Cold molecular ions on a chip

We report the sympathetic cooling and Coulomb crystallization of molecular ions above the surface of an ion-trap chip. N$_2^+$ and CaH$^+$ ions were confined in a surface-electrode radiofrequency ion trap and cooled by the interaction with laser-cooled Ca$^{+}$ ions to secular translational temperatures in the millikelvin range. The configuration of trapping potentials generated by the surface electrodes enabled the formation of planar bicomponent Coulomb crystals and the spatial separation of the molecular from the atomic ions on the chip. The structural and thermal properties of the Coulomb crystals were characterized using molecular dynamics simulations. The present study extends chip-based trapping techniques to Coulomb-crystallized molecular ions with potential applications in mass spectrometry, cold chemistry, quantum information science and spectroscopy.Comment: 5 pages, 4 figure

Superstatistical energy distributions of an ion in an ultracold buffer gas

An ion in a radiofrequency ion trap interacting with a buffer gas of ultracold neutral atoms is a driven dynamical system which has been found to develop a non-thermal energy distribution with a power law tail. The exact analytical form of this distribution is unknown, but has often been represented empirically by q-exponential (Tsallis) functions. Based on the concepts of superstatistics, we introduce a framework for the statistical mechanics of an ion trapped in an RF field subject to collisions with a buffer gas. We derive analytic ion secular energy distributions from first principles both neglecting and including the effects of the thermal energy of the buffer gas. For a buffer gas with a finite temperature, we prove that Tsallis statistics emerges from the combination of a constant heating term and multiplicative energy fluctuations. We show that the resulting distributions essentially depend on experimentally controllable parameters paving the way for an accurate control of the statistical properties of ion-atom hybrid systems.Comment: Main text 6 pages, 4 figures. Total length including supplemental material 11 pages, 6 figure

The energy distribution of an ion in a radiofrequency trap interacting with a nonuniform neutral buffer gas

An ion in a radiofrequency (rf) trap sympathetically cooled by a simultaneously trapped neutral buffer gas exhibits deviations from thermal statistics caused by collision-induced coupling of the rf field to the ion motion. For a uniform density distribution of the buffer gas, the energy distribution of the ion can be described by Tsallis statistics. Moreover, runaway heating of the ion occurs if the buffer gas particles are sufficiently heavy relative to the ion. In typical experiments, however, ultracold buffer gases are confined in traps resulting in localised, non-uniform density distributions. Using a superstatistical approach, we develop an analytical model for an ion interacting with a localised buffer gas. We demonstrate theoretically that limiting collisions to the centre of the ion trap enables cooling at far greater mass ratios than achievable using a uniform buffer gas, but that an upper limit to the usable mass ratio exists even in this case. Furthermore, we analytically derive the energy distribution for an ion interacting with a buffer gas held in a harmonic potential. The analytical distribution obtained is found to be in excellent agreement with the results of numerical simulations.Comment: 27 pages, 6 figure

Superstatistical velocity distributions of cold trapped ions in molecular dynamics simulations

We present a realistic molecular-dynamics treatment of laser-cooled ions in radiofrequency ion traps which avoids previously made simplifications such as modeling laser cooling as a friction force and combining individual heating mechanisms into a single effective heating force. Based on this implementation, we show that infrequent energetic collisions of single ions with background gas molecules lead to pronounced heating of the entire ion ensemble and a time-varying secular ensemble temperature which manifests itself in a superstatistical time-averaged velocity distribution of the ions. The effect of this finding on the experimental determination of ion temperatures and rate constants for cold chemical reactions is discussed.Comment: 13 pages, 12 figures, accepted for publication in Phys. Rev.

