Control over physical systems at the quantum level is a goal shared by scientists in fields as diverse as metrology, information processing, simulation and chemistry. For trapped atomic ions, the quantized motional and internal degrees of freedom can be coherently manipulated with laser light.1, 2 Similar control is difficult to achieve with radio frequency or microwave radiation because the essential coupling between internal degrees of freedom and motion requires significant field changes over the extent of the atoms' motion. 2, 3 The field gradients are negligible at these frequencies for freely propagating fields; however, stronger gradients can be generated in the near-field of microwave currents in structures smaller than the free-space wavelength. 4,5 In the experiments reported here, we coherently manipulate the internal quantum states of the ions on time scales of 20 ns. We also generate entanglement between the internal degrees of freedom of two atoms with a gate operation 4, 6-8 suitable for general quantum computation. 9 We implement both operations through the magnetic fields from 1 arXiv:1104.3573v3 [quant-ph]

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The principle of the equivalence of gravitational and inertial mass is one of the cornerstones of general relativity. Considerable efforts have been made and are still being made to verify its validity. A quantum-mechanical formulation of gravity allows for non-Newtonian contributions to the force which might lead to a difference in the gravitational force on matter and antimatter. While it is widely expected that the gravitational interaction of matter and of antimatter should be identical, this assertion has never been tested experimentally. With the production of large amounts of cold antihydrogen at the CERN Antiproton Decelerator, such a test with neutral antimatter atoms has now become feasible. For this purpose, we have proposed to set up the AEGIS experiment at 0168-583X/$ -see front matter Ó 2007 Published by Elsevier B.V.

We use trapped atomic ions forming a hybrid Coulomb crystal and exploit its phonons to study an isolated quantum system composed of a single spin coupled to an engineered bosonic environment. We increase the complexity of the system by adding ions and controlling coherent couplings and, thereby, we observe the emergence of thermalization: Time averages of spin observables approach microcanonical averages while related fluctuations decay. Our platform features precise control of system size, coupling strength, and isolation from the external world to explore the dynamics of equilibration and thermalization.

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.