Structural phase transitions in multipole traps

A small number of laser-cooled ions trapped in a linear radiofrequency multipole trap forms a hollow tube structure. We have studied, by means of molecular dynamics simulations, the structural transition from a double ring to a single ring of ions. We show that the single-ring configuration has the advantage to inhibit the thermal transfer from the rf-excited radial components of the motion to the axial component, allowing to reach the Doppler limit temperature along the direction of the trap axis. Once cooled in this particular configuration, the ions experience an angular dependency of the confinement if the local adiabaticity parameter exceeds the empirical limit. Bunching of the ion structures can then be observed and an analytic expression is proposed to take into account for this behaviour

About the dynamics and thermodynamics of trapped ions

This tutorial introduces the dynamics of charged particles in a radiofrequency trap in a very general manner to point out the differences between the dynamics in a quadrupole and in a multipole trap. When dense samples are trapped, the dynamics is modified by the Coulomb repulsion between ions. To take into account this repulsion, we propose to use a method, originally developed for particles in Penning trap, that model the ion cloud as a cold fluid. This method can not reproduce the organisation of cold clouds as crystals but it allows one to scale the size of large samples with the trapping parameters and the number of ions trapped, for different linear geometries of trap.Comment: accepted for publication in the "Modern Applications of Trapped Ions" special issu

Ion dynamics in a linear radio-frequency trap with a single cooling laser

We analyse the possibility of cooling ions with a single laser beam, due to the coupling between the three components of their motion induced by the Coulomb interaction. For this purpose, we numerically study the dynamics of ion clouds of up to 140 particles, trapped in a linear quadrupole potential and cooled with a laser beam propagating in the radial plane. We use Molecular Dynamics simulations and model the laser cooling by a stochastic process. For each component of the motion, we systematically study the dependence of the temperature with the anisotropy of the trapping potential. Results obtained using the full radio-frequency (rf) potential are compared to those of the corresponding pseudo-potential. In the rf case, the rotation symmetry of the potential has to be broken to keep ions inside the trap. Then, as for the pseudo-potential case, we show that the efficiency of the Coulomb coupling to thermalize the components of motion depends on the geometrical configuration of the cloud. Coulomb coupling appears to be not efficient when the ions organise as a line or a pancake and the three components of motion reach the same temperature only if the cloud extends in three dimensions

Terahertz frequency standard based on three-photon coherent population trapping

A scheme for a THz frequency standard based on three-photon coherent population trapping in stored ions is proposed. Assuming the propagation directions of the three lasers obey the phase matching condition, we show that stability of few 10$^{-14}$ at one second can be reached with a precision limited by power broadening to $10^{-11}$ in the less favorable case. The referenced THz signal can be propagated over long distances, the useful information being carried by the relative frequency of the three optical photons.Comment: article soumis a PRL le 21 mars 2007, accepte le 10 mai, version 2 (24/05/2007

Glory Oscillations in the Index of Refraction for Matter-Waves

We have measured the index of refraction for sodium de Broglie waves in gases of Ar, Kr, Xe, and nitrogen over a wide range of sodium velocities. We observe glory oscillations -- a velocity-dependent oscillation in the forward scattering amplitude. An atom interferometer was used to observe glory oscillations in the phase shift caused by the collision, which are larger than glory oscillations observed in the cross section. The glory oscillations depend sensitively on the shape of the interatomic potential, allowing us to discriminate among various predictions for these potentials, none of which completely agrees with our measurements

Coherent Control of Atomic Beam Diffraction by Standing Light

Quantum interference is shown to deliver a means of regulating the diffraction pattern of a thermal atomic beam interacting with two standing wave electric fields. Parameters have been identified to enhance the diffraction probability of one momentum component over the others, with specific application to Rb atoms.Comment: 5 figure

Ideal Multipole Ion Traps from Planar Ring Electrodes

We present designs for multipole ion traps based on a set of planar, annular, concentric electrodes which require only rf potentials to confine ions. We illustrate the desirable properties of the traps by considering a few simple cases of confined ions. We predict that mm-scale surface traps may have trap depths as high as tens of electron volts, or micromotion amplitudes in a 2-D ion crystal as low as tens of nanometers, when parameters of a magnitude common in the field are chosen. Several example traps are studied, and the scaling of those properties with voltage, frequency, and trap scale, for small numbers of ions, is derived. In addition, ions with very high charge-to-mass ratios may be confined in the trap, and species of very different charge-to-mass ratios may be simultaneously confined. Applications of these traps include quantum information science, frequency metrology, and cold ion-atom collisions.Comment: Section on trapping of a single ion added, two figures added, one formula corrected, otherwise minor change

Linear Paul trap design for an optical clock with Coulomb crystals

We report on the design of a segmented linear Paul trap for optical clock applications using trapped ion Coulomb crystals. For an optical clock with an improved short-term stability and a fractional frequency uncertainty of 10^-18, we propose 115In+ ions sympathetically cooled by 172Yb+. We discuss the systematic frequency shifts of such a frequency standard. In particular, we elaborate on high precision calculations of the electric radiofrequency field of the ion trap using the finite element method. These calculations are used to find a scalable design with minimized excess micromotion of the ions at a level at which the corresponding second- order Doppler shift contributes less than 10^-18 to the relative uncertainty of the frequency standard

Planck's scale dissipative effects in atom interferometry

Atom interferometers can be used to study phenomena leading to irreversibility and dissipation, induced by the dynamics of fundamental objects (strings and branes) at a large mass scale. Using an effective, but physically consistent description in terms of a master equation of Lindblad form, the modifications of the interferometric pattern induced by the new phenomena are analyzed in detail. We find that present experimental devices can in principle provide stringent bounds on the new effects.Comment: 12 pages, plain-Te

Atom Interferometers

Interference with atomic and molecular matter waves is a rich branch of atomic physics and quantum optics. It started with atom diffraction from crystal surfaces and the separated oscillatory fields technique used in atomic clocks. Atom interferometry is now reaching maturity as a powerful art with many applications in modern science. In this review we first describe the basic tools for coherent atom optics including diffraction by nanostructures and laser light, three-grating interferometers, and double wells on AtomChips. Then we review scientific advances in a broad range of fields that have resulted from the application of atom interferometers. These are grouped in three categories: (1) fundamental quantum science, (2) precision metrology and (3) atomic and molecular physics. Although some experiments with Bose Einstein condensates are included, the focus of the review is on linear matter wave optics, i.e. phenomena where each single atom interferes with itself.Comment: submitted to Reviews of Modern Physic