Nano-friction in cavity quantum electrodynamics

The dynamics of cold trapped ions in a high-finesse resonator results from the interplay between the long-range Coulomb repulsion and the cavity-induced interactions. The latter are due to multiple scatterings of laser photons inside the cavity and become relevant when the laser pump is sufficiently strong to overcome photon decay. We study the stationary states of ions coupled with a mode of a standing-wave cavity as a function of the cavity and laser parameters, when the typical length scales of the two self-organizing processes, Coulomb crystallization and photon-mediated interactions, are incommensurate. The dynamics are frustrated and in specific limiting cases can be cast in terms of the Frenkel-Kontorova model, which reproduces features of friction in one dimension. We numerically recover the sliding and pinned phases. For strong cavity nonlinearities, they are in general separated by bistable regions where superlubric and stick-slip dynamics coexist. The cavity, moreover, acts as a thermal reservoir and can cool the chain vibrations to temperatures controlled by the cavity parameters and by the ions phase. These features are imprinted in the radiation emitted by the cavity, which is readily measurable in state-of-art setups of cavity quantum electrodynamics.Comment: 9 pages, 7 figure

Calcareous nannofossil and foraminifer biostratigraphy of the Campanian–Maastrichtian chalk of the Femern Bælt (Denmark–Germany).

A new study based on calcareous nannofossil and benthic and planktonic foraminifer biostratigraphy is presented for the upper Campanian – Maastrichtian chalk of the Femern Bælt (Denmark and Germany; Fig.1). The results are consistent with recent studies of the Danish chalk for this interval, allowing correlation across the Danish Basin and forming the basis for correlation further afield within the Boreal Realm. Numerous studies have been carried out recently on the upper Campanian – Maastrichtian chalk of the Danish Basin, covering aspects such as sedimentology, depositional environment, macrofossil biostratigraphy, carbon isotope stratigraphy as well as nannofossil and dinoflagellate biostratigraphy. However, very few published studies on foraminifers exist across this interval in this area. The 09.A.006, 09.A.007 and 09.A.008 boreholes (Fig. 2) were drilled in 2009 in preparation for construction of a fixed link across the Femern Bælt, which will connect Denmark to Germany (Rambøll Arup JV 2011). The boreholes penetrated glacial till, Paleocene– Eocene clay and chalk (Sheldon et al. 2012). Here, for the first time, the Boreal foraminifer biostratigraphy of the late Campanian – Maastrichtian interval is investigated and presented alongside nannofossil biostratigraphy

Mechanical effects of optical resonators on driven trapped atoms: Ground state cooling in a high finesse cavity

We investigate theoretically the mechanical effects of light on atoms trapped by an external potential, whose dipole transition couples to the mode of an optical resonator and is driven by a laser. We derive an analytical expression for the quantum center-of-mass dynamics, which is valid in presence of a tight external potential. This equation has broad validity and allows for a transparent interpretation of the individual scattering processes leading to cooling. We show that the dynamics are a competition of the mechanical effects of the cavity and of the laser photons, which may mutually interfere. We focus onto the good-cavity limit and identify novel cooling schemes, which are based on quantum interference effects and lead to efficient ground state cooling in experimentally accessible parameter regimes.Comment: 17 pages, 6 figure

Photon-Mediated Interaction between Two Distant Atoms

We study the photonic interactions between two distant atoms which are coupled by an optical element (a lens or an optical fiber) focussing part of their emitted radiation onto each other. Two regimes are distinguished depending on the ratio between the radiative lifetime of the atomic excited state and the propagation time of a photon between the two atoms. In the two regimes, well below saturation the dynamics exhibit either typical features of a bad resonator, where the atoms act as the mirrors, or typical characteristics of dipole-dipole interaction. We study the coherence properties of the emitted light and show that it carries signatures of the multiple scattering processes between the atoms. The model predictions are compared with the experimental results in J. Eschner {\it et al.}, Nature {\bf 413}, 495 (2001).Comment: 18 pages, 15 figure

Laser cooling with electromagnetically induced transparency: Application to trapped samples of ions or neutral atoms

A novel method of ground state laser cooling of trapped atoms utilizes the absorption profile of a three (or multi-) level system which is tailored by a quantum interference. With cooling rates comparable to conventional sideband cooling, lower final temperatures may be achieved. The method was experimentally implemented to cool a single Ca$^+$ ion to its vibrational ground state. Since a broad band of vibrational frequencies can be cooled simultaneously, the technique will be particularly useful for the cooling of larger ion strings, thereby being of great practical importance for initializing a quantum register based on trapped ions. We also discuss its application to different level schemes and for ground state cooling of neutral atoms trapped by a far detuned standing wave laser field.Comment: 9 pages, 13 figures, submitted to Appl Phys B 200

Correlations and pair emission in the escape dynamics of ions from one-dimensional traps

We explore the non-equilibrium escape dynamics of long-range interacting ions in one-dimensional traps. The phase space of the few ion setup and its impact on the escape properties are studied. As a main result we show that an instantaneous reduction of the trap's potential depth leads to the synchronized emission of a sequence of ion pairs if the initial configurations are close to the crystalline ionic configuration. The corresponding time-intervals of the consecutive pair emission as well as the number of emitted pairs can be tuned by changing the final trap depth. Correlations between the escape times and kinetic energies of the ions are observed and analyzed.Comment: 17 pages, 9 figure

Quantum light by atomic arrays in optical resonators

Light scattering by a periodic atomic array is studied when the atoms couple with the mode of a high-finesse optical resonator and are driven by a laser. When the von-Laue condition is not satified, there is no coherent emission into the cavity mode, and the latter is pumped via inelastic scattering processes. We consider this situation and identify conditions for which different non-linear optical processes can occur. We show that these processes can be controlled by suitably tuning the strength of laser and cavity coupling, the angle between laser and cavity axis, and the array periodicity. We characterize the coherence properties of the light when the system can either operate as degenerate parametric amplifier or as a source of antibunched-light. Our study permits us to identify the individual multi-photon components of the nonlinear optical response of the atomic array and the corresponding parameter regimes, thereby in principle allowing one for controlling the nonlinear optical response of the medium.Comment: 11 pages, 10 figures, version to appear in Phys. Rev.

Inelastic scattering of light by a cold trapped atom: Effects of the quantum center-of-mass motion

The light scattered by a cold trapped ion, which is in the stationary state of laser cooling, presents features due to the mechanical effects of atom-photon interaction. These features appear as additional peaks (sidebands) in the spectrum of resonance fluorescence. Among these sidebands the literature has discussed the Stokes and anti-Stokes components, namely the sidebands of the elastic peak. In this manuscript we show that the motion also gives rise to sidebands of the inelastic peaks. These are not always visible, but, as we show, can be measured in parameter regimes which are experimentally accessible.Comment: 10 pages, 4 figures, submitted to Phys. Rev.