Abstract

In this paper, we present a method to measure transient fluorescent dynamics with single trapped ions in a Paul trap. We use $^{40}{\rm{C}}{{\rm{a}}^ +}$ ions that exhibit a $\Lambda$-type three-level system and measure the characteristic optical pumping times between the ground ${S_{1/2}}$ and the meta-stable ${D_{3/2}}$ levels. We prepare one of these states and then pump it to the opposite via the excited ${P_{1/2}}$ state. By measuring the scattered photons of the ion, we retrieve transient curves of the atomic fluorescence. These curves provide fundamental information about the atomic system, such as branching fractions and excited-state lifetimes, as well as experimental parameters like the efficiency of the detection system and the saturation parameter of one of the transitions. Finally, we study the time-dependent fluorescence as a function of optical power and detuning of the lasers and find a very good agreement with simulating the dynamics via a three-level open quantum system through a set of optical Bloch equations. Being able to record time-dependent fluorescence is of particular interest as it contains information about the temperature, cooling, and heating dynamics of the ion.

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