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

Abstract

A precisely controlled quantum system may reveal a fundamental understanding of another, less accessible system of interest. A universal quantum computer is currently out of reach, but an analogue quantum simulator that makes relevant observables, interactions and states of a quantum model accessible could permit insight into complex dynamics. Several platforms have been suggested and proof-of-principle experiments have been conducted. Here, we operate two-dimensional arrays of three trapped ions in individually controlled harmonic wells forming equilateral triangles with side lengths 40 and 80 μm. In our approach, which is scalable to arbitrary two-dimensional lattices, we demonstrate individual control of the electronic and motional degrees of freedom, preparation of a fiducial initial state with ion motion close to the ground state, as well as a tuning of couplings between ions within experimental sequences. Our work paves the way towards a quantum simulator of two-dimensional systems designed at will.

Motional-mode analysis of trapped ions

“…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.…”

“…We experimentally demonstrate both methods with single 25 Mg + ions harmonically confined in a surfaceelectrode trap array fabricated by Sandia National Laboratories [17,20] …”

“…Further, our methods can be readily extended to characterization of mode configurations of multiple ions. They may serve as standard procedures in experiments, where precise control of motional modes is inevitable, e.g., in two-dimensional ion trap arrays, used for quantum simulations [10,17,26]. Here, tuning the motional parameters in real time permits state preparation of sympathetically cooled ions at all sites simultaneously as well as setting inter-site Coulomb interactions.…”

“…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][16][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.…”

“…Typical motional frequencies are ω/(2π) ≈ {3.6, 4.8, 5.9} MHz. Our array provides 30 control electrodes that we offset to a constant voltage ∈ [−10, 10] V to control the motional degrees of freedom [17]. The l-th electrode biased at 1 V generates a potential φ l (r) with l ∈ {1, .…”