Rf Paul Trap Research Articles

Prospects of a thousand-ion Sn2+ Coulomb-crystal clock with sub-10−19 inaccuracy

Optical atomic clocks are the most accurate and precise measurement devices of any kind, enabling advances in international timekeeping, Earth science, fundamental physics, and more. However, there is a fundamental tradeoff between accuracy and precision, where higher precision is achieved by using more atoms, but this comes at the cost of larger interactions between the atoms that limit the accuracy. Here, we propose a many-ion optical atomic clock based on three-dimensional Coulomb crystals of order one thousand Sn2+ ions confined in a linear RF Paul trap with the potential to overcome this limitation. Sn2+ has a unique combination of features that is not available in previously considered ions: a 1S0 ↔ 3P0 clock transition between two states with zero electronic and nuclear angular momentum (I = J = F = 0) making it immune to nonscalar perturbations, a negative differential polarizability making it possible to operate the trap in a manner such that the two dominant shifts for three-dimensional ion crystals cancel each other, and a laser-accessible transition suitable for direct laser cooling and state readout. We present calculations of the differential polarizability, other relevant atomic properties, and the motion of ions in large Coulomb crystals, in order to estimate the achievable accuracy and precision of Sn2+ Coulomb-crystal clocks.

Effects of an Oscillating Electric Field on and Dipole Moment Measurement of a Single Molecular Ion.

We characterize and model the Stark effect due to the radio-frequency (rf) electric field experienced by a molecular ion in an rf Paul trap, a leading systematic in the uncertainty of the field-free rotational transition. The ion is deliberately displaced to sample different known rf electric fields and measure the resultant shifts in transition frequencies. With this method, we determine the permanent electric dipole moment of CaH^{+}, and find close agreement with theory. The characterization is performed by using a frequency comb which probes rotational transitions in the molecular ion. With improved coherence of the comb laser, a fractional statistical uncertainty for a transition line center of as low as 4.6×10^{-13} was achieved.

Transport of Multispecies Ion Crystals through a Junction in a Radio-Frequency Paul Trap.

We report on the first demonstration of transport of a multispecies ion crystal through a junction in a rf Paul trap. The trap is a two-dimensional surface-electrode trap with an X junction and segmented control electrodes to which time-varying voltages are applied to control the shape and position of potential wells above the trap surface. We transport either a single ^{171}Yb^{+} ion or a crystal composed of a ^{138}Ba^{+} ion cotrapped with the ^{171}Yb^{+} ion to any port of the junction. We characterize the motional excitation by performing multiple round-trips through the junction and back to the initial well position without cooling. The final excitation is then measured using sideband asymmetry. For a single ^{171}Yb^{+} ion, transport with a 4 m/s average speed induces between 0.013±0.001 and 0.014±0.001 quanta of excitation per round-trip, depending on the exit port. For a Ba-Yb crystal, transport at the same speed induces between 0.013±0.001 and 0.030±0.002 quanta per round-trip of excitation to the in-phase axial mode. Excitation in the out-of-phase axial mode ranges from 0.005±0.001 to 0.021±0.001 quanta per round-trip.

Resolved-sideband micromotion sensing in Yb+ on the 935 nm repump transition

Ions displaced from the potential minimum in an RF Paul trap exhibit excess micromotion. A host of well-established techniques are routinely used to sense (and null) this excessive motion in applications ranging from quantum computing to atomic clocks. The rich atomic structure of Yb+, a heavy ion, includes low-lying 2D3/2 states that must be repumped to permit Doppler cooling, typically using a 935 nm laser coupled to the 3D[3/2]1/2 states. In this article, we demonstrate the use of this transition to make resolved-sideband measurements of 3D micromotion in 172Yb+ and 171Yb+ ions. Relative to other sensing techniques, our approach has very low technical overhead and is distinctively compatible with surface-electrode ion traps.

