A single ion immersed in a neutral buffer gas is studied. An analytical model is developed that gives a complete description of the dynamics and steady-state properties of the ions. An extension of this model, using techniques borrowed from the mathematics of finance, is used to explain the recent observation of non-Maxwellian statistics for these systems. Taken together, these results offer an explanation of the longstanding issues associated with sympathetic cooling of an ion by a neutral buffer gas. PACS numbers:The fact that two isolated objects in thermal contact tend to the same temperature is the most basic tenet of thermodynamics. It is also the essence of the technique of sympathetic cooling, where a sample is prepared at a desired temperature by bringing it into thermal contact with a much larger body already at the desired temperature. It is difficult to overstate the importance of this technique as it underpins applications ranging from basic refrigeration to quantum information science. It may be considered surprising then that a gas of ions trapped in a radio-frequency Paul trap and immersed in a reservoir of neutral atoms, does not equilibrate to the same temperature as the neutral atoms. Instead, the ions are found to have a higher temperature than the neutral gas, and in some cases are heated so much that they escape the trap. Since the early work of Major and Dehmelt [1] it has been known that this apparent contradiction with the laws of thermodynamics is due to the fact that ions are subject to a time-dependent confining potential and are therefore not an isolated system. However, despite pioneering work by Dehmelt and others [2,3], an accurate analytical description of the relaxation process has not yet been achieved. Given the recent surge in interest in hybrid atom-ion systems [4][5][6][7][8][9][10][11][12][13], where ions are immersed in baths of ultracold atoms, there is currently a strong need for such a description so that these systems can be understood and optimized.Building upon the important work of Moriwaki et al .[2], here we present a simple kinematic model, which accurately describes the ion relaxation process. This model, which has been verified by detailed molecular dynamics simulations, provides a simple and accurate means to calculate both the relaxation dynamics and the properties of the ion steady state. This model also provides significant physical intuition for the problem and as such suggests several ways for optimizing ongoing and planned experiments in fields as diverse as quantum chemistry [4-13], mass spectrometry [14], and quantum information [15].In the remainder of this work, we first review the basics of ion trapping and introduce the time-averaged ion kinetic energy. We then consider the effect of a collision with a neutral particle on the evolution of the kinetic energy of a single ion in a Paul trap and show that due to the presence of the time-dependent potential the collision center-of-mass frame energy is not conserved. Following this result, we develop a ...

Compared with atoms, molecules have a rich internal structure that offers many opportunities for technological and scientific advancement. The study of this structure could yield critical insights into quantum chemistry, new methods for manipulating quantum information, and improved tests of discrete symmetry violation and fundamental constant variation. Harnessing this potential typically requires the preparation of cold molecules in their quantum rovibrational ground state. However, the molecular internal structure severely complicates efforts to produce such samples. Removal of energy stored in long-lived vibrational levels is particularly problematic because optical transitions between vibrational levels are not governed by strict selection rules, which makes laser cooling difficult. Additionally, traditional collisional, or sympathetic, cooling methods are inefficient at quenching molecular vibrational motion. Here we experimentally demonstrate that the vibrational motion of trapped BaCl(+) molecules is quenched by collisions with ultracold calcium atoms at a rate comparable to the classical scattering, or Langevin, rate. This is over four orders of magnitude more efficient than traditional sympathetic cooling schemes. The high cooling rate, a consequence of a strong interaction potential (due to the high polarizability of calcium), along with the low collision energies involved, leads to molecular samples with a vibrational ground-state occupancy of at least 90 per cent. Our demonstration uses a novel thermometry technique that relies on relative photodissociation yields. Although the decrease in vibrational temperature is modest, with straightforward improvements it should be possible to produce molecular samples with a vibrational ground-state occupancy greater than 99 per cent in less than 100 milliseconds. Because sympathetic cooling of molecular rotational motion is much more efficient than vibrational cooling in traditional systems, we expect that the method also allows efficient cooling of the rotational motion of the molecules. Moreover, the technique should work for many different combinations of ultracold atoms and molecules.

Ultracold 174Yb+ ions and 40Ca atoms are confined in a hybrid trap. The charge exchange chemical reaction rate constant between these two species is measured and found to be 4 orders of magnitude larger than recent measurements in other heteronuclear systems. The structure of the CaYb+ molecule is determined and used in a calculation that explains the fast chemical reaction as a consequence of strong radiative charge transfer. A possible explanation is offered for the apparent contradiction between typical theoretical predictions and measurements of the radiative association process in this and other recent experiments.

We demonstrate the integration of a linear quadrupole trap with a simple time-of-flight mass spectrometer with medium-mass resolution (m/Δm ∼ 50) geared towards the demands of atomic, molecular, and chemical physics experiments. By utilizing a novel radial ion extraction scheme from the linear quadrupole trap into the mass analyzer, a device with large trap capacity and high optical access is realized without sacrificing mass resolution. This provides the ability to address trapped ions with laser light and facilitates interactions with neutral background gases prior to analyzing the trapped ions. Here, we describe the construction and implementation of the device as well as present representative ToF spectra. We conclude by demonstrating the flexibility of the device with proof-of-principle experiments that include the observation of molecular-ion photodissociation and the measurement of trapped-ion chemical reaction rates.

Background Correct specification of cell lineages and establishing angiogenic privilege within the developing cornea are essential for normal vision but the mechanisms controlling these processes are poorly understood. Results We show that the homeodomain transcription factor PItX2 is expressed in mesenchymal cells of the developing and mature cornea and use a temporal gene knockout approach to demonstrate that PITX2 is required for corneal morphogenesis and the specification of cell fates within the surface ectoderm and mesenchymal primordia. PITX2 is also required to establish angiogenic privilege in the developing cornea. Further, the expression of Dkk2 and suppression of canonical Wnt signaling activity levels are key mechanisms by which PITX2 specifies ocular surface ectoderm as cornea. In contrast, specifying the underlying mesenchyme to corneal fates and establishing angiogenic privilege in the cornea are less sensitive to DKK2 activity. Finally, the cellular expression patterns of FOXC2, PITX1, and BARX2 in Pitx2 and Dkk2 mutants suggest that these transcription factors may be involved in specifying cell fate and establishing angiogenic privilege within the corneal mesenchyme. However, they are unlikely to play a role in specifying cell fate within the corneal ectoderm. Conclusions Together, these data provide important insights into the mechanisms regulating cornea development.