluorescence after the transfer of up to $30\%$ of the trapped atoms to this state. The radiative decay of the $5d^2{}^3{F}_2$ state cascades to the cooling cycle of the MOT with a probability of $96.0\left(7\right)\%$ corresponding to a trap loss of $4.0\left(7\right)\%$ and its lifetime is determined to $160\left(10\right)\mu \mathrm{s}$. This is in good agreement with the theoretically calculated lifetime of $190\mu \mathrm{s}$ [V. A. Dzuba and V. V. Flambaum, J. Phys. B 40, 227 (2007)]. The determined loss of $4.0\left(7\right)\%$ from the cooling cycle is compared with the theoretically calculated branching ratios. This measurement extends the efficacy of trapped atoms to measure lifetimes of higher, long-lived states and validate the atomic structure calculations of heavy multielectron systems.

Figure 1

Energy levels of atomic barium. :(a) Energy levels used for laser cooling and trapping of barium. The solid arrows indicate laser-driven transitions and the dashed black arrows indicate the decay channels. The vacuum wavelengths of the laser-driven transitions are given in ${\lambda }_i$. (b) Decay cascade of the $5d^2{}^3{F}_2$ level to lower lying states is shown. The cascading to the $6s5d$ ${}^3{D}_3$ state (red dashed arrows) constitutes the only loss channel from the cooling cycle of the MOT.

Figure 2

Schematic setup for the measurement of the $5d^2{}^3{F}_2$ state lifetime in a barium MOT. (a) The trapping light and the light at 667.7 nm (${\lambda }_2$) and 659.7 nm (${\lambda }_3)$ are overlapped before they are sent to the MOT. The ${\lambda }_2$ laser light (dashed brown arrow) is pulsed with an acousto-optic modulator. (b) Configuration for the observation of the fluorescence from the trapped atoms (green sphere). The light at ${\lambda }_2$ = $667.7$ nm and ${\lambda }_3=659.7$ nm optically pumps atoms to the $5d^2{}^3{F}_2$ state.

Figure 3

Fluorescence spectrum $s\left(t\right)$ from the trapped barium atoms detected at wavelength ${\lambda }_1$ from pulsed excitation of the $6s5d{}^3{D}_2\text{−}5d6p{}^3{D}_1$ transition at wavelength ${\lambda }_2$. The MOT fluorescence is normalized to the signal level before the light pulse at ${\lambda }_2$. The laser pulse at ${\lambda }_2$ is introduced from $t=-T_p\cdots 0.$ The fluorescence signal is fitted for $t\ge 0$ to the function (1) in order to obtain the lifetime of the $5d^2{}^3{F}_2$ state. This yielded a lifetime $\tau =160\left(10\right)\mu \mathrm{s}$ and a loss $L=4.2\left(2\right)\%$ of trapped atoms. Inset: Lifetime of the $5d^2{}^3{F}_2$ state at different ${\lambda }_2$ pulse lengths $T_p$.