On the Transport of Atomic Ions in Linear and Multidimensional Ion Trap Arrays

Trapped atomic ions have become one of the most promising architectures for a quantum computer, and current effort is now devoted to the transport of trapped ions through complex segmented ion trap structures in order to scale up to much larger numbers of trapped ion qubits. This paper covers several important issues relevant to ion transport in any type of complex multidimensional rf (Paul) ion trap array. We develop a general theoretical framework for the application of time-dependent electric fields to shuttle laser-cooled ions along any desired trajectory, and describe a method for determining the effect of arbitrary shuttling schedules on the quantum state of trapped ion motion. In addition to the general case of linear shuttling over short distances, we introduce issues particular to the shuttling through multidimensional junctions, which are required for the arbitrary control of the positions of large arrays of trapped ions. This includes the transport of ions around a corner, through a cross or T junction, and the swapping of positions of multiple ions in a laser-cooled crystal. Where possible, we make connections to recent experimental results in a multidimensional T junction trap, where arbitrary 2-dimensional transport was realized.