Convex Hull of Arithmetic Automata

Arithmetic automata recognize infinite words of digits denoting decompositions of real and integer vectors. These automata are known expressive and efficient enough to represent the whole set of solutions of complex linear constraints combining both integral and real variables. In this paper, the closed convex hull of arithmetic automata is proved rational polyhedral. Moreover an algorithm computing the linear constraints defining these convex set is provided. Such an algorithm is useful for effectively extracting geometrical properties of the whole set of solutions of complex constraints symbolically represented by arithmetic automata

Implementation of Cavity Squeezing of a Collective Atomic Spin

We squeeze unconditionally the collective spin of a dilute ensemble of laser-cooled rubidium-87 atoms using their interaction with a driven optical resonator. The shape and size of the resulting spin uncertainty region are well described by a simple analytical model [M.H.S., I.D.L., V.V., arXiv:0911.3936] through two orders of magnitude in the effective interaction strength, without free parameters. We deterministically generate states with up to 5.6(6) dB of metrologically relevant spin squeezing on the canonical rubidium-87 hyperfine clock transition.Comment: 4 pages, 2 figures. To be published in Phys. Rev. Lett. Some additional details and clarified wording in response to referee comments. Figures and results unchange

Squeezing the Collective Spin of a Dilute Atomic Ensemble by Cavity Feedback

We propose and analyze a simple method to squeeze dynamically and unconditionally the collective spin of a dilute atomic ensemble by interaction with a driven mode of an optical resonator, as recently demonstrated [I. D. L., M. H. S., and V. V., Phys. Rev. Lett. 104, 073602 (2010)]. We show that substantial squeezing can be achieved in the regime of strong collective ensemble-resonator coupling. The squeezing is ultimately limited either by photon emission into free space or by the curvature of the Bloch sphere. We derive both limits and show where each prevails.Comment: 4 pages, 2 figures. Minor revision. To appear in Phys. Rev.

Quantum Algorithmic Readout in Multi-Ion Clocks

Optical clocks based on ensembles of trapped ions offer the perspective of record frequency uncertainty with good short-term stability. Most suitable atomic species lack closed transitions for fast detection such that the clock signal has to be read out indirectly through transferring the quantum state of clock ions to co-trapped logic ions by means of quantum logic operations. For ensembles of clock ions existing methods for quantum logic readout require a linear overhead in either time or the number of logic ions. Here we report a quantum algorithmic readout whose overhead scales logarithmically with the number of clock ions in both of these respects. We show that the readout algorithm can be implemented with a single application of a multi-species quantum gate, which we describe in detail for a crystal of Aluminum and Calcium ions.Comment: 4 pages + 7 pages appendix; 5 figures; v3: published versio

States of an Ensemble of Two-Level Atoms with Reduced Quantum Uncertainty

We generate entangled states of an ensemble of 5*10^4 rubidium-87 atoms by optical quantum nondemolition measurement. The resonator-enhanced measurement leaves the atomic ensemble, prepared in a superposition of hyperfine clock levels, in a squeezed spin state. By comparing the resulting reduction of quantum projection noise (up to 8.8(8) dB) with the concomitant reduction of coherence, we demonstrate a clock input state with spectroscopic sensitivity 3.0(8) dB beyond the standard quantum limit.Comment: Letter (4 pages, 3 figures) followed by Auxiliary Material (10 pages, 6 figures). Minor changes in presentation and analysis of data. Significant expansion of Auxiliary Material. Broken images fixe

Controlling the potential landscape and normal modes of ion Coulomb crystals by a standing wave optical potential

Light-induced control of ions within small Coulomb crystals is investigated. By intense intracavity optical standing wave fields, subwavelength localization of individual ions is achieved for one-, two-, and three-dimensional crystals. Based on these findings, we illustrate numerically how the application of such optical potentials can be used to tailor the normal mode spectra and patterns of multi-dimensional Coulomb crystals. The results represent, among others, important steps towards controlling the crystalline structure of Coulomb crystals, investigating heat transfer processes at the quantum limit and quantum simulations of many-body systems.Comment: 6+12 pages. arXiv admin note: substantial text overlap with arXiv:1703.0508

Pinning an Ion with an Intracavity Optical Lattice

We report one-dimensional pinning of a single ion by an optical lattice. The lattice potential is produced by a standing-wave cavity along the rf-field-free axis of a linear Paul trap. The ion's localization is detected by measuring its fluorescence when excited by standing-wave fields with the same period, but different spatial phases. The experiments agree with an analytical model of the localization process, which we test against numerical simulations. For the best localization achieved, the ion's average coupling to the cavity field is enhanced from 50% to 81(3)% of its maximum possible value, and we infer that the ion is bound in a lattice well with over 97% probability.Comment: 5 pages, 4 figures; Text edited for clarity, results unchange