Energy distributions of an ion in a radiofrequency trap immersed in a buffer gas under the influence of additional external forces

An ion held in a radiofrequency trap interacting with a uniform buffer gas of neutral atoms develops a steady-state energy distribution characterised by a power-law tail at high energies instead of the exponential decay characteristic of thermal equilibrium. We have previously shown that the Tsallis statistics frequently used as an empirical model for this distribution is a good approximation when the ion is heated due to a combination of micromotion interruption and exchange of kinetic energy with the buffer gas [I. Rouse and S. Willitsch, Phys. Rev. Lett. 118, 143401 (2017)]. Here, we extend our treatment to include the heating due to additional motion of the ion caused by external forces, including the "excess micromotion" induced by uniform electric fields and rf phase offsets. We show that this also leads to a Tsallis distribution with a potentially different power-law exponent from that observed in the absence of this additional forced motion, with the difference increasing as the ratio of the mass of the neutral atoms to that of the ion decreases. Our results indicate that unless the excess micromotion is minimised to a very high degree, then even a system with very light neutrals and a heavy ion does not exhibit a thermal distribution.Comment: 16 pages, 9 figure

Ion Coulomb crystals: From quantum technology to chemistry close to the absolute zero point

Ion Coulomb crystals are ordered structures of atomic or molecular ions stored in ion traps at temperatures close to the absolute zero point. These unusual “crystals” form the basis of extremely accurate clocks, provide an environment for precise studies of chemical reactions and enable advanced implementations of the technology for a quantum computer. In this article, we discuss the techniques for generating atomic and molecular Coulomb crystals and highlight some of their applications

Classical and quantum dynamics of a trapped ion coupled to a charged nanowire

We study theoretically the mechanical drive of a trapped ultracold ion by a charged nanowire through their mutual Coulomb interaction. We characterize the perturbation of the trapping potential for the ion by the nanowire and discuss the parameters determining the dynamics of the ion under the action of the nanooscillator. We explore the classical dynamics as well as motional quantum states of the ion which can be generated and manipulated with the resonant drive of the nanowire and the effects of anharmonicities of the ion-trap potential on the system. Our modelling indicates that unusual quantum states of the ion motion can be generated with this approach and that sympathetic cooling and quantum entanglement can be realised when both subsystems operate in the quantum regime. The present ion-mechanical hybrid system might prove interesting as a new quantum device, for quantum sensing experiments, for spectroscopy and for mass spectrometry

A traveling wave Zeeman decelerator

We developed a new-concept Zeeman decelerator which produces a traveling magnetic trap. Atoms and molecules possessing a magnetic dipole moment, in so-called low field seeking states, are trapped around a node of a propagating wave provided that the initial velocity of the wave matches a velocity populated in the supersonic beam. In addition, three dimensional confinement is achieved by controlling the radial orientation of the trap, which can be done fully independently from its longitudinal motion

Rotational state-changing collisions between N2+_2^+ and Rb at low energies

We present a theoretical study of rotationally elastic and inelastic collisions between molecular nitrogen ions and Rb atoms in the sub-Kelvin temperature regime prevalent in ion-atom hybrid trapping experiments. The cross sections for rotational excitation and de-excitation collisions were calculated using quantum-scattering methods on ab-initio potential energy surfaces for the energetically lowest singlet electronic channel of the system. We find that the rotationally inelastic collision rates are at least an order of magnitude smaller than the charge-exchange rates found in this system, rendering inelastic processes a minor channel under the conditions of typical hybrid trapping experiments.Comment: 6 pages, 5 figures, Computational study of rotational state changing collision

N-2(+)((2)Sigma(g)) and Rb(S-2) in a hybrid trap: modeling ion losses from radiative association paths

By employing ab initio computed intermolecular potential energy surfaces we calculate the radiative association probabilities and rates for two different associative mechanisms involving trapped molecular ions N-2(+)((2)sigma(g)) interacting either directly with ultracold Rb atoms or undergoing charge-exchange (CE) processes leading to the formation of complexes of the strongly exothermic products N-2(X-1 sigma(g)) plus Rb+(S-1(0)). The two processes are expected to provide possible paths to ion losses in the trap within the timescale of experiments. The present calculations suggest that the associative rates for the vibrational' direct process are too small to be of any significant importance at the millikelvin temperatures considered in the experiments, while the vibronic' path into radiatively associating the CE products has a probability of occurring which is several orders of magnitude larger. However the reaction rate constants attributed to non-adiabatic CE [F. H. J. Hall and S. Willist, Phys. Rev. Lett., 2012, 109, 233202] are in turn several orders of magnitude larger than the radiative ones calculated here, thereby making the primary experimental process substantially unaffected by the radiative losses channel