We present a study of dynamical decoupling schemes for the suppression of phase errors from various noise
environments using ions in a Penning trap as a model ensemble of qubits. By injecting frequency noise we
demonstrate that in an ohmic noise spectrum with a sharp, high-frequency cutoff the recently proposed UDD
decoupling sequence gives noise suppression superior to the traditional CPMG technique. Under only the influence
of ambient magnetic field fluctuations with a 1/ω<sup>4</sup> power spectrum, we find little benefit from using the
UDD sequence, consistent with theoretical predictions for dynamical decoupling performance in the presence of
noise spectra with soft cutoffs. Finally, we implement an optimization algorithm using measurement feedback,
demonstrating that local optimization of dynamical decoupling can further lead to significant gains in error
suppression over known sequences.
Single-trapped-ion frequency standards based on a 282 nm transition in <sup>199</sup>Hg+ and on a 267 nm transition in
<sup>27</sup>Al<sup>+</sup> have been developed at NIST over the past several years. Their frequencies are measured relative to each
other and to the NIST primary frequency standard, the NIST-F1 cesium fountain, by means of a self-referenced
femtosecond laser frequency comb. Both ion standards have demonstrated instabilities and inaccuracies of less
than 1 × 10<sup>-16</sup>.
Atomic ions confined in segmented trap arrays provide a system for quantum information processing. We
report on the execution of two simple quantum algorithms, quantum error correction and the quantum Fourier
transform, using this implementation. The demonstration of these algorithms in a scalable system is one step
towards the execution of useful, large-scale quantum algorithms.
Using a laser that is frequency-locked to a Fabry-Perot etalon of high finesse and stability, we probed the 5d<SUP>10</SUP>6s <SUP>2</SUP>S<SUB>1/2</SUB>(F equals O, m<SUB>F</SUB> equals O) $ARLR 5d<SUP>9</SUP>6s<SUP>2</SUP> <SUP>2</SUP>D<SUB>5/2</SUB> (F equals 2, m<SUB>F</SUB> equals O) electric-quadrupole transition of a single laser-cooled <SUP>199</SUP>Hg<SUP>+</SUP> ion stored in a cryogenic radio-frequency ion trap. We observed Fourier-transform limited linewidths as narrow as 6.7 Hz at 282 nm (1.06 X 10<SUP>15</SUP> Hz). The functional form and estimated values of some of the frequency shifts of the <SUP>2</SUP>S<SUB>1/2</SUB> $ARLR <SUP>2</SUP>D<SUB>5/2</SUB> clock transition (including the quadrupole shift), which have been calculated using a combination of measured atomic parameters and ab initio calculations, are given.
We discuss frequency standards based on laser-cooled <SUP>199</SUP>Hg<SUP>+</SUP> ions confined in cryogenic rf traps. In one experiment, the frequency of a microwave source is served to the ions' ground-state hyperfine transition at 40.5 GHz. For seven ions and a Ramsey free precession time of 100 s, the fractional frequency stability is 3.3 (2) X 10<SUP>-13</SUP> (tau) <SUP>-1/2</SUP> for measurement times (tau) < 2 h. The ground-state hyperfine interval is measured to be 40 507 347 996.841 59 (14) (41) Hz, where the first number in parentheses is the uncertainty due to statistics and systematic errors, and the second is the uncertainty in the frequency of the time scale to which the standard is compared. In a second experiment under development, a strong-binding cryogenic trap will confine a single ion used for an optical frequency standard based on a narrow electric quadrupole transition at 282 nm. The bandwidth of the laser used to drive this transition is less than 10 Hz at 563 nm.
A miniature, elliptical ring rf ion trap has been sued in recent experiments toward realizing a quantum computer in a trapped ion system. With the combination of small spatial dimensions and high rf drive potentials, around 500 V amplitude, we have achieved secular oscillation frequencies in the range of 5-20 MHz. The equilibrium positions of pairs of ions that are crystallized in this trap lie along the long axis of the ellipse. By adding a static potential to the trap, the micromotion of two crystallized ions may be reduced relative to the case of pure rf confinement. The presence of micromotion reduces the strength of internal transitions in the ion, an effect that is characterized by a Debye-Waller factor, in analogy with the reduction of Bragg scattering at finite temperature in a crystal lattice. We have demonstrated the dependence of the rates of internal transitions on the amplitude of micromotion, and we propose a scheme to use this effect to differentially address the ions.
We laser-cool single beryllium ions in a Paul trap to the ground (n equals 0) quantum harmonic oscillator state with greater than 90% probability. From this starting point, we can put the atom into various quantum states of motion by application of optical and rf electric fields. Some of these states resemble classical states (the coherent states), while others are intrinsically quantum, such as number states or squeezed states. We have created entangled position and spin superposition states (Schrodinger cat states), where the atom's spatial wavefunction is split into two widely separated wave packets. We have developed methods to reconstruct the density matrices and Wigner functions of arbitrary motional quantum states. These methods should make it possible to study decoherence of quantum superposition states and the transition from quantum to classical behavior. Calculations of the decoherence of superpositions of coherent states are presented.
Spectroscopy of ions in electromagnetic traps using laser-cooling and detection has reached a sensitivity where it is now possible to unambiguously monitor state changes in a single ion. While these techniques may not be generally applicable, the sensitivity and precision that is obtained for laser-cooled ions give broad opportunities for experiments in many areas of fundamental physics and-high resolution spectroscopy. In this paper, the authors describe two experiments with a single laser-cooled Hg+ ion. In one they achieve the highest fractional resolution (highest Q) in atomic or molecular spectroscopy, and in the second they cool the ion to its zero-point energy.