High-accuracy determination of Paul-trap stability parameters for electric-quadrupole-shift prediction

The motion of an ion in a radiofrequency (rf) Paul trap is described by the Mathieu equation and the associated stability parameters that are proportional to the rf and dc electric field gradients. Here, a higher-order, iterative method to accurately solve the stability parameters from measured secular frequencies is presented. It is then used to characterize an endcap trap by showing that the trap’s radial asymmetry is dominated by the dc field gradients and by measuring the relation between the applied voltages and the gradients. The results are shown to be in good agreement with an electrostatic finite-element-method simulation of the trap. Furthermore, a method to determine the direction of the radial trap axes using a “tickler” voltage is presented, and the temperature dependence of the rf voltage is discussed. As an application for optical ion clocks, the method is used to predict and minimize the electric quadrupole shift (EQS) using the applied dc voltages. Finally, a lower limit of 1070 for the cancellation factor of the Zeeman-averaging EQS cancellation method is determined in an interleaved low-/high-EQS clock measurement. This reduces the EQS uncertainty of our 88Sr+ optical clock to ≲1×10−19 in fractional frequency units.

Motional heating of spatially extended ion crystals

We study heating of motional modes of a single ion and of extended ion crystals trapped in a linear radio frequency (rf) Paul trap with a precision of phonons s−1. Single-ion axial and radial heating rates are consistent and electric field noise has been stable over the course of four years. At a secular frequency of ω sec = 2π × 620 kHz, we measure phonons s−1 per ion for the center-of-mass (com) mode of linear chains of up to 11 ions and observe no significant heating of the out-of-phase (oop) modes. By displacing the ions away from the nodal line, inducing excess micromotion, rf noise heats the com mode quadratically as a function of radial displacement r by phonons s−1 μm−2 per ion, while the oop modes are protected from rf-noise induced heating in linear chains. By changing the quality factor of the resonant rf circuit from Q = 542 to Q = 204, we observe an increase of rf noise by a factor of up to 3. We show that the rf-noise induced heating of motional modes of extended crystals also depends on the symmetry of the crystal and of the mode itself. As an example, we consider several 2D and 3D crystal configurations. Heating rates of up to 500 ph s−1 are observed for individual modes, giving rise to a total kinetic energy increase and thus a fractional time dilation shift of up to −0.3 × 10−18 s−1 of the total system. In addition, we detail how the excitation probability of the individual ions is reduced and decoherence is increased due to the Debye–Waller effect.

Loading a linear Paul trap to saturation from a magneto-optical trap

We present experimental measurements of the steady-state ion number in a linear Paul trap (LPT) as a function of the ion-loading rate. These measurements, taken with (a) constant Paul trap stability parameter $q$, (b) constant radio-frequency (rf) amplitude, or (c) constant rf frequency, show nonlinear behavior. At the loading rates achieved in this experiment, a plot of the steady-state ion number as a function of loading rate has two regions: a monotonic rise (region I) followed by a plateau (region II). Also described are simulations and analytical theory which match the experimental results. Region I is caused by rf heating and is fundamentally due to the time dependence of the rf Paul-trap forces. We show that the time-independent pseudopotential, frequently used in the analytical investigation of trapping experiments, cannot explain region I, but explains the plateau in region II and can be used to predict the steady-state ion number in that region. An important feature of our experimental LPT is the existence of a radial cut-off $\hat R_{\rm cut}$ that limits the ion capacity of our LPT and features prominently in the analytical and numerical analysis of our LPT-loading results. We explain the dynamical origin of $\hat R_{\rm cut}$ and relate it to the chaos border of the fractal of non-escaping trajectories in our LPT. We also present an improved model of LPT ion-loading as a function of time.

Active stabilization of ion trap radiofrequency potentials.

We actively stabilize the harmonic oscillation frequency of a laser-cooled atomic ion confined in a radiofrequency (rf) Paul trap by sampling and rectifying the high voltage rf applied to the trap electrodes. We are able to stabilize the 1 MHz atomic oscillation frequency to be better than 10 Hz or 10 ppm. This represents a suppression of ambient noise on the rf circuit by 34 dB. This technique could impact the sensitivity of ion trap mass spectrometry and the fidelity of quantum operations in ion trap quantum information applications.

