We present a simple Paul trap that stably accommodates up to a couple of
dozens of \ensuremath{^{171}\mathrm{Yb}^+~} ions in a stationary
two-dimensional lattice. The trap is constructed on a single plate of
gold-plated laser-machined alumina and can produce a pancake-like
pseudo-potential that makes ions form a self-assembly two-dimensional crystal
which locates on the plane composed of axial and one of the transverse axes
with around 5 μm spacing. We use Raman laser beams to coherently manipulate
these ion-qubits where the net propagation direction is perpendicular to the
plane of the crystal and micromotion. We perform the coherent operations and
study the spectrum of vibrational modes through globally addressed Raman
laser-beams on a dozen of ions in the two-dimensional crystal. We measure the
amplitude of micro-motion by comparing the strengths of carrier and
micro-motion sideband transitions with three ions, where the micro-motion
amplitude is similar to that of a single ion. The spacings of ions are small
enough for large coupling strengths, which is a favorable condition for
two-dimensional quantum simulation.Comment: 10 pages, 9 figure