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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.
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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. Holtkemeier et al., Phys. Rev. Lett. 116, 233003 (2016)]. By transforming the collisional processes into a frame, where the ions micromotion is assigned to the buffer gas atoms, our model allows one to investigate the influence of non-homogeneous 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 ions energy distribution in equilibrium. We provide analytic expressions and numerical simulations of the ions energy distribution, spatial profile and cooling rates for these different regimes. Based on these findings, a method for actively decreasing the ions energy by reducing the spatial expansion of the buffer gas arises (Forced Sympathetic Cooling).
We demonstrate ground-state cooling of a trapped ion using radio-frequency (RF) radiation. This is a powerful tool for the implementation of quantum operations, where RF or microwave radiation instead of lasers is used for motional quantum state engineering. We measure a mean phonon number of $overline{n} = 0.13(4)$ after sideband cooling, corresponding to a ground-state occupation probability of 88(7)%. After preparing in the vibrational ground state, we demonstrate motional state engineering by driving Rabi oscillations between the n=0 and n=1 Fock states. We also use the ability to ground-state cool to accurately measure the motional heating rate and report a reduction by almost two orders of magnitude compared to our previously measured result, which we attribute to carefully eliminating sources of electrical noise in the system.
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 sympathethic cooling times before crystallization occurs. Our key result is a new technique for detecting the loading of an initially hot ion with energy in the eV range by monitoring the motional state of a Doppler-cooled ion already present in the trap. This technique not only detects the ion but also provides information about dynamics of the sympathetic cooling process.
Trapped ion in the Lamb-Dicke regime with the Lamb-Dicke parameter $etall1$ can be cooled down to its motional ground state using sideband cooling. Standard sideband cooling works in the weak sideband coupling limit, where the sideband coupling strength is small compared to the natural linewidth $gamma$ of the internal excited state, with a cooling rate much less than $gamma$. Here we consider cooling schemes in the strong sideband coupling regime, where the sideband coupling strength is comparable or even greater than $gamma$. We derive analytic expressions for the cooling rate and the average occupation of the motional steady state in this regime, based on which we show that one can reach a cooling rate which is proportional to $gamma$, while at the same time the steady state occupation increases by a correction term proportional to $eta^{2}$ compared to the weak sideband coupling limit. We demonstrate with numerical simulations that our analytic expressions faithfully recover the exact dynamics in the strong sideband coupling regime.
Modern computation relies crucially on modular architectures, breaking a complex algorithm into self-contained subroutines. A client can then call upon a remote server to implement parts of the computation independently via an application programming interface (API). Present APIs relay only classical information. Here we implement a quantum API that enables a client to estimate the absolute value of the trace of a server-provided unitary $U$. We demonstrate that the algorithm functions correctly irrespective of what unitary $U$ the server implements or how the server specifically realizes $U$. Our experiment involves pioneering techniques to coherently swap qubits encoded within the motional states of a trapped Yb ion, controlled on its hyperfine state. This constitutes the first demonstration of modular computation in the quantum regime, providing a step towards scalable, parallelization of quantum computation.
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