We report sympathetic cooling of $^{113}$Cd$^+$ by laser-cooled $^{40}$Ca$^+$ in a linear Paul trap for microwave clocks. Long-term low-temperature confinement of $^{113}$Cd$^+$ ions was achieved. The temperature of these ions was measured at $90(10)$ mK, and the corresponding uncertainty arising from the second-order Doppler shifts was estimated to a level of $2\times10^{-17}$. Up to $4.2\times10^5$ Cd$^+$ ions were confined in the trap, and the confinement time constant was measured to be 84 hours. After three hours of confinement, there were still $10^5$ Cd$^+$ ions present, indicating that this Ca$^+$--Cd$^+$ dual ion system is surprisingly stable. The ac Stark shift was induced by the Ca$^+$ lasers and fluorescence, which was carefully estimated to an accuracy of $5.4(0.5)\times10^{-17}$ using a high-accuracy \textit{ab initio} approach. The Dick-effect-limited Allan deviation was also deduced because deadtimes were shorter. These results indicate that a microwave clock based on this sympathetic cooling scheme holds promise in providing ultra-high frequency accuracy and stability.
This paper reports the direct temperature determination of sympathetically cooled 113Cd+ ions with laser-cooled 24Mg+ in a linear Paul trap. The sympathetically cooled ion species distribute in the outer shell of the large ensembles, which contain up to 3.3E5 ions. With optimized parameters, the minimum temperature of the sympathetically cooled 113Cd+ ions was measured to be tens of mK. These results indicate promising performance for microwave atomic clocks. The second order Doppler frequency shift is two orders of magnitudes lower and the Dick effect is suppressed.
Sympathetic laser cooling of ions stored within a linear-geometry, radio frequency, electric-quadrupole trap has been investigated using computational and theoretical techniques. The simulation, which allows 5 sample ions to interact with 35 laser-cooled atomic ions, revealed an instability heating mechanism, which can prevent ions below a certain critical mass from being sympathetically cooled. This critical mass can however be varied by changing the trapping field parameters thus allowing ions with a very large range of masses to be sympathetically cooled using a single ion species. A theore…
We report frequency measurement of the clock transition in an 115In+ ion sympathetically-cooled with Ca+ ions in a linear rf trap. The Ca+ ions are used as a probe of the external electromagnetic field and as the coolant for preparing the cold In+. The frequency is determined to be 1 267 402 452 901 049.9 (6.9) Hz by averaging 36 measurements using an optical frequency comb referenced to the frequency standards located in the same site.
The ion microwave frequency standard is a candidate for the next generation of microwave frequency standard with the potential for very wide applications. The Dick effect and second-order Doppler frequency shift (SODFS) limit the performance of ion microwave frequency standards. The introduction of sympathetic cooling technology can suppress the Dick effect and SODFS and improve the stability and accuracy of the frequency standard. However, the sympathetically-cooled ion microwave frequency standard has seldom been studied before. This paper reports the first sympathetically-cooled ion microwa…
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.
We demonstrate sympathetic sideband cooling of a $^{40}$CaH$^{+}$ molecular ion co-trapped with a $^{40}$Ca$^{+}$ atomic ion in a linear Paul trap. Both axial modes of the two-ion chain are simultaneously cooled to near the ground state of motion. The center of mass mode is cooled to an average quanta of harmonic motion $\overline{n}_{\mathrm{COM}} = 0.13 \pm 0.03$, corresponding to a temperature of $12.47 \pm 0.03 ~μ$K. The breathing mode is cooled to $\overline{n}_{\mathrm{BM}} = 0.05 \pm 0.02$, corresponding to a temperature of $15.36 \pm 0.01~μ$K.
We study sympathetic cooling of the radial ion motion in a linear RF trap in mixed barium-ytterbium chains. Barium ions are Doppler-cooled, while ytterbium ions are cooled through their interaction with cold barium ions. We estimate the efficiency of sympathetic cooling by measuring the average occupation quantum numbers, and thus the temperature, of all radial normal modes of motion in the ion chain. The full set of orderings in a chain of two barium and two ytterbium ions have been probed, and we show that the average thermal occupation numbers for all chain configurations strongly depend on…
We present first indications of sympathetic cooling between two neutral, optically trapped atomic species. Lithium and cesium atoms are simultaneously stored in an optical dipole trap formed by the focus of a CO$_2$ laser, and allowed to interact for a given period of time. The temperature of the lithium gas is found to decrease when in thermal contact with cold cesium. The timescale of thermalization yields an estimate for the Li-Cs cross-section.
