Spontaneous Emission Lifetime of a Single Trapped ${\mathrm{Ca}}^{+}$ Ion in a High Finesse Cavity

We investigate the spontaneous emission lifetime of a single trapped ${}^{40}\mathrm{Ca}^{+}$ ion placed at different positions in the vacuum standing wave inside a high finesse cavity which is stabilized to the atomic transition. The lifetime is measured by quantum state detection after $\pi$-pulse excitation. The result for the natural lifetime of the $D_{5/2}$ metastable state of 1161(22) ms agrees, within 1 standard deviation, with the most precise published value. We observe a reduction of the spontaneous emission lifetime of $\approx 15\%$ in the node of the vacuum field.

Figure 1

(a) ${\mathrm{Ca}}^{+}$-level scheme with relevant transitions. (b) Sketch of the experimental setup with a single ion in the standing wave of a two-mirror near-confocal cavity at 729 nm. Laser beam 1 is used to measure the ion’s position in the SW; beam 2 prepares the ion in the $D$ state by a $\pi$ pulse. (c) Schematic pulse sequence of one experimental cycle for the lifetime measurement (see text for details).

Figure 2

Decay of the $D_{5/2}$ level as a function of waiting time. An exponential fit (solid line) yields the natural lifetime.

Figure 3

Total decay rate from the $D_{5/2}$ state versus ac Stark shift on the $S_{1/2}\mathrm{\text{−}}{D}_{5/2}$ transition induced by the transfer laser. The open dot represents the decay rate in free space measured without transfer laser.

Figure 4

$D_{5/2}$ state lifetime measured at various positions in the cavity vacuum standing-wave field. The solid line shows a simulation of the Purcell effect, assuming $\tau =1075\mathrm{ms}$, a Purcell factor $F=1.175$, and a visibility of $V=0.9$. The inset shows a measurement of an intense cavity standing wave by coherent excitation (c.f. 3, 19).