Controlled inter-site coupling in a two-dimensional ion trap array

The understanding of quantum mechanical systems is essential to modern physics and its applications. However, already for entangled systems of a few tens of constituents, exact numerical simulations on classical computers can become impossible. Quantum simulators based on well-controlled quantum system might provide the only effective approach to these systems. Trapped atomic ions offer a uniquely precise and controllable platform. They are used as platforms for, e.g., future quantum computers, quantum simulators, and extremely precise clocks. Quantum-simulation problems of interest and out-of-reach for modern theoretical methods include the dynamics of one-dimensional systems on long time scales and more-than-one dimensional systems with long-range interaction. For the latter, two-dimensional arrays of ions, individually trapped and controlled above microfabricated surface-electrode traps, present a promising approach. In the first realizations so far, the inter-site distance between the ions was too large to allow for sufficient inter-site coupling. We aim for a scalable approach to an analog quantum simulator based on a two-dimensional array of individually trapped ions. As a first demonstration, we operate an array of three magnesium ions in triangular arrangement with a side-length of 40 μm. Therein, we previously demonstrated the individual control of internal (electronic) and external (motional) degrees of freedom of the ions. Here, we present the first realization of inter-site coupling in the two-dimensional array. We demonstrate the coupling by a transfer of large coherent states of motion between the sites. We investigate the influence of the amplitude of these motional states in the anharmonic trapping potential and extrapolate to future experiments on the single-phonon level. We apply the real-time control of the coupling and concatenate the two-site coupling to transfer motional excitation between all three sites of the array. To demonstrate the scalability of our techniques, we couple all three sites simultaneously and investigate the evolution of an initial excitation at one and two sites of the array. The latter shows interference effects of the different pathways in the triangle. Current motional heating rates on the order of the inter-site coupling, preclude working with single phonons near the motional ground-state. We present a new experimental apparatus and vacuum chamber which will allow in-situ cleaning of surface-electrode traps. This has shown to reduce motional heating rates by two orders of magnitude. In this apparatus, we additionally realize a magnetic-field insensitive qubit in 25Mg+ with a coherence time exceeding six seconds. We generate the magnetic field around 10.9 mT by a hybrid magnet assembly based on solid-state magnets and fine-tuned by electric coils. Once we have reduced the heating rate in the triangle trap array using the new setup, first quantum simulation experiments, investigating spin-frustration or artificial gauge fields, will come in reach. Here our triangle represents a basic, scalable, building block of future latices designed at will.