Classical collisions with an ideal gas generate non-Maxwellian distribution functions for a single ion in a radio frequency ion trap. The distributions have power-law tails whose exponent depends on the ratio of buffer gas to ion mass. This provides a statistical explanation for the previously observed transition from cooling to heating. Monte Carlo results approximate a Tsallis distribution over a wide range of parameters and have ab initio agreement with experiment.
We demonstrate an improvement in short-term stability by a factor of 10 over a previous generation miniature buffer gas cooled trapped ion clock. We describe the enhancement to detection SNR that has enabled this improvement, the method of clock operation, and the measurement of clock short-term stability. Additionally, we numerically investigate the magnitude of the Dick effect in our pulsed ion clock.
We provide a comprehensive theoretical framework for describing the dynamics of a single trapped ion interacting with a neutral buffer gas, thus extending our previous studies on buffer-gas cooling of ions beyond the critical mass ratio [B. Höltkemeier et al., Phys. Rev. Lett. 116, 233003 (2016)]. By transforming the collisional processes into a frame, where the ion's micromotion is assigned to the buffer gas atoms, our model allows one to investigate the influence of non-homogeneous buffer gas configurations as well as higher multipole orders of the radio-frequency trap in great detail. Depen…
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 distributi…
Great advances in precision quantum measurement have been achieved with trapped ions and atomic gases at the lowest possible temperatures. These successes have inspired ideas to merge the two systems. In this way one can study the unique properties of ionic impurities inside a quantum fluid or explore buffer gas cooling of the trapped ion quantum computer. Remarkably, in spite of its importance, experiments with atom-ion mixtures remained firmly confined to the classical collision regime. We report a collision energy of 1.15(0.23) times the $s$-wave energy (or 9.9(2.0)~$μ$K) for a trapped ytte…
We ask and answer a basic question about the length scales involved in quantum decoherence: how far apart in space do two parts of a quantum system have to be, before a common quantum environment decoheres them as if they were entirely separate? We frame this question specifically in a cold atom context. How far apart do two populations of bosons have to be, before an environment of thermal atoms of a different species (`buffer gas') responds to their two particle numbers separately? An initial guess for this length scale is the thermal coherence length of the buffer gas; we show that a standa…
Individual Ba ions are trapped in a gas-filled linear ion trap and observed with a high signal-to-noise ratio by resonance fluorescence. Single-ion storage times of ~5 min (~1 min) are achieved using He (Ar) as a buffer gas at pressures in the range 8e-5 - 4e-3 torr. Trap dynamics in buffer gases are experimentally studied in the simple case of single ions. In particular, the cooling effects of light gases such as He and Ar and the destabilizing properties of heavier gases such as Xe are studied. A simple model is offered to explain the observed phenomenology.
