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

Abstract

An ensemble of atoms in steady-state, whether in thermal equilibrium or not, 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 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.

Direct Observation of Atom-Ion Nonequilibrium Sympathetic Cooling

“…The narrow distribution sets an upper limit for the SSDCT stability of ∼1%. The accuracy of this method was estimated to be on the level of 5% in [27]. The LRT identified 98.4% of the exper-FIG.…”

“…We use a newly developed thermometry technique [27] which is similar to Doppler-cooling thermometry (DCT) [28,29], however, utilizes different analytic tools and is suited for a different energy regime. DCT is used to extract the temperature of the ion assuming an underlying energy distribution and requires extensive averaging over many experimental realizations due to photon shot noise.…”

“…We then excite the ion using a short oscillating electric field pulse close to resonance with the axial (or radial) mode frequency. This results in a narrow Gaussian distribution of energies [27]. At this point, we move the atoms to overlap the ion.…”

“…We then use the SSDCT to detect the ion energy and mode of motion for the specific experimental instance. This method (SSDCT) is described in detail in [27] and will only be briefly discussed in the following.…”

“…We perform a likelihood ratio-test (LRT) for the fluorescence curve of each single-shot experimental repetition with all the calculated numerical fluorescence trajectories and choose the one with the maximal likelihood value (see [31] and [27]). We performed a stochastic numerical simulation to analyze the LRT method.…”