We report on a study of cold reactive collisions between sympathetically-cooled molecular ions and laser-cooled atoms in an ion-atom hybrid trap. Chemical reactions were studied at average collision energies <Ecoll>/k > 20 mK, about two orders of magnitude lower than has been achieved in previous experiments with molecular ions. Choosing N2+ +Rb as a prototypical system, we find that the reaction rate is independent of the collision energy, but strongly dependent on the internal state of Rb. Highly efficient charge exchange about four times faster than the Langevin rate was observed with Rb in…
We demonstrate rotational excitation of molecular ions that are sympathetically cooled by laser-cooled atomic ions to a temperature as low as ca. 10 mK. The molecular hydrogen ions HD+ and the fundamental rotational transition $(v=0,\, N=0)\rightarrow(v'=0,\, N'=1)$ at 1.3 THz, the most fundamental dipole-allowed rotational transition of any molecule, are used as a test case. This transition is here observed for the first time directly. Rotational laser cooling was employed in order to increase the signal, and resonance-enhanced multiphoton dissociation was used as detection method. The black-…
Current precision experiments with single (anti)protons to test CPT symmetry progress at a rapid pace, but are complicated by the need to cool particles to sub-thermal energies. We describe a cryogenic Penning-trap setup for $^9$Be$^+$ ions designed to allow coupling of single (anti)protons to laser-cooled atomic ions for sympathetic cooling and quantum logic spectroscopy. We report on trapping and laser cooling of clouds and single $^9$Be$^+$ ions. We discuss prospects for a microfabricated trap to allow coupling of single (anti)protons to laser-cooled $^9$Be$^+$ ions for sympathetic laser co…
The $^{27}$Al$^+$ ion optical clock is one of the most attractive optical clocks due to its own advantages, such as low blackbody radiation shift at room temperature and insensitive to the magnetic drift. However, it cannot be laser-cooled directly in the absence of 167 nm laser to date. This problem can be solved by sympathetic cooling. In this work, a linear Paul trap is used to trap both $^{40}$Ca$^{+}$ and $^{27}$Al$^+$ ions simultaneously, and a single Doppler-cooled $^{40}$Ca$^+$ ion is employed to sympathetically cool a single $^{27}$Al$^+$ ion. Thus a "bright-dark" two-ion crystal has …
We demonstrate the trapping and sympathetic cooling of B$^{+}$ ions in a Coulomb crystal of laser-cooled Ca$^{+}$, We non-destructively confirm the presence of the both B$^+$ isotopes by resonant excitation of the secular motion. The B$^{+}$ ions are loaded by ablation of boron and the secular excitation spectrum also reveals features consistent with ions of the form B$_{n}^{+}$.
We report the measurement of the 1$^{1}Σ\longrightarrow$ 2$^{1}Σ$ transition of CaH$^+$ by resonance-enhanced photodissociation of CaH$^+$ that is co-trapped with laser-cooled Ca$^+$ . We observe four resonances that we assign to transitions from the vibrational $v$=0 ground state to the $v'$=1-4 excited states based on theoretical predictions. A simple theoretical model that assumes instantaneous dissociation after resonant excitation yield results in good agreement with the observed spectral features except for the unobserved $v'$=0 peak. The resolution of our experiment is limited by the mo…
Long range polarization forces between ions and neutral atoms result in large elastic scattering cross sections, e.g., 10^6 a.u. for Na+ on Na or Ca+ on Na at cold and ultracold temperatures. This suggests that a hybrid ion-neutral trap should offer a general means for significant sympathetic cooling of atomic or molecular ions. We present SIMION 7.0 simulation results concerning the advantages and limitations of sympathetic cooling within a hybrid trap apparatus, consisting of a linear rf Paul trap concentric with a Na magneto-optical trap (MOT). This paper explores the impact of various heat…
We present and derive analytic expressions for a fundamental limit to the sympathetic cooling of ions in radio-frequency traps using cold atoms. The limit arises from the work done by the trap electric field during a long-range ion-atom collision and applies even to cooling by a zero-temperature atomic gas in a perfectly compensated trap. We conclude that in current experimental implementations this collisional heating prevents access to the regimes of single-partial-wave atom-ion interaction or quantized ion motion. We determine conditions on the atom-ion mass ratio and on the trap parameters…
We investigate the dynamics of an ion sympathetically cooled by another laser-cooled ion or small ion crystal. To this end, we develop simple models of the cooling dynamics in the limit of weak Coulomb interactions. Experimentally, we create a two-ion crystal of Ca$^+$ and Al$^+$ by photo-ionization of neutral atoms produced by laser ablation. We characterize the velocity distribution of the laser-ablated atoms crossing the trap by time-resolved fluorescence spectroscopy. We observe neutral atom velocities much higher than the ones of thermally heated samples and find as a consequence long sym…
We present an experiment to sympathetically cool protons and antiprotons in a Penning trap by resonantly coupling the particles to laser cooled beryllium ions using a common endcap technique. Our analysis shows that preparation of (anti)protons at mK temperatures on timescales of tens of seconds is feasible. Successful implementation of the technique will have immediate and significant impact on high-precision comparisons of the fundamental properties of protons and antiprotons. This in turn will provide some of the most stringent tests of the fundamental symmetries of the Standard Model.
