Phonon-phonon interactions due to non-linear effects in a linear ion trap

We examine in detail the theory of the intrinsic non-linearities in the dynamics of trapped ions due to the Coulomb interaction. In particular the possibility of mode-mode coupling, which can be a source of decoherence in trapped ion quantum computation, or, alternatively, can be exploited for parametric down-conversion of phonons, is discussed and conditions under which such coupling is possible are derived.Comment: 25 pages, 4 figure

Visibility of Young's interference fringes: Scattered light from small ion crystals

We observe interference in the light scattered from trapped $^{40}$Ca$^+$ ion crystals. By varying the intensity of the excitation laser, we study the influence of elastic and inelastic scattering on the visibility of the fringe pattern and discriminate its effect from that of the ion temperature and wave-packet localization. In this way we determine the complex degree of coherence and the mutual coherence of light fields produced by individual atoms. We obtain interference fringes from crystals consisting of two, three and four ions in a harmonic trap. Control of the trapping potential allows for the adjustment of the interatomic distances and thus the formation of linear arrays of atoms serving as a regular grating of microscopic scatterers.Comment: Main text: 5 pages, 4 figures. Supplemental Material: 2pages, 1 figur

Two-dimensional spectroscopy for the study of ion coulomb crystals.

Ion Coulomb crystals are currently establishing themselves as a highly controllable test bed for mesoscopic systems of statistical mechanics. The detailed experimental interrogation of the dynamics of these crystals, however, remains an experimental challenge. In this work, we show how to extend the concepts of multidimensional nonlinear spectroscopy to the study of the dynamics of ion Coulomb crystals. The scheme we present can be realized with state-of-the-art technology and gives direct access to the dynamics, revealing nonlinear couplings even in the presence of thermal excitations. We illustrate the advantages of our proposal showing how two-dimensional spectroscopy can be used to detect signatures of a structural phase transition of the ion crystal, as well as resonant energy exchange between modes. Furthermore, we demonstrate in these examples how different decoherence mechanisms can be identified