The realization of superfluidity in a dilute gas of fermionic atoms, analogous to superconductivity in metals, represents a long-standing goal of ultracold gas research. In such a fermionic superfluid, it should be possible to adjust the interaction strength and tune the system continuously between two limits: a Bardeen–Cooper–Schrieffer (BCS)-type superfluid (involving correlated atom pairs in momentum space) and a Bose–Einstein condensate (BEC), in which spatially local pairs of atoms are bound together. This crossover between BCS-type superfluidity and the BEC limit has long been of theoretical interest, motivated in part by the discovery of high-temperature superconductors. In atomic Fermi gas experiments superfluidity has not yet been demonstrated; however, long-lived molecules consisting of locally paired fermions have been reversibly created. Here we report the direct observation of a molecular Bose–Einstein condensate created solely by adjusting the interaction strength in an ultracold Fermi gas of atoms. This state of matter represents one extreme of the predicted BCS–BEC continuum.

Emergence of a molecular Bose-Einstein condensate from a Fermi gas

Hybrid systems of laser-cooled trapped ions and ultracold atoms combined in a single experimental setup have recently emerged as a new platform for fundamental research in quantum physics. This paper reviews the theoretical and experimental progress in research on cold hybrid ion-atom systems which aim to combine the best features of the two well-established fields. A broad overview is provided of the theoretical description of ion-atom mixtures and their applications, and a report is given on advances in experiments with ions trapped in Paul or dipole traps overlapped with a cloud of cold atoms, and with ions directly produced in a Bose-Einstein condensate. This review begins with microscopic models describing the electronic structure, interactions, and collisional physics of ion-atom systems at low and ultralow temperatures, including radiative and nonradiative charge-transfer processes and their control with magnetically tunable Feshbach resonances. Then the relevant experimental techniques and the intrinsic properties of hybrid systems are described. In particular, the impact is discussed of the micromotion of ions in Paul traps on ion-atom hybrid systems. Next, a review of recent proposals is given for using ions immersed in ultracold gases for studying cold collisions, chemistry, many-body physics, quantum simulation, and quantum computation and their experimental realizations. The last part focuses on the formation of molecular ions via spontaneous radiative association, photoassociation, magnetoassociation, and sympathetic cooling. Applications and prospects are discussed of cold molecular ions for cold controlled chemistry and precision spectroscopy.

/pdf/cold-hybrid-ion-atom-systems-3dsxduwczx.pdf

Cold hybrid ion-atom systems

Controlling quantum entanglement between parts of a many-body system is the key to unlocking the power of quantum information processing for applications such as quantum computation, highprecision sensing, and simulation of many-body physics. Spin degrees of freedom of ultracold neutral atoms in their ground electronic state provide a natural platform given their long coherence times and our ability to control them with magneto-optical fields, but creating strong coherent coupling between spins has been challenging. We demonstrate a Rydberg-dressed ground-state blockade that provides a strong tunable interaction energy (∼1 MHz in units of Planck’s constant) between spins of individually trapped cesium atoms. With this interaction we directly produce Bell-state entanglement between two atoms with a fidelity ≥ 81(2)%, excluding atom loss events, and ≥ 60(3)% when loss is included.

Entangling Atomic Spins with a Strong Rydberg-Dressed Interaction

Rydberg atoms immersed in a Bose-Einstein condensate interact with the quantum gas via electron-atom and ion-atom interaction. To suppress the typically dominant electron-neutral interaction, Rydberg states with a principal quantum number up to n=190 are excited from a dense and tightly trapped micron-sized condensate. This allows us to explore a regime where the Rydberg orbit exceeds the size of the atomic sample by far. In this case, a detailed line shape analysis of the Rydberg excitation spectrum provides clear evidence for ion-atom interaction at temperatures well below a microkelvin. Our results may open up ways to enter the quantum regime of ion-atom scattering for the exploration of charged quantum impurities and associated polaron physics.

Ionic Impurity in a Bose-Einstein Condensate at Submicrokelvin Temperatures.

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 for reaching the s-wave collision regime and the trap ground state.

Micromotion-Induced Limit to Atom-Ion Sympathetic Cooling in Paul Traps

We report on the observation of cold collisions between $^{6}\mathrm{Li}$ atoms and ${\mathrm{Yb}}^{+}$ ions. This combination of species has recently been proposed as the most suitable for reaching the quantum limit in hybrid atom-ion systems, due to its large mass ratio. For atoms and ions prepared in the $^{2}S_{1/2}$ ground state, the charge-transfer and association rate is found to be at least ${10}^{3}$ times smaller than the Langevin collision rate. These results confirm the excellent prospects of $^{6}\mathrm{Li}\ensuremath{-}{\mathrm{Yb}}^{+}$ for sympathetic cooling and quantum information applications. For ions prepared in the excited electronic states $^{2}P_{1/2}, ^{2}D_{3/2}$, and $^{2}F_{7/2}$, we find that the reaction rate is dominated by charge transfer and does not depend on the ionic isotope or the collision energy in the range $\ensuremath{\sim}1--120\phantom{\rule{0.16em}{0ex}}\mathrm{mK}$. The low charge-transfer rate for ground-state collisions is corroborated by theory, but the $4f$ shell in the ${\mathrm{Yb}}^{+}$ ion prevents an accurate prediction for the charge-transfer rate of the $^{2}P_{1/2}, ^{2}D_{3/2}$, and $^{2}F_{7/2}$ states. Using ab initio methods of quantum chemistry we calculate the atom-ion interaction potentials up to energies of $30\ifmmode\times\else\texttimes\fi{}{10}^{3}\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$, and use these to give qualitative explanations of the observed rates.