The immersion of a single ion confined by a radiofrequency trap in an ultracold atomic gas extends the concept of buffer gas cooling to a new temperature regime. The steady state energy distribution of the ion is determined by its kinetics in the radiofrequency field rather than the temperature of the buffer gas. Moreover, the finite size of the ultracold gas facilitates the observation of back-action of the ion onto the buffer gas. We numerically investigate the system's properties depending on atom-ion mass ratio, trap geometry, differential cross-section, and non-uniform neutral atom densit…
Direct loading of lanthanide atoms into magneto-optical traps (MOTs) from a very slow cryogenic buffer gas beam source is achieved, without the need for laser slowing. The beam source has an average forward velocity of 60-70\,m/s and a velocity half-width of ~35 m/s, which allows for direct MOT loading of Yb, Tm, Er and Ho. Residual helium background gas originating from the beam results in a maximum trap lifetime of about 80 ms (with Yb). The addition of a single-frequency slowing laser applied to the Yb in the buffer gas beam increases the number of trapped Yb atoms to 1.3(0.7) x 10^8 with a…
We describe and characterize an experimental apparatus that has been used to study interactions between ultracold lithium atoms and ytterbium ions. The preparation of ultracold clouds of Li atoms is described as well as their subsequent transport and overlap with Yb$^+$ ions trapped in a Paul trap. We show how the kinetic energy of the ion after interacting with the atoms can be obtained by laser spectroscopy. From analyzing the dynamics of the ion in the absence of atoms, we conclude that background heating, due to electric field noise, limits attainable buffer gas cooling temperatures. We su…
We theoretically investigate the dynamics of a trapped ion immersed in a spatially localized buffer gas. For a homogeneous buffer gas, the ion reaches a stable equilibrium only if the mass ratio of the buffer gas atom to the ion is below a critical value. We show how this limitation can be overcome by using multipole traps and 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 derived for arbitrary buffer gas distributions and trap parameters. Three regimes characterized by the analytical form…
We report the successful buffer-gas cooling and magnetic trapping of chromium atoms with densities exceeding $10^{12}$ atoms per cm$^{3}$ at a temperature of 350 mK for the trapped sample. The possibilities to extend the method to buffer-gas cool and magnetically trap molecules are discussed. To minimize the most important loss mechanism in magnetic trapping, molecules with a small spin-spin interaction and a large rotational constant are preferred. Both the CrH ($^6Σ^+$ ground state) and MnH ($^7Σ^+$) radicals appear to be suitable systems for future experiments.
We have trapped large numbers of copper and silver atoms using buffer gas cooling. Up to 3x10^12 copper atoms and 4x10^13 silver atoms are trapped. Lifetimes are as long as 5 s, limited by collisions with the buffer gas. Ratios of elastic to inelastic collision rates with He are >~ 10^6, suggesting copper and silver are favorable for use in ultracold applications. The temperature dependence of the silver-helium-3 collision rate varies as T^5.8. We find that this temperature dependence is inconsistent with the behavior predicted for relaxation arising from the spin-rotation interaction, and con…
We treat the interaction of a trapped ion with a standing-wave light field relaxing the previous condition of the trapping ion being on the node of the standing wave. In addition we work to second order in the Lamb-Dicke parameter $η$, the extension to higher orders in $η$ is also indicated. Only a simple transformation to the ``dressed basis'' [subject to the constraint of Pauli algebra] is required in order to show that the ion interacting with a standing light-wave may be described by the Jaynes-Cummings Hamiltonian.
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…
We demonstrated sympathetic cooling of a single ion in a buffer gas of ultracold atoms with small mass. Efficient collisional cooling was realized by suppressing collision-induced heating. We attempt to explain the experimental results with a simple rate equation model and provide a quantitative discussion of the cooling efficiency per collision. The knowledge we obtained in this work is an important ingredient for advancing the technique of sympathetic cooling of ions with neutral atoms.
