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An ensemble of atoms in a steady state, whether or not in thermal equilibrium, has a well-defined energy distribution. Since the energy of single atoms within the ensemble cannot be individually measured, energy distributions are typically inferred from statistical averages. Here, we show how to measure the energy of a single atom in a single experimental realization (single shot). The energy distribution of the atom over many experimental realizations can thus be readily and directly obtained. We apply this method to a single ion trapped in a linear Paul trap for which the energy measurement in a single shot is applicable from 10 K×kB and above. Our energy measurement agrees within 5% to a different thermometry method which requires extensive averaging. Apart from the total energy, we also show that the motion of the ion in different trap modes can be distinguished. We believe that this method will have profound implications on single-particle chemistry and collision experiments. [ABSTRACT FROM AUTHOR]

We study the time-dependent fluorescence of an initially hot, multilevel, single atomic ion trapped in a radio-frequency Paul trap during Doppler cooling. We have developed an analytical model that describes the fluorescence dynamics during Doppler cooling which is used to extract the initial energy of the ion. While previous models of Doppler cooling thermometry were limited to atoms with a two-level energy structure and neglected the effect of the trap oscillating electric fields, our model applies to atoms with multilevel energy structure and takes into account the influence of micromotion on the cooling dynamics. This thermometry applies to any initial energy distribution. We experimentally test our model with an ion prepared in coherent, thermal, and Tsallis energy distributions. [ABSTRACT FROM AUTHOR]