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arXiv:1608.03376 · Nature Communications

Blue-sky bifurcation of ion energies and the limits of neutral-gas sympathetic cooling of trapped ions

Steven J. Schowalter, Alexander J. Dunning, Kuang Chen, Prateek Puri, Christian Schneider, Eric R. Hudson

Published Aug 11, 2016• 30 citations
arXivHTMLPDF

Abstract

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 10 barium ions immersed in a gas of three-million laser-cooled calcium atoms. We observe and explain the emergence of nonequilibrium behaviour as evidenced by bifurcations in the ion steady-state temperature, parameterized by ion number. We show that this behaviour leads to the limitations in creating and maintaining translationally cold samples of trapped ions using neutral-gas sympathetic cooling. These results may provide a route to studying non-equilibrium thermodynamics at the atomic level.

DOI
10.1038/ncomms12448

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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 10 barium ions immersed in a gas of three-million laser-cooled calcium atoms. We observe and explain the emergence of nonequilibrium behaviour as evidenced by bifurcations in the ion steady-state temperature, parameterized by ion number. We show that this behaviour leads to the limitations in creating and maintaining translationally cold samples of trapped ions using neutral-gas sympathetic cooling. These results may provide a route to studying non-equilibrium thermodynamics at the atomic level.
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Using a laser-cooled ion trapping apparatus, we have investigated laser-induced chemical reactions between cold trapped Ba+{\mathrm{Ba}}^{+}Ba+ ions and several neutral molecular gases at room temperature, O2{\mathrm{O}}_{2}O2​, CO2\mathrm{C}{\mathrm{O}}_{2}CO2​, and N2O{\mathrm{N}}_{2}\mathrm{O}N2​O, leading to the production of cold trapped $(\ensuremath{\approx}20\phantom{\rule{0.3em}{0ex}}\mathrm{mK})$ BaO+\mathrm{Ba}{\mathrm{O}}^{+}BaO+ ions. The BaO+\mathrm{Ba}{\mathrm{O}}^{+}BaO+ ions were converted back to Ba+{\mathrm{Ba}}^{+}Ba+ ions via reaction with room-temperature CO. Reaction rates were determined by employing molecular dynamics simulations. The cold mixed-species ion ensembles produced were used for studying the efficiency of sympathetic cooling, by variation of the ratio of laser-cooled to sympathetically cooled ion numbers. In one extreme case, 20 laser-cooled 138Ba+^{138}\mathrm{Ba}^{+}138Ba+ ions were capable of maintaining the translational temperature of 120 sympathetically cooled barium isotopes (135−−137Ba+)(^{135--137}\mathrm{Ba}^{+})(135−−137Ba+) and 430 138Ba16O+^{138}\mathrm{Ba}^{16}{\mathrm{O}}^{+}138Ba16O+ molecules at approximately 25mK25\phantom{\rule{0.3em}{0ex}}\mathrm{mK}25mK.
This thesis reports on experimental and theoretical studies of the sympathetic cooling of complex molecular ions demonstrating that this general method for cooling atomic and molecular ions is reliable and efficient. For this purpose, complex molecular ions and barium ions have been confined simultaneously in a linear Paul trap. The complex molecular ions are generated in an electrospray ionization system and transferred to the trap via a 2 m long octopole ion guide. These molecular ions are pre-cooled by room temperature helium buffer gas so that they can be captured by the trap. The atomic barium ions are loaded from a barium evaporator oven and are laser-cooled by a 493 nm cooling laser and a 650 nm repumping laser. Due to the mutual Coulomb interaction among these charged particles, the kinetic energy of the complex molecular ions can be reduced significantly. In our experiments we have demonstrated the sympathetic cooling of various molecules (CO2, Alexa Fluor 350, glycyrrhetinic acid, cytochrome c) covering a wide mass range from a few tens to 13000 amu. In every case the molecular ions could be cooled down to millikelvin temperatures. Photo-chemical reactions of the 138Ba+ ions in the (2P1/2) excited state with gases such as O2, CO2, or N2O, could be observed. If the initial 138Ba+ ion ensemble is cold, the produced 138BaO+ ions are cold as well, with a similar temperature as the laser-cooled barium ions (a few tens of millikelvin). The back-reaction of 138BaO+ ions with neutral CO to 138Ba+ is possible and was observed in our experiments as well. A powerful molecular dynamics (MD) simulation program has been developed. With this program dynamic properties of ion ensembles, such as sympathetic interactions or heating effects, have been investigated and experimental results have been analyzed to obtain, for example, ion numbers and temperatures. Additionally, the feasibility of nondestructive spectroscopy via an optical dipole excitation and the lineshape of rovibrational transitions of 1.4 and 5.1 μm have been studied.
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. H\"oltkemeier 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 us to investigate the influence of nonhomogeneous buffer-gas configurations as well as higher multipole orders of the radio-frequency trap in great detail. Depending on the neutral-to-ion mass ratio, three regimes of sympathetic cooling are identified which are characterized by the form of the ion's energy distribution in equilibrium. We provide analytic expressions and numerical simulations of the ion's energy distribution, spatial profile, and cooling rates for these different regimes. Based on these findings, a method for actively decreasing the ion's energy by reducing the spatial expansion of the buffer gas arises (forced sympathetic cooling).
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 employed in the mathematics of economics and finance, is used to explain the recent observation of non-Maxwellian statistics for these systems. Taken together, these results offer an explanation of the long-standing issues associated with sympathetic cooling of an ion by a neutral buffer gas.