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Laser cooled ions trapped in a linear Paul trap are long-standing ideal candidates for realizing quantum simulation, especially of many-body systems. The properties that contribute to this also provide the opportunity to demonstrate…
We demonstrate the Doppler laser cooling of $^{40}$Ca$^+$ ions confined in a segmented linear Paul trap in the presence of a strong quadrupolar magnetic field generated by two permanent ring magnets. Magnetic field gradients of 800 to 1600…
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…
Sympathetic cooling of molecular ions through the Coulomb interaction with laser-cooled atomic ions is an efficient tool to prepare translationally cold molecules without, ideally, affecting the internal state of the molecular ions.…
Sympathetic laser cooling of ions stored within a linear-geometry, radio frequency, electric-quadrupole trap has been investigated using computational and theoretical techniques. The simulation, which allows 5 sample ions to interact with…
We study from the point of view of quantum logic the properties of the collective oscillations of a linear chain of ions trapped in a linear Paul trap and composed of two ion species. We discuss extensively sympathetic cooling of the chain…
We show that the physical system consisting of trapped ions interacting with lasers may undergo a rich variety of quantum phase transitions. By changing the laser intensities and polarizations the dynamics of the internal states of the ions…
The quadrupole linear Paul trap is one of the key instruments in building highly stable atomic clocks. However, a frequency reference based on a single trapped ion is limited in stability due to the time needed for the interrogation cycle…
We investigate the dynamics of an ion sympathetically cooled by another laser-cooled ion or small ion crystal. To this end, we develop simple models of the cooling dynamics in the limit of weak Coulomb interactions. Experimentally, we…
We demonstrate a spatial-imaging thermometry technique for ions in a one-dimensional Coulomb crystal by relating their imaged spatial extent along the linear radiofrequency ion trap axis to normal modes of vibration of coupled oscillators…
Laser-cooled and trapped atomic ions form an ideal standard for the simulation of interacting quantum spin models. Effective spins are represented by appropriate internal energy levels within each ion, and the spins can be measured with…
Samples of ultracold 174 Yb+ ions, confined in a linear radio-frequency Paul trap, are heated via self-induced micromotion interruption, while their temperature, density, and therefore structural phase are monitored and simulated. The…
We present experiments on polarization gradient cooling of Ca$^+$ multi-ion Coulomb crystals in a linear Paul trap. Polarization gradient cooling of the collective modes of motion whose eigenvectors have overlap with the symmetry axis of…
We demonstrate tunable spin-spin couplings between trapped atomic ions, mediated by laser forces on multiple transverse collective modes of motion. A $\sigma_x \sigma_x$-type Ising interaction is realized between quantum bits stored in the…
Interacting many-particle systems can self-organize into a rich variety of crystalline structures. While symmetry provides a powerful framework for predicting whether transitions between crystal states are continuous or discontinuous,…
Cooling of ions or other charged particles in electromagnetic traps is an essential tool to achieve control over their degrees of freedom on the quantum level. For many objects, there is no viable route for direct cooling, such as an…
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…
A direct numerical simulation of many interacting ions in a Penning trap with a rotating wall is presented. The ion dynamics is modelled classically. Both axial and planar Doppler laser cooling are modeled using stochastic momentum impulses…
Hybrid traps for the simultaneous confinement of neutrals and ions have recently emerged as versatile tools for studying interactions between these species at very low temperatures. Such traps rely on the combination of different types of…
In this tutorial we review physical implementation of quantum computing using a system of cold trapped ions. We discuss systematically all the aspects for making the implementation possible. Firstly, we go through the loading and confining…