Quantum motion of three trapped ions in one dimension

Shi‐Biao Zheng

B. Kneer, C. K. Law

We present a scheme that deterministically generates an arbitrary prescribed quantum entangled state of a trapped ion. The quantum entanglement is between the external (center-of-mass motion in one dimension) and the internal (electronic) state of the trapped ion. We examine the influence of technical errors in our scheme. Further we show how to entangle the center-of-mass motion of the confined ion in two dimensions.

Jiaju Yin

Jiaju Yin, Juha Javanainen

We develop models for the motion of two trapped ions in one dimension, including both harmonic trapping forces and the Coulomb interaction between the ions. Mathematical and physical consistency dictates that the divergence of the Coulomb interaction at small distances be tempered with a soft core. A split-operator method is used to analyze numerically the energies and eigenstates of the motion of the two ions. Classification and closed-form expressions are also presented for the energies and the eigenstates in the limits when the equilibrium distance due to the Coulomb repulsion is either much smaller or much larger than the amplitude of the zero-point motion of the ions. Implications of the results for the properties of two identical ions with Bose-Einstein or Fermi-Dirac statistics are discussed.

Jonathan Magnolia Gilligan, Christopher R. Monroe, David J. Wineland

We report on development of a miniature linear rf ion trap and preliminary efforts to trap and laser-cool {sup 24}Mg{sup +} ions. This trap has a radial dimension of 50 {mu}m, one tenth the size of our previous trap. The rms confinement of a trapped ion scales as R{sup -2}, where R is the trap radius, so tight confinement of ions is possible at a modest rf voltage. Although the three-dimensional trapping potential for our trap cannot be calculated analytically, it can be described in terms of dimensionless parameters, measured by studying macroscopic charged particles in a much larger model of the trap. We expect that with this trap it will be possible to achieve secular frequencies high enough for resolved-sideband cooling of light ions using allowed dipole transitions. This will make it much easier to perform experiments on the quantum motion of trapped ions. This trap uses a two-wire design rather than the more common four-wire one, so the trap electrodes occlude a much smaller solid angle than either a four-wire linear trap or the more common quadrupole trap. Thus, it will be possible to couple optical devices, such as high-finesse cavities, much more efficiently to trapped ions.

Pan‐Yu Hou