Quantum technologies exploit entanglement to revolutionize computing, measurements, and communications. This has stimulated the research in different areas of physics to engineer and manipulate fragile many-particle entangled states. Progress has been particularly rapid for atoms. Thanks to the large and tunable nonlinearities and the well developed techniques for trapping, controlling and counting, many groundbreaking experiments have demonstrated the generation of entangled states of trapped ions, cold and ultracold gases of neutral atoms. Moreover, atoms can couple strongly to external forces and light fields, which makes them ideal for ultra-precise sensing and time keeping. All these factors call for generating non-classical atomic states designed for phase estimation in atomic clocks and atom interferometers, exploiting many-body entanglement to increase the sensitivity of precision measurements. The goal of this article is to review and illustrate the theory and the experiments with atomic ensembles that have demonstrated many-particle entanglement and quantum-enhanced metrology.References 60

In this article, recent developments in HElium NanoDroplet Isolation (HENDI) spectroscopy are reviewed, with an emphasis on the infrared region of the spectrum. We discuss how molecular beam spectroscopy and matrix isolation spectroscopy can be usefully combined into a method that provides a unique tool to tackle physical and chemical problems which had been outside our experimental possibilities. Next, in reviewing the experimental methodology, we present design criteria for droplet beam formation and its seeding with the chromophore(s) of interest, followed by a discussion of the merits and shortcomings of radiation sources currently used in this type of spectroscopy. In a second, more conceptual part of the review, we discuss several HENDI issues which are understood by the community to a varied level of depth and precision. In this context, we show first how a superfluid helium cluster adopts the symmetry of the molecule or complex seeded in it and discuss the nature of the potential well (and its isotropy) that acts on a solute inside a droplet, and of the energy levels that arise because of this confinement. Second, we treat the question of the homogeneous versus inhomogeneous broadening of the spectral profiles, moving after this to a discussion of the rotational dynamics of the molecules and of the surrounding superfluid medium. The change in rotational constants from their gas phase values, and their dependence on the angular velocity and vibrational quantum number are discussed. Finally, the spectral shifts generated by this very gentle matrix are analyzed and shown to be small because of a cancellation between the opposing action of the attractive and repulsive parts of the potential of interaction between molecules and their solvent. The review concludes with a discussion of three recent applications to (a) the synthesis of far-fromequilibrium molecular aggregates that could hardly be prepared in any other way, (b) the study of the influence of a simple and rather homogeneous solvent on large amplitude molecular motions, and (c) the study of mixed 3 He/ 4 He and other highly quantum clusters (e.g., H2 clusters) prepared inside helium droplets and interrogated by measuring the IR spectra of molecules embedded in them. In spite of the many open questions, we hope to convince the reader that HENDI has a great potential for the solution of several problems in modern chemistry and condensed matter physics, and that, even more interestingly, this unusual environment has the potential to generate new sets of issues which were not in our minds before its introduction.

Characterizing many-body systems through the quantum correlations between their constituent particles is a major goal of quantum physics. Although entanglement is routinely observed in many systems, we report here the detection of stronger correlations--Bell correlations--between the spins of about 480 atoms in a Bose-Einstein condensate. We derive a Bell correlation witness from a many-particle Bell inequality involving only one- and two-body correlation functions. Our measurement on a spin-squeezed state exceeds the threshold for Bell correlations by 3.8 standard deviations. Our work shows that the strongest possible nonclassical correlations are experimentally accessible in many-body systems and that they can be revealed by collective measurements.

We use a small Bose-Einstein condensate on an atom chip as an interferometric scanning probe to map out a microwave field near the chip surface with a few micrometers resolution. With the use of entanglement between the atoms, our interferometer overcomes the standard quantum limit of interferometry by 4 dB and maintains enhanced performance for interrogation times up to 10 ms. This corresponds to a microwave magnetic field sensitivity of 77 pT/√Hz in a probe volume of 20 μm(3). Quantum metrology with entangled atoms is useful in measurements with high spatial resolution, since the atom number in the probe volume is limited by collisional loss. High-resolution measurements of microwave near fields, as demonstrated here, are important for the development of integrated microwave circuits for quantum information processing and applications in communication technology.

Trapped ions offer long internal state (spin) coherence times and strong interparticle interactions mediated by the Coulomb force. This makes them interesting candidates for quantum simulation of coupled lattices. To this end, it is desirable to be able to trap ions in arbitrary conformations with precisely controlled local potentials. We provide a general method for optimizing periodic planar radio-frequency electrodes for generating ion trapping potentials with specified trap locations and curvatures above the electrode plane. A linear-programming algorithm guarantees globally optimal electrode shapes that require only a single radio-frequency voltage source for operation. The optimization method produces final electrode shapes that are smooth and exhibit low fragmentation. Such characteristics are desirable for practical fabrication of surface-electrode trap lattices.

We propose loading trapped ions into microtraps formed by an optical lattice. For harmonic microtraps, the Coulomb coupling of the spatial motions of neighboring ions can be used to construct a broad class of effective short-range Hamiltonians acting on an internal degree of freedom of the ions. For large anharmonicities, on the other hand, the spatial motion of the ions itself represents a spin-1/2 model with frustrated dipolar XY interactions. We illustrate the latter setup with three systems: the linear chain, the zig-zag ladder, and the triangular lattice. In the frustrated zig-zag ladder with dipolar interactions we find chiral ordering beyond what was predicted previously for a next-nearestneighbor model. In the frustrated anisotropic triangular lattice with nearestneighbor interactions we find that the transition from the one-dimensional gapless spin-liquid phase to the two-dimensional spiraling ordered phase passes through a gapped spin-liquid phase, similar to what has been predicted for the same model with Heisenberg interactions. Further, a second gapped spin-liquid phase marks the transition to the two-dimensional Néel-ordered phase.

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.

We study the ground state phases of the S = 1/2 Heisenberg quantum antiferromagnet on the spatially anisotropic triangular lattice and on the square lattice with up to next-next-nearest neighbor coupling (the J 1 J 2 J 3 model), making use of Takahashi's modified spin-wave (MSW) theory supplemented by ordering vector optimization. We compare the MSW results with exact diagonalization and projectedentangled-pair-states calculations, demonstrating their qualitative and quantitative reliability. We find that MSW theory correctly accounts for strong quantum effects on the ordering vector of the magnetic phases of the models under investigation: in particular collinear magnetic order is promoted at the expenses of non-collinear (spiral) order, and several spiral states which are stable at the classical level, disappear from the quantum phase diagram. Moreover, collinear states and non-collinear ones are never connected continuously, but they are separated by parameter regions in which MSW breaks down, signaling the possible appearance of a non-magnetic ground state.In the case of the spatially anisotropic triangular lattice, a large breakdown region appears also for weak couplings between the chains composing the lattice, suggesting the possible occurrence of a large non-magnetic region continuously connected with arXiv:1012.4491v1 [cond-mat.str-el] 20 Dec 2010 the spin-liquid state of the uncoupled chains.