We consider how trapped molecules can be sympathetically cooled by ultracold atoms. As a prototypical system, we study LiH molecules co-trapped with ultracold Li atoms. We calculate the elastic and inelastic collision cross sections of LiH + Li with the molecules initially in the ground state and in the first rotationally excited state. We then use these cross sections to simulate sympathetic cooling in a static electric trap, an ac electric trap, and a microwave trap. In the static trap we find that inelastic losses are too great for cooling to be feasible for this system. The ac and microwav…
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…
The coupled motion of ions in a radiofrequency trap has been used to connect the frequency- dependent laser-induced heating of a sympathetically cooled spectroscopy ion with changes in the fluorescence of a laser-cooled control ion. This technique, sympathetic heating spectroscopy, is demonstrated using two isotopes of calcium. In the experiment, a few scattered photons from the spectroscopy ion are transformed into a large deviation from the steady-state fluorescence of the control ion. This allows us to detect an optical transition where the number of scattered photons is below our fluoresce…
We describe a method for cooling neutral molecules that have magnetic and electric dipole moments using collisions with cold ions. An external magnetic field is used to split the ground rovibrational energy levels of the molecule. The highest energy state within the ground rovibrational manifold increases in energy as the distance to the ion decreases leading to a repelling potential. At low energy, inelastic collisions are strongly suppressed due to the large distance of closest approach. Thus, a collision between a neutral molecule and a cold ion will lead to a decrease in the molecule's kin…
We consider the prospect of using ultracold hydrogen atoms for sympathetic cooling of fluorine atoms to microkelvin temperatures. We carry out quantum-mechanical calculations on collisions between cold F and H atoms in magnetically trappable states and show that the ratio of elastic to inelastic cross sections remains high across a wide range of temperatures and magnetic fields. For F atoms initially in the spin-stretched state ($^2$P$_{3/2}$, $f=m_f=+2$), sympathetic cooling appears likely to succeed from starting temperatures around 1 K or even higher. This occurs because inelastic collision…
We report on observations of thermal motion of a single, Doppler-cooled ion along the axis of a linear radio-frequency quadrupole trap. We show that for a harmonic potential the thermal occupation of energy levels leads to Gaussian distribution of the ion's axial position. The dependence of the spatial thermal spread on the trap potential is used for precise calibration of our imaging system's point spread function and sub-milliKelvin thermometry. We employ this technique to investigate the laser detuning dependence of the Doppler temperature.
We have generated Coulomb crystals of ultracold $^4$He$^+$ ions in a linear radiofrequency trap, by sympathetic cooling via laser--cooled $^9$Be$^+$. Stable crystals containing up to 150 localized He$^+$ ions at $\sim$20 mK were obtained. Ensembles or single ultracold He$^+$ ions open up interesting perspectives for performing precision tests of QED and measurements of nuclear radii. The present work also indicates the feasibility of cooling and crystallizing highly charged atomic ions using $^9$Be$^+$ as coolant.