We show that weakly bound He-containing van der Waals molecules can be produced and magnetically trapped in buffer-gas cooling experiments, and provide a general model for the formation and dynamics of these molecules. Our analysis shows that, at typical experimental parameters, thermodynamics favors the formation of van der Waals complexes composed of a helium atom bound to most open-shell atoms and molecules, and that complex formation occurs quickly enough to ensure chemical equilibrium. For molecular pairs composed of a He atom and an S-state atom, the molecular spin is stable during forma…
We show that a large class of helium-containing cold polar molecules form readily in a cryogenic buffer gas, achieving densities as high as 10^12 cm^-3. We explore the spin relaxation of these molecules in buffer gas loaded magnetic traps, and identify a loss mechanism based on Landau-Zener transitions arising from the anisotropic hyperfine interaction. Our results show that the recently observed strong T^6 thermal dependence of spin change in buffer gas trapped silver (Ag) is accounted for by the formation and spin change of AgHe, thus providing evidence for molecular formation in a buffer ga…
Sympathetic cooling of trapped ions through collisions with neutral buffer gases is critical to a variety of modern scientific fields, including fundamental chemistry, mass spectrometry, nuclear and particle physics, and atomic and molecular physics. Despite its widespread use over four decades, there remain open questions regarding its fundamental limitations. To probe these limits, here we examine the steady-state evolution of up to ten barium ions immersed in a gas of three-million laser-cooled calcium atoms. We observe and explain the emergence of nonequilibrium behavior as evidenced by bi…
We have measured the reaction rates of trapped, buffer gas cooled Th$^{3+}$ and various gases and have analyzed the reaction products using trapped ion mass spectrometry techniques. Ion trap lifetimes are usually limited by reactions with background molecules, and the high electron affinity of multiply charged ions such as Th$^{3+}$ make them more prone to loss. Our results show that reactions of Th$^{3+}$ with carbon dioxide, methane, and oxygen all occur near the classical Langevin rate, while reaction rates with argon, hydrogen, and nitrogen are orders of magnitude lower. Reactions of Th$^{…
We identify plain evaporation of ions as the fundamental loss mechanism out of a multipole ion trap. Using thermalized negative Cl- ions we find that the evaporative loss rate is proportional to a Boltzmann factor. This thermodynamic description sheds new light on the dynamics of particles in time-varying confining potentials. It specifically allows us to extract the effective depth of the ion trap as the activation energy for evaporation. As a function of the rf amplitude we find two distinct regimes related to the stability of motion of the trapped ions. For low amplitudes the entire trap al…
We discuss the transition from a fully decoherent to a (quasi-)condensate regime in a harmonically trapped weakly interacting 1D Bose gas. By using analytic approaches and verifying them against exact numerical solutions, we find a characteristic crossover temperature and crossover atom number that depend on the interaction strength and the trap frequency. We then identify the conditions for observing either an interaction-induced crossover scenario or else a finite-size Bose-Einstein condensation phenomenon characteristic of an \textit{ideal} trapped 1D gas.
Motivated by several experimental efforts to understand spin diffusion and transport in ultracold fermionic gases, we study the spin dynamics of initially spin-polarized ensembles of harmonically trapped non-interacting spin-1/2 fermionic atoms, subjected to a magnetic field gradient. We obtain simple analytic expressions for spin observables in the presence of both constant and linear magnetic field gradients, with and without a spin-echo pulse, and at zero and finite temperatures. The analysis shows the relevance of spin-motional coupling in the non-interacting regime where the demagnetizati…
We observe magnetic trapping of atomic nitrogen (14^N) and cotrapping of ground state imidogen (14^NH, X-triplet-Sigma-). Both are loaded directly from a room temperature beam via buffer gas cooling. We trap approximately 1 * 10^11 14^N atoms at a peak density of 5 * 10^11 cm^-3 at 550 mK. The 12 +5/-3 s 1/e lifetime of atomic nitrogen in the trap is limited by elastic collisions with the helium buffer gas. Cotrapping of 14^N and 14^NH is accomplished, with 10^8 NH trapped molecules at a peak density of 10^8 cm^-3. We observe no spin relaxation of nitrogen in collisions with helium.
