Neutral Gas Sympathetic Cooling of an Ion in a Paul Trap

Abstract

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 ...

Design and characterization of a linear quadrupole ion trap for high-resolution Coulomb-crystal time-of-flight mass spectrometry

“…The Ca beam is generated by a resistively heated Ca oven (Alvatec). The 40 Ca + ions are laser cooled by two laser beams at 397 nm and 866 nm propagating along the trap axis [6]. The 397 and 866 nm light is generated by two external cavity-enhanced diode lasers that are frequency stabilized using a wavemeter (HighFinesse WSU 30) and a computer controlled feedback loop.…”

“…The base pressure in this setup is < 5 · 10 −10 mbar. 40 Ca + ions are generated by non-resonant multi photon ionisation of an atomic beam of Ca by the third harmonic (355 nm) of a Nd:YAG laser. The Ca beam is generated by a resistively heated Ca oven (Alvatec).…”

Collisional Cooling of Light Ions by Cotrapped Heavy Atoms

“…The atom-ion mass ratios ( = 2.179 for 85 Rb- Cs- 85 Rb + ) we demonstrate cooling for, exceed the critical mass ratios (CMRs) [15][16][17][18] beyond which ion heating is predicted for uniform atomic gas densities. The experiment is consistent with our Monte Carlo (MC) simulations and other theoretical models [19] that consider collisions with centrally localized density (as opposed to uniform density) of cold atoms.…”

“…In practice, the cooling by buffer gas has found extensive applications when [23]. In recent years, several independent theoretical analyses for ion cooling by neutral atoms have arrived at limiting CMRs [16][17][18] Exceeding these CMRs results in the heating of ions (and below these cooling occurs) if the ion is assumed to be located within a cold gas of uniform density. However, in hybrid ion-atom traps the atomic density is localized, for example in a MOT, and is located at the centre of the ion trap [see Figs.…”

“…This is partly because calculations show that trapped ions in a uniform buffer gas will heat up when the ratio of the atom mass ( ) to the ion mass ( ) exceeds a critical value [15][16][17][18]. In recent years, theoretical studies suggest a possible experimental resolution by using a localized ensemble of ultracold neutral atoms placed precisely at the centre of the ion trap [12,19].In ) we demonstrate cooling for, exceed the critical mass ratios (CMRs) [15][16][17][18] beyond which ion heating is predicted for uniform atomic gas densities. The experiment is consistent with our Monte Carlo (MC) simulations and other theoretical models [19] that consider collisions with centrally localized density (as opposed to uniform density) of cold atoms.…”