Kilian Singer

Suppression of Excitation and Spectral Broadening Induced by Interactions in a Cold Gas of Rydberg Atoms

We report on the observation of ultralong range interactions in a gas of cold rubidium Rydberg atoms. The van der Waals interaction between a pair of Rydberg atoms separated as far as 100,000 Bohr radii features two important effects: spectral broadening of the resonance lines and suppression of excitation with increasing density. The density dependence of these effects is investigated in detail for the S- and P-Rydberg states with principal quantum numbers n approximately 60 and n approximately 80 excited by narrow-band continuous-wave laser light. The density-dependent suppression of excitation can be interpreted as the onset of an interaction-induced local blockade.

A single atom heat engine

Making a teeny tiny engine Steam locomotives, cars, and the drinking bird toy all convert heat into useful work as it cycles between two reservoirs at different temperatures. Usually, the working substance where the heat-work conversion occurs is a liquid or a gas, consisting of many molecules. Roβnagel et al. have made a working substance of a single calcium ion in a tapered ion trap. A laser-cooling beam plays the part of a cold reservoir for the calcium ion, and in turn, electric field noise acts as a hot reservoir. Science, this issue p. 325 A calcium ion held in a tapered trap is used as the working substance of a tiny thermodynamic engine. Heat engines convert thermal energy into mechanical work and generally involve a large number of particles. We report the experimental realization of a single-atom heat engine. An ion is confined in a linear Paul trap with tapered geometry and driven thermally by coupling it alternately to hot and cold reservoirs. The output power of the engine is used to drive a harmonic oscillation. From direct measurements of the ion dynamics, we were able to determine the thermodynamic cycles for various temperature differences of the reservoirs. We then used these cycles to evaluate the power P and efficiency η of the engine, obtaining values up to P = 3.4 × 10–22 joules per second and η = 0.28%, consistent with analytical estimations. Our results demonstrate that thermal machines can be reduced to the limit of single atoms.

Controlling Fast Transport of Cold Trapped Ions

We realize fast transport of ions in a segmented microstructured Paul trap. The ion is shuttled over a distance of more than 10(4) times its ground state wave function size during only five motional cycles of the trap (280 μm in 3.6 μs). Starting from a ground-state-cooled ion, we find an optimized transport such that the energy increase is as low as 0.10±0.01 motional quanta. In addition, we demonstrate that quantum information stored in a spin-motion entangled state is preserved throughout the transport. Shuttling operations are concatenated, as a proof-of-principle for the shuttling-based architecture to scalable ion trap quantum computing.

Single-Ion Heat Engine at Maximum Power

O. Abah, J. Roßnagel, G. Jacob, S. Deffner, 3 F. Schmidt-Kaler, K. Singer, and E. Lutz 4 Department of Physics, University of Augsburg, D-86159 Augsburg, Germany Institut für Quantenphysik, Universität Mainz, 55128 Mainz, Germany Department of Chemistry and Biochemistry and Institute for Physical Sciences and Technology, University of Maryland, College Park, MD 20742, USA Dahlem Center for Complex Quantum Systems, FU Berlin, D-14195 Berlin, Germany

Observation of the Kibble–Zurek scaling law for defect formation in ion crystals

Traversal of a symmetry-breaking phase transition at finite rates can lead to causally separated regions with incompatible symmetries and the formation of defects at their boundaries, which has a crucial role in quantum and statistical mechanics, cosmology and condensed matter physics. This mechanism is conjectured to follow universal scaling laws prescribed by the Kibble-Zurek mechanism. Here we determine the scaling law for defect formation in a crystal of 16 laser-cooled trapped ions, which are conducive to the precise control of structural phases and the detection of defects. The experiment reveals an exponential scaling of defect formation γ(β), where γ is the rate of traversal of the critical point and β=2.68±0.06. This supports the prediction of β=8/3≈2.67 for finite inhomogeneous systems. Our result demonstrates that the scaling laws also apply in the mesoscopic regime and emphasizes the potential for further tests of non-equilibrium thermodynamics with ion crystals.