Ion–neutral-atom sympathetic cooling in a hybrid linear rf Paul and magneto-optical trap

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 heating mechanisms on the hybrid system and how parameters related to the MOT, Paul trap, number of ions, and ion species affect the efficiency of the sympathetic cooling.

Absorption imaging of a single atom

Absorption imaging has played a key role in the advancement of science from van Leeuwenhoek's discovery of red blood cells to modern observations of dust clouds in stellar nebulas and Bose-Einstein condensates. Here we show the first absorption imaging of a single atom isolated in a vacuum. The optical properties of atoms are thoroughly understood, so a single atom is an ideal system for testing the limits of absorption imaging. A single atomic ion was confined in an RF Paul trap and the absorption imaged at near wavelength resolution with a phase Fresnel lens. The observed image contrast of 3.1 (3)% is the maximum theoretically allowed for the imaging resolution of our set-up. The absorption of photons by single atoms is of immediate interest for quantum information processing. Our results also point out new opportunities in imaging of light-sensitive samples both in the optical and X-ray regimes.

Quantum control of 88Sr+ in a miniature linear Paul trap

We report on the construction and characterization of an apparatus for quantum information experiments using 88Sr+ ions. A miniature linear radio-frequency (rf) Paul trap was designed and built. Trap frequencies above 1 MHz in all directions are obtained with 50 V on the trap end-caps and less than 1 W of rf power. We encode a quantum bit (qubit) in the two spin states of the S 1/2 electronic ground-state of the ion. We constructed all the necessary laser sources for laser cooling and full coherent manipulation of the ions’ external and internal states. Oscillating magnetic fields are used for coherent spin rotations. High-fidelity readout as well as a coherence time of 2.5 ms are demonstrated. Following resolved sideband cooling the average axial vibrational quanta of a single trapped ion is $\bar{n}=0.05$ and a heating rate of $\dot{\bar{n}}=0.016~\mathrm{ms}^{-1}$ is measured.

A bead on a hoop rotating about a horizontal axis: A one-dimensional ponderomotive trap

We describe a simple mechanical system that operates as a ponderomotive particle trap. The system consists of a circular hoop and a frictionless bead, with the hoop rotating about a horizontal axis lying in the plane of the hoop. The system is analyzed in the ideal case of small displacements from the minimum, and the motion of the particle is shown to satisfy the Mathieu equation. If the axis of rotation is tangential to the hoop, the system is an exact analog to the rf Paul ion trap. Various complicating factors such as anharmonic terms, friction, and noise are considered. A working model of the system was constructed using a ball-bearing rolling in a tube along the outside of a bicycle rim. The apparatus demonstrates the operation of an rf Paul trap by reproducing the dynamics of trapped atomic ions and illustrating the manner in which the electric potential varies with time.

Multiply Charged Thorium Crystals for Nuclear Laser Spectroscopy

We have produced laser-cooled crystals of 232Th3+ in a linear rf Paul trap. This is the first time that a multiply charged ion has been laser cooled. Our work opens an avenue for excitation of the nuclear transition in a trapped, cold 229Th3+ ion. Laser excitation of nuclear states would establish a new bridge between atomic and nuclear physics, with the promise of new levels of metrological precision.

Observation of Three-Dimensional Long-Range Order in Small Ion Coulomb Crystals in an rf Trap

Three-dimensional long-range ordered structures in smaller and near-spherically symmetric Coulomb crystals of (40)Ca(+) ions confined in a linear rf Paul trap have been observed when the number of ions exceeds approximately 1,000 ions. This result is unexpected from ground state molecular dynamics (MD) simulations, but found to be in agreement with MD simulations of metastable ion configurations. Previously, three-dimensional long-range ordered structures have only been reported in Penning traps in systems of approximately 50,000 ions or more.

