Single-shot energy measurement of a single atom and the direct reconstruction of its energy distribution

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.