An apparatus for immersing trapped ions into an ultracold gas of neutral atoms

Electronic structure, cold ion-atom elastic collision properties and possibility of laser cooling of BeCs+ molecular ion

The BeCs⁺ system represents a possible future candidate for the realization of samples of cold or ultra-cold molecular ion species that have not yet been investigated experimentally or theoretically. With the aim of highlighting the spectroscopic and electronic structure of the cesium and beryllium cation BeCs⁺, we theoretically investigate ground and low lying excited states of ^1,3Σ⁺, ^1,3Π and ^1,3Δ symmetries below the first nine asymptotic limits dissociating into Be⁺(2s) + Cs(6s, 6p, 5d) and Be(2s², 2s2p, 2s3s, 2p²) + Cs⁺. We used a quantum chemistry approach based on a semi-empirical pseudo potential for Be²⁺ and Cs⁺ cores, core polarization potentials (CPP), large Gaussian basis sets and full configuration interaction (FCI) method for the valence electrons. Additional calculations have been performed for the ground state using CCSD(T)/CI methods with different basis sets. Adiabatic potential energy curves, spectroscopic constants, vibrational levels, and permanent and transition dipole moments are reported in this work. Furthermore, the elastic scattering properties at low energy for both ground 1¹Σ⁺ and second excited states 3¹Σ⁺, of BeCs⁺ are theoretically investigated, and isotopic effects on cold and ultra-cold energy collisions are also detected. Vibrational lifetimes of the ground state 1¹Σ⁺ are calculated taking into account both spontaneous and stimulated emissions and also the absorption induced by black body radiation at room temperature (T = 300 K). Vibrational radiative lifetimes for the first 2¹Σ⁺ and second 3¹Σ⁺ excited states are also calculated and extensively analyzed. We found that the radiative lifetimes of the lower vibrational levels of the 1¹Σ⁺ state have an order of magnitude of seconds (s), while those of 2¹Σ⁺ and 3¹Σ⁺ states have an order of nanoseconds (ns). The Franck-Condon factors are also calculated for transitions from the low lying excited 2¹Σ⁺, 3¹Σ⁺, 1¹Π states to the ground state 1¹Σ⁺. We found that the favourite vibrational transition to the 1¹Σ⁺(v = 0) ground state is obtained for 1¹Π (v''' = 0)-1¹Σ⁺(v = 0) with a diagonal structure and a large Franck-Condon factor value of 0.94. This Franck-Condon factor value is sufficiently large to make the BeCs⁺ system a favorable candidate for direct laser cooling.

Loading a Paul Trap: Densities, Capacities, and Scaling in the Saturation Regime

Providing ideal conditions for the study of ion-neutral collisions, we investigate here the properties of the saturated, steady state of a three-dimensional Paul trap, loaded from a magneto-optic trap. In particular, we study three assumptions that are sometimes made under saturated, steady-state conditions: (i) The pseudopotential provides a good approximation for the number, Ns, of ions in the saturation regime, (ii) the maximum of Ns occurs at a loading rate of approximately 1 ion per rf cycle, and (iii) the ion density is approximately constant. We find that none of these assumptions are generally valid. However, based on detailed classical molecular dynamics simulations, and as a function of loading rate and trap control parameter, we show where to find convenient dynamical regimes for ion-neutral collision experiments, or how to rescale to the pseudo-potential predictions. We also investigate the fate of the electrons generated during the loading process and present a new heating mechanism, insertion heating, that in some regimes of trapping and loading may rival and even exceed the rf-heating power of the trap.

Hyperfine Magnetic Substate Resolved State-to-State Chemistry

We extend state-to-state chemistry to a realm where besides vibrational, rotational, and hyperfine quantum states magnetic quantum numbers are also resolved. For this, we make use of the Zeeman effect, which energetically splits levels of different magnetic quantum numbers. The chemical reaction which we choose to study is three-body recombination in an ultracold quantum gas of ^{87}Rb atoms forming weakly bound Rb_{2} molecules. Here, we find the propensity rule that the total m_{F} quantum number of the two atoms forming the molecule is conserved. Our method can be employed for many other reactions and inelastic collisions and will allow for novel insights into few-body processes.

Buffer-Gas Cooling of a Single Ion in a Multipole Radio Frequency Trap Beyond the Critical Mass Ratio

We theoretically investigate the dynamics of a trapped ion immersed in a spatially localized buffer gas. For a homogeneous buffer gas, the ion's energy distribution reaches a stable equilibrium only if the mass of the buffer gas atoms is below a critical value. This limitation can be overcome by using multipole traps in combination with a spatially confined buffer gas. Using a generalized model for elastic collisions of the ion with the buffer-gas atoms, the ion's energy distribution is numerically determined for arbitrary buffer-gas distributions and trap parameters. Three regimes characterized by the respective analytic form of the ion's equilibrium energy distribution are found. Final ion temperatures down to the millikelvin regime can be achieved by adiabatically decreasing the spatial extension of the buffer gas and the effective ion trap depth (forced sympathetic cooling).

Energy Scaling of Cold Atom-Atom-Ion Three-Body Recombination

We study three-body recombination of Ba^{+}+Rb+Rb in the mK regime where a single ^{138}Ba^{+} ion in a Paul trap is immersed into a cloud of ultracold ^{87}Rb atoms. We measure the energy dependence of the three-body rate coefficient k_{3} and compare the results to the theoretical prediction, k_{3}∝E_{col}^{-3/4}, where E_{col} is the collision energy. We find agreement if we assume that the nonthermal ion energy distribution is determined by at least two different micromotion induced energy scales. Furthermore, using classical trajectory calculations we predict how the median binding energy of the formed molecules scales with the collision energy. Our studies give new insights into the kinetics of an ion immersed in an ultracold atom cloud and yield important prospects for atom-ion experiments targeting the s-wave regime.

Note: A novel design of a microwave feed for a microwave frequency standard with a linear ion trap

Linear ion traps are important tools in many applications, particularly in mass spectrum analyzers and frequency standards. Here a novel design of a microwave feed integrated into one electrode of a linear quadrupole ion trap is demonstrated for the application of a microwave frequency standard based on cadmium ions. The mechanical structure of the microwave feed is compact and easy to build. The ion trap integrated with this microwave feed is successfully applied to measure the hyperfine splitting of the ground state of (113)Cd(+), thus demonstrating the practicality and reliability of the microwave feed.

Single ion as a three-body reaction center in an ultracold atomic gas

We report on three-body recombination of a single trapped Rb(+) ion and two neutral Rb atoms in an ultracold atom cloud. We observe that the corresponding rate coefficient K(3) depends on collision energy and is about a factor of 1000 larger than for three colliding neutral Rb atoms. In the three-body recombination process large energies up to several 0.1 eV are released leading to an ejection of the ion from the atom cloud. It is sympathetically recooled back into the cloud via elastic binary collisions with cold atoms. Further, we find that the final ionic product of the three-body processes is again an atomic Rb(+) ion suggesting that the ion merely acts as a catalyzer, possibly in the formation of deeply bound Rb(2) molecules.