We perform numerical simulations of trapped $^{171}$Yb$^+$ ions that are buffer gas cooled by a cold cloud of $^6$Li atoms. This species combination has been suggested to be the most promising for reaching the quantum regime of interacting atoms and ions in a Paul trap. Treating the atoms and ions classically, we compute that the collision energy indeed reaches below the quantum limit for a perfect linear Paul trap. We analyze the effect of imperfections in the ion trap that cause excess micromotion. We find that the suppression of excess micromotion required to reach the quantum limit should …
For exploration of quantum effects with hybrid atom-ion systems, reaching ultracold temperatures is the major limiting factor. In this work, we present results on numerical simulations of trapped ion buffer gas cooling using an ultracold atomic gas in a large number of experimentally realistic scenarios. We explore the suppression of micromotion-induced heating effects through optimization of trap parameters for various radio-frequency (rf) traps and rf driving schemes including linear and octupole traps, digital Paul traps, rotating traps and hybrid optical/rf traps. We find that very similar…
We compute numerically the yrast line for harmonically trapped boson systems with a weak repulsive contact interaction, studying the transition to a vortex state as the angular momentum L increases and approaches N, the number of bosons. The L=N eigenstate is indeed dominated by particles with unit angular momentum, but the state has other significant components beyond the pure vortex configuration. There is a smooth crossover between low and high L with no indication of a quantum phase transition. Most strikingly, the energy and wave function appear to be analytical functions of L over the en…
We study the interaction of a light beams carrying angular momentum with a single, trapped and well localized ion. We provide a detailed calculation of selection rules and excitation probabilities for quadrupole transitions. The results show the dependencies on the angular momentum and polarization of the laser beam as well as the direction of the quantization magnetic field. In order to observe optimally the specific effects, focusing the angular momentum beam close to the diffraction limit is required. We discuss a protocol for examining experimentally the effects on the S$_{1/2}$ to D$_{5/2…
Cryogenic 22-pole ion traps have found many applications in ion-molecule reaction kinetics and in high resolution molecular spectroscopy. For most of these applications it is important to know the translational and internal temperatures of the trapped ions. Here, we present detailed rotational state thermometry measurements over an extended temperature range for the two ion/buffer gas systems OH-/He and OD-/HD with ion-to-neutral mass ratios of 4.25 and 6 respectively. The measured rotational temperatures show a termination of the thermalisation with the buffer gas around 25K, independent of m…
We provide a detailed theoretical and conceptual study of a planned experiment to excite Rydberg states of ions trapped in a Paul trap. The ultimate goal is to exploit the strong state dependent interactions between Rydberg ions to implement quantum information processing protocols and to simulate the dynamics of strongly interacting spin systems. We highlight the promises of this approach when combining the high degree of control and readout of quantum states in trapped ion crystals with the novel and fast gate schemes based on interacting giant Rydberg atomic dipole moments. We discuss antic…
We investigate trapped resonant fermions with unequal populations within the local density approximation above the superfluid transition temperature. By tuning the attractive interaction between fermions via Feshbach resonance, the system evolves from weakly interacting fermi gas to strongly interacting fermi gas, and finally becomes bose-fermi mixture. The density profiles of fermions are examined and compared with experiments. We also point out the simple relationships between the local density, the axial density, and the gas pressure within the local density approximation.
We report on the dynamics of thermalization by extending a generalization of the Caldeira-Leggett model, developed in the context of cold atomic gases confined in a harmonic trap, to higher dimensions. Universal characteristics en route to thermalization which appear to be independent of dimensionality are highlighted, which additionally suggest a scaling analogous to turbulent mixing in fluid dynamics. We then focus on features dependent on dimensionality, with particular regard to the role of angular momentum of the two atomic clouds, having in mind the goal of efficient thermalization betwe…
Using the ab initio computed Potential Energy Surface (PES) for the electronic interaction of the MgH$^+$ ($^1Σ$) ion with the He($^1$S) atom, we calculate the relevant state-changing rotationally inelastic collision cross sections from a quantum treatment of the multichannel scattering problem. We focus on the quantum dynamics at the translationally low energies for the present partners discussed in the earlier, cold ion trap experiments (see below) which we wish to model in detail. The corresponding state-changing rates computed between the lower rotational states of the molecular ion are em…
Linear arrays of trapped and laser cooled atomic ions are a versatile platform for studying emergent phenomena in strongly-interacting many-body systems. Effective spins are encoded in long-lived electronic levels of each ion and made to interact through laser mediated optical dipole forces. The advantages of experiments with cold trapped ions, including high spatiotemporal resolution, decoupling from the external environment, and control over the system Hamiltonian, are used to measure quantum effects not always accessible in natural condensed matter samples. In this review we highlight recen…
