Non-Destructive Identification of Cold and Extremely Localized Single Molecular Ions

A simple and non-destructive method for identification of a single molecular ion sympathetically cooled by a single laser cooled atomic ion in a linear Paul trap is demonstrated. The technique is based on a precise determination of the molecular ion mass through a measurement of the eigenfrequency of a common motional mode of the two ions. The demonstrated mass resolution is sufficiently high that a particular molecular ion species can be distinguished from other equally charged atomic or molecular ions having the same total number of nucleons

Modes of Oscillation in Radiofrequency Paul Traps

We examine the time-dependent dynamics of ion crystals in radiofrequency traps. The problem of stable trapping of general three-dimensional crystals is considered and the validity of the pseudopotential approximation is discussed. We derive analytically the micromotion amplitude of the ions, rigorously proving well-known experimental observations. We use a method of infinite determinants to find the modes which diagonalize the linearized time-dependent dynamical problem. This allows obtaining explicitly the ('Floquet-Lyapunov') transformation to coordinates of decoupled linear oscillators. We demonstrate the utility of the method by analyzing the modes of a small `peculiar' crystal in a linear Paul trap. The calculations can be readily generalized to multispecies ion crystals in general multipole traps, and time-dependent quantum wavefunctions of ion oscillations in such traps can be obtained.Comment: 24 pages, 3 figures, v2 adds citations and small correction

Probabilistic state preparation of a single molecular ion by projection measurement

We show how to prepare a single molecular ion in a specific internal quantum state in a situation where the molecule is trapped and sympathetically cooled by an atomic ion and where its internal degrees of freedom are initially in thermal equilibrium with the surroundings. The scheme is based on conditional creation of correlation between the internal state of the molecule and the translational state of the collective motion of the two ions, followed by a projection measurement of this collective mode by atomic ion shelving techniques. State preparation in a large number of internal states is possible.Comment: 4 pages, 2 figures, 2 table

Collective strong coupling between ion Coulomb crystals and an optical cavity field: Theory and experiment

A detailed description and theoretical analysis of experiments achieving coherent coupling between an ion Coulomb crystal and an optical cavity field are presented. The various methods used to measure the coherent coupling rate between large ion Coulomb crystals in a linear quadrupole radiofrequency ion trap and a single field mode of a moderately high-finesse cavity are described in detail. Theoretical models based on a semiclassical approach are applied in assessment of the experimental results of [P. F. Herskind et al., Nature Phys. 5, 494 (2009)] and of complementary new measurements. Generally, a very good agreement between theory and experiments is obtained.Comment: 15 pages, 15 figure

Rotational cooling of molecules using lamps

We investigate theoretically the application of tailored incoherent far-infrared fields in combination with laser excitation of a single rovibrational transition for rotational cooling of translationally cold polar diatomic molecules. The cooling schemes are effective on a timescale shorter than typical unperturbed trapping times in ion traps and comparable to obtainable confinement times of neutral molecules.Comment: 5 pages, 2 figure

Rotational cooling of heteronuclear molecular ions with ^1-Sigma, ^2-Sigma, ^3-Sigma and ^2-Pi electronic ground states

The translational motion of molecular ions can be effectively cooled sympathetically to translational temperatures below 100 mK in ion traps through Coulomb interactions with laser-cooled atomic ions. The ro-vibrational degrees of freedom, however, are expected to be largely unaffected during translational cooling. We have previously proposed schemes for cooling of the internal degrees of freedom of such translationally cold but internally hot heteronuclear diatomic ions in the simplest case of ^1-Sigma electronic ground state molecules. Here we present a significant simplification of these schemes and make a generalization to the most frequently encountered electronic ground states of heteronuclear molecular ions: ^1-Sigma, ^2-Sigma, ^3-Sigma and ^2-Pi. The schemes are relying on one or two laser driven transitions with the possible inclusion of a tailored incoherent far infrared radiation field.Comment: 16 pages, 13 figure

Thermal and quantum fluctuations in chains of ultracold polar molecules

Ultracold polar molecules, in highly anisotropic traps and interacting via a repulsive dipolar potential, may form one-dimensional chains at high densities. According to classical theory, at low temperatures there exists a critical value of the density at which a second order phase transition from a linear to a zigzag chain occurs. We study the effect of thermal and quantum fluctuations on these self-organized structures using classical and quantum Monte Carlo methods, by means of which we evaluate the pair correlation function and the static structure factor. Depending on the parameters, these functions exhibit properties typical of a crystalline or of a liquid system. We compare the thermal and the quantum results, identifying analogies and differences. Finally, we discuss experimental parameter regimes where the effects of quantum fluctuations on the linear - zigzag transition can be observed.Comment: Submitted to the Special issue on modern applications of trapped ions, J. Phys. B: At. Mol. Opt. Phy

Blackbody-radiation-assisted molecular laser cooling

The translational motion of molecular ions can be effectively cooled sympathetically to temperatures below 100 mK in ion traps through Coulomb interactions with laser-cooled atomic ions. The distribution of internal rovibrational states, however, gets in thermal equilibrium with the typically much higher temperature of the environment within tens of seconds. We consider a concept for rotational cooling of such internally hot, but translationally cold heteronuclear diatomic molecular ions. The scheme relies on a combination of optical pumping from a few specific rotational levels into a ``dark state'' with redistribution of rotational populations mediated by blackbody radiation.Comment: 4 pages, 5 figure

Large ion Coulomb crystals: a near-ideal medium for coupling optical cavity modes to matter

We present an investigation of the coherent coupling of various transverse field modes of an optical cavity to ion Coulomb crystals. The obtained experimental results, which include the demonstration of identical collective coupling rates for different transverse modes of a cavity field to ions in the same large Coulomb crystal, are in excellent agreement with theoretical predictions. The results furthermore suggest that Coulomb crystals in the future may serve as near-ideal media for highfidelity multi-mode quantum information processing and communication purposes, including the generation and storage of single photon qubits encoded in different transverse modes.Comment: 4 pages, 5 figure