Long-range interactions between alkali Rydberg atom pairs correlated to the ns–ns, np–np and nd–nd asymptotes

We have calculated the long-range interaction potential curves of highly excited Rydberg atom pairs for the combinations Li–Li, Na–Na, K–K, Rb–Rb and Cs–Cs in a perturbative approach. The dispersion C-coefficients are determined for all symmetries of molecular states that correlate to the ns–ns, np–np and nd–nd asymptotes. Fitted parameters are given for the scaling of the C-coefficients as a function of the principal quantum number n for all homonuclear pairs of alkali metal atoms.

Sympathetic cooling with two atomic species in an optical trap

We simultaneously trap ultracold lithium and cesium atoms in an optical dipole trap formed by the focus of a CO2 laser and study the exchange of thermal energy between the gases. The optically cooled cesium gas efficiently decreases the temperature of the lithium gas through sympathetic cooling. Equilibrium temperatures down to 25 microK have been reached. The measured cross section for thermalizing 133Cs-7Li collisions is 8 x 10(-12) cm(2), for both species unpolarized in their lowest hyperfine ground state. Besides thermalization, we observe evaporation of lithium purely through elastic cesium-lithium collisions (sympathetic evaporation).

Colloquium: Trapped ions as quantum bits: Essential numerical tools

Trapped, laser-cooled atoms and ions are quantum systems which can be experimentally controlled with an as yet unmatched degree of precision. Due to the control of the motion and the internal degrees of freedom, these quantum systems can be adequately described by a well known Hamiltonian. In this colloquium, we present powerful numerical tools for the optimization of the external control of the motional and internal states of trapped neutral atoms, explicitly applied to the case of trapped laser-cooled ions in a segmented ion-trap. We then delve into solving inverse problems, when optimizing trapping potentials for ions. Our presentation is complemented by a quantum mechanical treatment of the wavepacket dynamics of a trapped ion. Efficient numerical solvers for both time-independent and time-dependent problems are provided. Shaping the motional wavefunctions and optimizing a quantum gate is realized by the application of quantum optimal control techniques. The numerical methods presented can also be used to gain an intuitive understanding of quantum experiments with trapped ions by performing virtual simulated experiments on a personal computer. Code and executables are supplied as supplementary online material (this http URL).

Optimization of segmented linear Paul traps and transport of stored particles

Single ions held in linear Paul traps are promising candidates for a future quantum computer. Here, we discuss a two-layer microstructured segmented linear ion trap. The radial and axial potentials are obtained from numeric field simulations and the geometry of the trap is optimized. As the trap electrodes are segmented in the axial direction, the trap allows the transport of ions between different spatial regions. Starting with realistic numerically obtained axial potentials, we optimize the transport of an ion such that the motional degrees of freedom are not excited, even though the transport speed far exceeds the adiabatic regime. In our optimization we achieve a transport within roughly two oscillation periods in the axial trap potential compared to typical adiabatic transports that take of the order 102 oscillations. Furthermore heating due to quantum mechanical effects is estimated and suppression strategies are proposed.

Deterministic Ultracold Ion Source Targeting the Heisenberg Limit

The major challenges to fabricate quantum processors and future nano-solid-state devices are material modification techniques with nanometer resolution and suppression of statistical fluctuations of dopants or qubit carriers. Based on a segmented ion trap with mK laser-cooled ions we have realized a deterministic single-ion source which could operate with a huge range of sympathetically cooled ion species, isotopes or ionic molecules. We have deterministically extracted a predetermined number of ions on demand and have measured a longitudinal velocity uncertainty of 6.3 m/s and a spatial beam divergence of 600 microrad. We show in numerical simulations that if the ions are cooled to the motional ground state (Heisenberg limit) nanometer spatial resolution can be achieved.