Precision measurement of the branching fractions of the $5p{}^{2}P_{1/2}$ state in ${}^{88}\mathrm{Sr}^{+}$ with a single ion in a microfabricated surface trap

We measured the branching fractions for the decay of the $5p{}^{2}P_{1/2}$ state of ${}^{88}\mathrm{Sr}^{+}$ by applying a recently demonstrated photon-counting sequential method [M. Ramm, T. Pruttivarasin, M. Kokish, I. Talukdar, and H. Häffner, Phys. Rev. Lett. 111, 023004 (2013)] to a single ion laser cooled in a microfabricated surface trap. The branching fraction for the decay into the $5s{}^{2}S_{1/2}$ ground level was found to be $p=0.9449\left(5\right)$. This result is in good agreement with recent theoretical calculations but disagrees with previous experimental measurements, however affected by a one-order-of-magnitude larger uncertainty. This experiment demonstrates that microtrap technology is also applicable in the domain of precision measurements and spectroscopy.

Figure 1

Schematic view of the surface ion trap. Cooling, repumping, and photoionizing laser beams propagate parallel to the trap surface aligned at ${45}^{\circ }$ with respect to the trap axis. During normal operation, a magnetic field ${\mathbf{B}}_{\mathbf{0}}$ of the order of $1\times {10}^{-4}$ T defines a quantization axis parallel to the propagation direction of laser beams. While testing systematic effects possibly induced by polarization sensitivity in the detection chain, the magnetic field ($B_{\text{test}}$) has the same amplitude as ${\mathbf{B}}_{\mathbf{0}}$ but its direction is orthogonal to the trap surface.

Figure 2

Low-energy levels of ${}^{88}\mathrm{Sr}^{+}$. Two laser sources are used to produce fluorescence cycles of ${}^{88}\mathrm{Sr}^{+}$: a cooling laser at 711 THz (421.7 nm) and a repumping laser at 275 THz (1092 nm). Starting in the $5p{}^{2}P_{1/2}$ energy level, the electronic excitation can relax either to the ground state (with a probability $p$) or to the metastable state $4d{}^{2}D_{3/2}$ (with probability $1-p$).

Figure 3

Typical acquisition sequence used in a single detection cycle. (a) Laser cooling ($80\mu \mathrm{s}$, both lasers turned on). (b) Optical pumping in the ground state ($80\mu \mathrm{s}$, 711-THz laser turned off). (c) Measurement of $N_b$ blue photons ($160\mu \mathrm{s}$, 711-THz laser turned on, 275-THz laser turned off). (d) Measurement of $N_r$ blue photons ($80\mu \mathrm{s}$, 711-THz laser turned off, 275-THz laser turned on). (e) Measurement of the background signal $N_r^B$ associated with phase (d) ($80\mu \mathrm{s}$, 711-THz laser turned off, 275-THz laser turned on). (f) Optical pumping in the metastable $4d{}^{2}D_{3/2}$ state to prepare the measurement of the background signal $N_b^B$ associated with phase (c) ($160\mu \mathrm{s}$, 711-THz laser turned on, 275-THz laser turned off). (g) Measurement of the background signal $N_b^B$ associated with phase (c) ($160\mu \mathrm{s}$, 711-THz laser turned on, 275-THz laser turned off). This sequence of duration $850\mu \mathrm{s}$ is typically repeated $\simeq 50\times {10}^6$ times. This sequence has been used for the third acquisition run (see Sec. 3).

Figure 4

Histogram of time durations of collision events observed during 43 h of operation in the surface trap. Each event is characterized by an abrupt disappearance of the fluorescence that reappears later in time. The fluorescence is acquired with an integration time of 5 ms and, within this resolution, the reappearance of the fluorescence is also abrupt. The solid line is a fit of the experimental data (with the exclusion of the shortest time bin of the histogram) with an exponential distribution characterized by an imposed decay time ${\tau }_{D_{5/2}}=390.8$ ms (fixed parameter) and an amplitude on the first bin (adjustable parameter) of 29 events. The statistical weights of the populations associated to the two classes in this bimodal histogram are 54% for the short-lived events and 46% for the exponentially distributed events, respectively.

Figure 5

Comparison of our measurement of the branching ratio $B$ (filled diamond, red) with other experimental measurements or theoretical calculations. Vertical axis separation is used to offset the data from different works. The error bars (whenever present) represent the standard error associated to the determination of $B$. Reference [33] does not give information about standard error.

Figure 6

Comparison of measurements and calculations of the transition probability $A_{SP}$. Vertical axis separation is used to offset different measurements. In this work we obtain $A_{SP}=127.9\left(1.3\right)\times {10}^6{\mathrm{s}}^{-1}$.

Figure 7

Comparison of measurements and calculations of the transition probability $A_{PD}$. Vertical axis separation is used to offset different measurements. In this work we obtain $A_{PD}=7.46\left(14\right)\times {10}^6{\mathrm{s}}^{-1}$.

Figure 8

Systematic shifts affecting $p$ as a function of the Rabi frequency of the cooling laser ${\mathrm{\Omega }}_1$ as calculated solving the OBE for the sequence presented in Fig. 3. Red filled squares: contribution induced by the finite lifetime of the $4d{}^{2}D_{3/2}$ state and the finite duration of the sequence time windows. Green open circles: contribution induced by the dead time of the photodetection chain. Black filled diamonds: sum of the two contributions.