Observation of collisions between cold Li atoms and Yb+ ions

Great advances in precision measurements in the quantum regime have been achieved with trapped ions and atomic gases at the lowest possible temperatures1–3. These successes have inspired ideas to merge the two systems4. In this way, we can study the unique properties of ionic impurities inside a quantum fluid5–12 or explore buffer gas cooling of a trapped-ion quantum computer13. Remarkably, in spite of its importance, experiments with atom–ion mixtures have remained firmly confined to the classical collision regime14. We report a collision energy of 1.15(±0.23) times the s-wave energy (or 9.9(±2.0) μK) for a trapped ytterbium ion in an ultracold lithium gas. We observed a deviation from classical Langevin theory by studying the spin-exchange dynamics, indicating quantum effects in the atom–ion collisions. Our results open up numerous opportunities, such as the exploration of atom–ion Feshbach resonances15,16, in analogy to neutral systems17. Cooling an atom–ion hybrid system and bringing it into the quantum regime is challenging owing to the unavoidable heating caused by atom–ion collisions. Here a new record low is achieved in such a system, and the quantum effect starts to manifest.

Buffer gas cooling of a trapped ion to the quantum regime

We report on the observation of interactions between ultracold Rydberg atoms and ions in a Paul trap. The rate of observed inelastic collisions, which manifest themselves as charge transfer between the Rydberg atoms and ions, exceeds that of Langevin collisions for ground state atoms by about 3 orders of magnitude. This indicates a huge increase in interaction strength. We study the effect of the vacant Paul trap's electric fields on the Rydberg excitation spectra. To quantitatively describe the exhibited shape of the ion loss spectra, we need to include the ion-induced Stark shift on the Rydberg atoms. Furthermore, we demonstrate Rydberg excitation on a dipole-forbidden transition with the aid of the electric field of a single trapped ion. Our results confirm that interactions between ultracold atoms and trapped ions can be controlled by laser coupling to Rydberg states. Adding dynamic Rydberg dressing may allow for the creation of spin-spin interactions between atoms and ions, and the elimination of collisional heating due to ionic micromotion in atom-ion mixtures.

/pdf/observation-of-interactions-between-trapped-ions-and-22zs2942zl.pdf

Observation of Interactions between Trapped Ions and Ultracold Rydberg Atoms.

We report on observations of spin dynamics in single ${\mathrm{Yb}}^{+}$ ions immersed in a cold cloud of spin-polarized $^{6}\mathrm{Li}$ atoms. This species combination has been proposed to be the most suitable system to reach the quantum regime in atom-ion experiments. For $^{174}\mathrm{Yb}^{+}$, we find that the atomic bath polarizes the spin of the ion by 93(4)% after a few Langevin collisions, pointing to strong spin-exchange rates. For the hyperfine ground states of $^{171}\mathrm{Yb}^{+}$, we also find strong rates towards spin polarization. However, relaxation towards the $F=0$ ground state occurs after 7.7(1.5) Langevin collisions. We investigate spin impurity atoms as a possible source of apparent spin-relaxation leading us to interpret the observed spin-relaxation rates as an upper limit. Using ab initio electronic structure and quantum scattering calculations, we explain the observed rates and analyze their implications for the possible observation of Feshbach resonances between atoms and ions once the quantum regime is reached.

/pdf/dynamics-of-a-single-ion-spin-impurity-in-a-spin-polarized-1fhuq34le9.pdf

Dynamics of a single ion-spin impurity in a spin-polarized atomic bath

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)~$\mu$K) for a trapped ytterbium ion in an ultracold lithium gas. We observed a deviation from classical Langevin theory by studying the spin-exchange dynamics, indicating quantum behavior in the atom-ion collisions. Our results open up numerous opportunities, such as the exploration of atom-ion Feshbach resonances, in analogy to neutral systems.

N. V. Ewald

Papers

Observation of collisions between cold Li atoms and Yb+ ions

Buffer gas cooling of a trapped ion to the quantum regime

Observation of Interactions between Trapped Ions and Ultracold Rydberg Atoms.

Dynamics of a single ion-spin impurity in a spin-polarized atomic bath

Buffer gas cooling of a trapped ion to the quantum regime