Efficient cooling of trapped charged particles is essential to many fundamental physics experiments, to high-precision metrology, and to quantum technology. Until now, sympathetic cooling has required close-range Coulomb interactions, but there has been a sustained desire to bring laser-cooling techniques to particles in macroscopically separated traps, extending quantum control techniques to previously inaccessible particles such as highly charged ions, molecular ions and antimatter. Here we demonstrate sympathetic cooling of a single proton using laser-cooled Be+ ions in spatially separated …
We trap cold, ground-state, argon atoms in a deep optical dipole trap produced by a build-up cavity. The atoms, which are a general source for the sympathetic cooling of molecules, are loaded in the trap by quenching them from a cloud of laser-cooled metastable argon atoms. Although the ground state atoms cannot be directly probed, we detect them by observing the collisional loss of co-trapped metastable argon atoms using a new type of parametric loss spectroscopy. Using this technique we also determine the polarizability ratio between the ground and the metastable 4s[3/2]$_2$ state to be 40$\…
A proposal for cooling the translational motion of optically levitated magnetic nanoparticles is presented. The theoretical cooling scheme involves the sympathetic cooling of a ferromagnetic YIG nanosphere with a spin-polarized atomic gas. Particle-atom cloud coupling is mediated through the magnetic dipole-dipole interaction. When the particle and atom oscillations are small compared to their separation, the interaction potential becomes dominantly linear which allows the particle to exchange energy with the $N$ atoms. While the atoms are continuously Doppler cooled, energy is able to be remo…
We reported the realization of a $^{174}\mathrm{Yb}^+$-$^{113}\mathrm{Cd}^+$ bi-species Coulomb crystal comprising $^{174}\mathrm{Yb}^+$ ions as coolant and verified its potential for application as a $^{113}\mathrm{Cd}^+$ microwave frequency standard employing sympathetic cooling.The two species of massive ions stably trapped in a Paul trap make up this large two-component crystal. The $^{113}\mathrm{Cd}^+$ ions are trapped in the center, which reduces considerably RF heating and excess micromotion to which the $^{113}\mathrm{Cd}^+$ ions are subjected. Under this scheme, the uncertainty due t…
We are developing a new hybrid atom-ion trap to study the interaction of ultracold rubidium atoms with mass-selected OH- molecules. The ions are trapped inside an octupole rf-trap made of thin wires instead of the commonly used rods. This ensures good optical access to the center of the trap where the ions can be overlapped with laser cooled rubidium atoms stored in a dark spontaneous force optical trap (dark SPOT). This setup provides high collision rates since the density in a dark SPOT is about one order of magnitude higher than in a standard magneto-optical trap. Further, inelastic collisi…
We simultaneously trap ultracold lithium and cesium atoms in an optical dipole trap formed by the focus of a CO$_2$ laser and study the exchange of thermal energy between the gases. The cesium gas, which is optically cooled to $20 μ$K, efficiently decreases the temperature of the lithium gas through sympathetic cooling. The measured cross section for thermalizing $^{133}$Cs-$^7$Li collisions is $8 \times 10^{-12}$ cm$^2$, for both species in their lowest hyperfine ground state. Besides thermalization, we observe evaporation of lithium purely through elastic cesium-lithium collisions (sympathet…
Gas-phase multiply charged proteins have been sympathetically cooled to translational temperatures below 1 K by Coulomb interaction with laser-cooled barium ions in a linear ion trap. In one case, an ensemble of 53 cytochrome c molecules (mass ~ 12390 amu, charge +17 e) was cooled by ~ 160 laser-cooled barium ions to less than 0.75 K. Storage times of more than 20 minutes have been observed and could easily be extended to more than an hour. The technique is applicable to a wide variety of complex molecules.
We measured by laser spectroscopy the isotope shifts between naturally-occurring even-isotopes of strontium ions for both the $5s\,\,^2S_{1/2}\to 5p\,\,^2P_{1/2}$ (violet) and the $4d\,\,^2D_{3/2}\to 5p\,\,^2P_{1/2}$ (infrared) dipole-allowed optical transitions. Fluorescence spectra were taken by simultaneous measurements on a two-component Coulomb crystal in a linear Paul trap containing $10^3$--$10^4$ laser-cooled Sr$^+$ ions. The isotope shifts are extracted from the experimental spectra by fitting the data with the analytical solution of the optical Bloch equations describing a three-leve…
We have produced sympathetically cooled barium monohalide ions BaX$^+$ (X = F, Cl, Br) by reacting trapped, laser cooled Ba$^+$ ions with room temperature gas phase neutral halogen-containing molecules. Reaction rates for two of these (SF$_6$ and CH$_3$Cl) have been measured and are in agreement with classical models. BaX$^+$ ions are promising candidates for cooling to the rovibrational ground state, and our method presents a straightforward way to produce these polar molecular ions.