Optical frequency standards and measurements

We describe the performance characteristics and frequency measurements of two high-accuracy high-stability laser-cooled atomic frequency standards. One is a 657-nm (456-THz) reference using magneto-optically trapped Ca atoms, and the other is a 282-nm (1064-THz) reference based on a single Hg/sup +/ ion confined in an RF-Paul trap. A femtosecond mode-locked laser combined with a nonlinear microstructure fiber produces a broad and stable comb of optical modes that is used to measure the frequencies of the reference lasers locked to the atomic standards. The measurement system is referenced to the primary frequency standard NIST F-1, a Cs atomic fountain clock. Both optical standards demonstrate exceptional short-term instability (/spl ap/5/spl times/10/sup -15/ at 1 s), as well as excellent reproducibility over time. In light of our expectations for the future of optical frequency standards, we consider the present performance of the femtosecond optical frequency comb, along with its limitations and future requirements.

Sub-kHz “clock” transition linewidths in a cold trapped 88Sr + ion in low magnetic fields using 1092-nm polarisation switching

A small RF (Paul) trap has been developed, which allows Lamb–Dicke confinement of a single strontium ion. This paper describes the trap and the diagnostics used to verify Lamb–Dicke confinement. In particular, it is necessary to operate in a near zero magnetic field, so that the Zeeman splitting is minimised. In such low magnetic fields, the ion fluorescence at the 2S 1/2– 2P 1/2 cooling wavelength at 422 nm normally falls to zero. This arises from optical pumping into some of the Zeeman sub-levels of the 2D 3/2 state, which occurs because the laser which drives the 1092 nm transition ( 2P 1/2– 2D 3/2) has a fixed polarisation state. However, if the polarisation state of this laser is rapidly switched, the fluorescence is recovered. A scan over the strontium ion 2S 1/2– 2D 5/2 quadrupole transition shows only the carrier and sidebands corresponding to the radial and axial secular frequencies. Short range high resolution scans over a part of the carrier reveal Zeeman structure with ≤1 kHz-linewidth features.

All-diode-laser cooling of single Ca+ ions

ions. The Ca+ ions are trapped in a miniature rf Paul trap and irradiated by light from a frequency-doubled diode laser at 397 nm and by light from a diode laser at 866 nm. We are able to cool a single ion and observe its fluorescence continuously with the laser diode locked to the external frequency-doubling cavity. Quantum jumps in the fluorescence light of a single ion and of a small cloud of five ions have been induced by driving the “clock” transition at 729 nm. We were able to resolve the influence of the micromotion on the excitation spectrum of the small ion cloud.

Experimental preparation and measurement of quantum states of motion of a trapped atom

Abstract We report the creation and full determination of several quantum states of motion of a 9Be+ ion bound in a RF (Paul) trap. The states are coherently prepared from an ion which has been initially laser cooled to the zero-point of motion. We create states having both classical and non-classical character including thermal, number, coherent, squeezed, and ‚Schrödinger cat‘ states. The motional quantum state is fully reconstructed using two novel schemes that determine the density matrix in the number state basis or the Wigner function. Our techniques allow well controlled experiments decoherence and related phenomena on the quantum-classical borderline.

Experimental preparation and measurement of quantum states of motion of a trapped atom

We report the creation and full determination of several quantum states of motion of a 9Be+ ion bound in a RF (Paul) trap. The states are coherently prepared from an ion which has been initially laser cooled to the zero-point of motion. We create states having both classical and non-classical character including thermal, number, coherent, squeezed, and ‚Schrödinger cat’ states. The motional quantum state is fully reconstructed using two novel schemes that determine the density matrix in the number state basis or the Wigner function. Our techniques allow well controlled experiments decoherence and related phenomena on the quantum-classical borderline.

Charge exchange and cluster formation in an rf Paul trap: interaction of alkali atoms with C +60

A Paul ion trap was used to study the formation of clusters under controlled temperature and pressure conditions. Exposure of cold C + 60 ions to Li flux leads to the formation of Li n C + 60 clusters ( n = 1–18) occurring by the sequential association of Li atoms. Cluster formation dependence on He pressure displayed a competition between vibrational relaxation and unimolecular dissociation. Collisions with Na, K, Rb and Cs atoms resulted in dissociative charge exchange. Decay rates of C + 60 ions resulting from these low-energy charge exchange collisions were consistent with Langevin capture rates.