Robust long-distance entanglement and a loophole-free Bell test with ions and photons

Two trapped ions that are kilometers apart can be entangled by the joint detection of two photons, each coming from one of the ions, in a basis of entangled states. Such a detection is possible with linear optical elements. The use of two-photon interference allows entanglement distribution without interferometric sensitivity to the path length of the photons. The present method of creating entangled ions also opens up the possibility of a loophole-free test of Bell's inequalities.Comment: published versio

Entangled states of trapped ions allow measuring the magnetic field gradient of a single atomic spin

Using trapped ions in an entangled state we propose detecting a magnetic dipole of a single atom at distance of a few $\mu$m. This requires a measurement of the magnetic field gradient at a level of about 10$^{-13}$ Tesla/$\mu$m. We discuss applications e.g. in determining a wide variation of ionic magnetic moments, for investigating the magnetic substructure of ions with a level structure not accessible for optical cooling and detection,and for studying exotic or rare ions, and molecular ions. The scheme may also be used for measureing spin imbalances of neutral atoms or atomic ensembles trapped by optical dipole forces. As the proposed method relies on techniques well established in ion trap quantum information processing it is within reach of current technology.Comment: 4 pages, 2 fi

He 2-104: A link between symbiotic stars and planetary nebulae

Ultraviolet, optical and infrared observations of He 2-104 are presented, and estimates for some of the physical properties of the nebular shell are made. It is argued that He 2-104 is in transition between the D-type symbiotic star and bipolar planetary nebula phases and, as such, represents a link between subclasses of these two types of objects. The model includes a binary system with a Mira variable and a hot, evolved star. Previous mass loss has resulted in the formation of a disk of gas and dust around the whole system, while the hot star has an accretion disk which produces the observed highly ionized emission line spectrum. Emission lines from cooler, lower density gas is also observed to come from the nebula. In addition, matter is flowing out of the system in a direction perpendicular to the disk with a high velocity and is impacting upon the previously-ejected red giant wind and/or the ambient interstellar medium

Nature of the Darwin term and (Zα)4m3/M2{(Z\alpha)^4 m^3/M^2} contribution to the Lamb shift for an arbitrary spin of the nucleus

The contact Darwin term is demonstrated to be of the same origin as the spin-orbit interaction. The $(Z\alpha)^4 m^3/M^2$ correction to the Lamb shift, generated by the Darwin term, is found for an arbitrary nonvanishing spin of the nucleus, both half-integer and integer. There is also a contribution of the same nature to the nuclear quadrupole moment.Comment: 9 pages, latex, no figure

Precise Experimental Investigation of Eigenmodes in a Planar Ion Crystal

The accurate characterization of eigenmodes and eigenfrequencies of two-dimensional ion crystals provides the foundation for the use of such structures for quantum simulation purposes. We present a combined experimental and theoretical study of two-dimensional ion crystals. We demonstrate that standard pseudopotential theory accurately predicts the positions of the ions and the location of structural transitions between different crystal configurations. However, pseudopotential theory is insufficient to determine eigenfrequencies of the two-dimensional ion crystals accurately but shows significant deviations from the experimental data obtained from resolved sideband spectroscopy. Agreement at the level of 2.5 x 10^(-3) is found with the full time-dependent Coulomb theory using the Floquet-Lyapunov approach and the effect is understood from the dynamics of two-dimensional ion crystals in the Paul trap. The results represent initial steps towards an exploitation of these structures for quantum simulation schemes.Comment: 5 pages, 4 figures, supplemental material (mathematica and matlab files) available upon reques

Experiments towards quantum information with trapped Calcium ions

Ground state cooling and coherent manipulation of ions in an rf-(Paul) trap is the prerequisite for quantum information experiments with trapped ions. With resolved sideband cooling on the optical S1/2 - D5/2 quadrupole transition we have cooled one and two 40Ca+ ions to the ground state of vibration with up to 99.9% probability. With a novel cooling scheme utilizing electromagnetically induced transparency on the S1/2 - P1/2 manifold we have achieved simultaneous ground state cooling of two motional sidebands 1.7 MHz apart. Starting from the motional ground state we have demonstrated coherent quantum state manipulation on the S1/2 - D5/2 quadrupole transition at 729 nm. Up to 30 Rabi oscillations within 1.4 ms have been observed in the motional ground state and in the n=1 Fock state. In the linear quadrupole rf-trap with 700 kHz trap frequency along the symmetry axis (2 MHz in radial direction) the minimum ion spacing is more than 5 micron for up to 4 ions. We are able to cool two ions to the ground state in the trap and individually address the ions with laser pulses through a special optical addressing channel.Comment: Proceedings of the ICAP 2000, Firenz

Observation of the Kibble-Zurek scaling law for defect formation in ion crystals

Traversal of a symmetry-breaking phase transition at a finite rate can lead to causallyseparated regions with incompatible symmetries and the formation of defects at their boundaries. The defect formation follows universal scaling laws prescribed by the Kibble-Zurek mechanism (KZM) important to the study of phase transitions in fields as diverse as quantum and statistical mechanics, condensed matter physics and cosmology. Here, we observe the KZM in a crystal of cold trapped ions, which is conducive to the precise control of structural phases and the detection of defects. The experiment confirms a scaling law with an exponent of 2.68 +/- 0.06, as predicted from the KZM in the finite inhomogeneous case. Such precision makes it feasible to use ion crystals for quantitative tests of classical and quantum statistical mechanics