We model sympathetic cooling of ground-state CaF molecules by ultracold Li and Rb atoms. The molecules are moving in a microwave trap, while the atoms are trapped magnetically. We calculate the differential elastic cross sections for CaF-Li and CaF-Rb collisions, using model Lennard-Jones potentials adjusted to give typical values for the s-wave scattering length. Together with trajectory calculations, these differential cross sections are used to simulate the cooling of the molecules, the heating of the atoms, and the loss of atoms from the trap. We show that a hard-sphere collision model bas…
Sympathetic cooling of trapped ions has become an indispensable tool for quantum information processing and precision spectroscopy. In the simplest situation a single Doppler-cooled ion sympathetically cools another ion which typically has a different mass. We analytically investigate the effect of the mass ratio of such an ion crystal on the achievable temperature limit in the presence of external heating. As an example, we show that cooling of a single Al+ with Be+, Mg+ and Ca+ ions provides similar results for heating rates typically observed in ion traps, whereas cooling ions with a larger…
Precision optical spectroscopy of exotic ions reveals accurate information about nuclear properties such as charge radii and magnetic and quadrupole moments. Thorium ions exhibit unique nuclear properties with high relevance for testing symmetries of nature. We report loading and trapping of single $^{232}$Th$^+$ ions in a linear Paul trap, embedded into and sympathetically cooled by small crystals of trapped $^{40}$Ca$^+$ ions. Trapped Th ions are identified in a non-destructive manner from the voids in the laser-induced Ca fluorescence pattern emitted by the crystal, and alternatively, by me…
We have performed laser cooling of Mg ions confined in a Penning trap. The externally produced ions were captured in flight, stored and laser cooled. Laser-induced fluorescence was observed perpendicular to the cooling laser axis. Optical detection down to the single ion level together with electronic detection of the ion oscillations inside the Penning trap have been used to acquire information on the ion storage time, ion number and ion temperature. Evidence for formation of ion crystals has been observed. These investigations are an important prerequisite for sympathetic cooling of simultan…
We report on the design of a segmented linear Paul trap for optical clock applications using trapped ion Coulomb crystals. For an optical clock with an improved short-term stability and a fractional frequency uncertainty of 10^-18, we propose 115In+ ions sympathetically cooled by 172Yb+. We discuss the systematic frequency shifts of such a frequency standard. In particular, we elaborate on high precision calculations of the electric radiofrequency field of the ion trap using the finite element method. These calculations are used to find a scalable design with minimized excess micromotion of th…
We present a new method for the generation of rotationally and vibrationally state-selected, translationally cold molecular ions in ion traps. Our technique is based on the state-selective threshold photoionization of neutral molecules followed by sympathetic cooling of the resulting ions with laser-cooled calcium ions. Using N$_2^+$ ions as a test system, we achieve > 90 % selectivity in the preparation of the ground rovibrational level and state lifetimes on the order of 15 minutes limited by collisions with background-gas molecules. The technique can be employed to produce a wide range of a…
Trapping molecular ions that have been sympathetically cooled with laser-cooled atomic ions is a useful platform for exploring cold ion chemistry. We designed and characterized a new experimental apparatus for probing chemical reaction dynamics between molecular cations and neutral radicals at temperatures below 1 K. The ions are trapped in a linear quadrupole radio-frequency trap and sympathetically cooled by co-trapped, laser-cooled, atomic ions. The ion trap is coupled to a time-of-flight mass spectrometer to readily identify product ion species, as well as to accurately determine trapped i…
A mixed system of cooled and trapped, ions and atoms, paves the way for ion assisted cold chemistry and novel many body studies. Due to the different individual trapping mechanisms, trapped atoms are significantly colder than trapped ions, therefore in the combined system, the strong binary ion$-$atom interaction results in heat flow from ions to atoms. Conversely, trapped ions can also get collisionally heated by the cold atoms, making the resulting equilibrium between ions and atoms intriguing. Here we experimentally demonstrate, Rubidium ions (Rb$^+$) cool in contact with magneto-optically …
We propose a new way for sympathetic cooling of ions in an electromagnetic Paul trap: it implies the use for this purpose of cold buffer atoms in the region of atom-ion confinement-induced resonance (CIR). The problem is that the unavoidable micromotion of the ion and the long-range nature of its interaction with the environment of colder atoms in a hybrid atomic-ion trap prevent its sympathetic cooling. We show that the destructive effect of ion micromotion on its sympathetic cooling can however be suppressed in the vicinity of the atom-ion CIR. The origin of this is the "fermionization" of t…
Cooling of particles to mK-temperatures is essential for a variety of experiments with trapped charged particles. However, many species of interest lack suitable electronic transitions for direct laser cooling. We study theoretically the remote sympathetic cooling of a single proton with laser-cooled $^9$Be$^+$ in a double-Penning-trap system. We investigate three different cooling schemes and find, based on analytical calculations and numerical simulations, that two of them are capable of achieving proton temperatures of about 10 mK with cooling times on the order of 10 s. In contrast, establ…
