Motional-mode analysis of trapped ions

Abstract

We present two methods for characterization of motional-mode configurations that are generally applicable to the weak and strong-binding limit of single or multiple trapped atomic ions. Our methods are essential to realize control of the individual as well as the common motional degrees of freedom. In particular, when implementing scalable radio-frequency trap architectures with decreasing ion-electrode distances, local curvatures of electric potentials need to be measured and adjusted precisely, e.g., to tune phonon tunneling and control effective spin-spin interaction. We demonstrate both methods using single 25 Mg + ions that are individually confined 40 µm above a surface-electrode trap array and prepared close to the ground state of motion in three dimensions. [14], yielding increasing interaction strengths by decreasing system length scales. Correspondingly, higher-order terms need to be considered, in order to enable precise control of interaction potentials. For example, in microfabricated surface-electrode ion trap arrays [15-17] local potentials, dominated by applied electric trapping potentials, define motional modes. For envisioned quantum simulations, motional degrees of freedom can be exploited either within individual sites or between different sites. This, in turn, requires adjustment of motional-mode configurations, i.e., individual orientation of the normal-mode vectors and related motional frequencies, to enable individual, tunable inter-site interactions [17]. In this letter, we introduce and experimentally demonstrate two distinct methods for the analysis of motional-mode configurations that are generally applicable to the weak and strong-binding limit. For the latter, we cool single ions close to the ground state of motion in three dimensions.To introduce our system, we consider a single ion with charge Q and mass m, harmonically bound in three di-

Arrays of individually controlled ions suitable for two-dimensional quantum simulations

“…Data points for U rot2 =−1.62 V are shown as blue rectangles and for −2.43 V as grey rectangles. We fit each data set to a theoretical model (blue and grey lines) to extract the angles 51 and distributions of Fock-state populations of each mode (shown as histograms): we find ϕ 1, x =24.7(2)° for U rot2 =−1.62 V and ϕ 1, x =36.1(2)° for U rot2 =−2.43 V, whereas average occupation numbers range between ≃0.05 and ≃0.6. Adding measurements along Δk y and taking into account that the normal modes have to be mutually orthogonal would allow to fully reconstruct all mode orientations.…”

Phase-space study of surface-electrode Paul traps: Integrable, chaotic, and mixed motions

“…It should be stressed that the escape probability shown in Fig. 13 is strictly different from the exponential decay of a simple thermal activation mechanism above a barrier, and also cannot be explained as a linear or parametric resonance of a harmonic oscillator, relevant in the low amplitude regime [56,57]. This rich nonmonotonic behaviour remains to be explored with a more detailed analysis of the phase space, the pockets and the statistical properties of the motion, but the salient features could be observed with a relatively simple experiment.…”

Hybrid setup for stable magnetic fields enabling robust quantum control

“…Fluorescence photons are detected by a photon-multiplier tube (PMT) detector; more details on our laser setups, state preparation and detection techniques are described in refs. 40 – 44 . Further, we can coherently manipulate the internal states via a pulsed application of microwaves between MHz and MHz or radio-frequency waves at MHz.…”

“…For state detection, a single laser beam induces resonant fluorescence and we can discriminate the |3, 3 (bright) state from the other hyperfine ground (dark) states. Fluorescence photons are detected by a photon-multiplier tube (PMT) detector; more details on our laser setups, state preparation and detection techniques are described in[37][38][39][40][41] . Further, we can coherently manipulate the internal states via a pulsed application of microwaves between ω MW /(2π) 1, 300 MHz and 1, 850 MHz or radio-frequency waves at ω RF /(2π) 55 3.…”