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.
We experimentally study two-dimensional (2D) Coulomb crystals in the "radial-2D" phase of a linear Paul trap. This phase is identified by a 2D ion lattice aligned entirely with the radial plane and is created by imposing a large ratio of axial to radial trapping potentials. Using arrays of up to 19 ^{171}Yb^{+} ions, we demonstrate that the structural phase boundaries of such crystals are well described by the pseudopotential approximation, despite the time-dependent ion positions driven by intrinsic micromotion. We further observe that micromotion-induced heating of the radial-2D crystal is confined to the radial plane. Finally, we verify that the transverse motional modes, which are used in most ion-trap quantum simulation schemes, are well-predictable numerically and remain decoupled and cold in this geometry. Our results establish radial-2D ion crystals as a robust experimental platform for realizing a variety of theoretical proposals in quantum simulation and computation.
We have developed a trapped ion system for producing two-dimensional (2D) ion crystals for applications in scalable quantum computing, quantum simulations, and 2D crystal phase transition and defect studies. The trap is a modification of a Paul trap with its ring electrode flattened and split into eight identical sectors and its two endcap electrodes shaped as truncated hollow cones for laser and imaging optics access. All ten trap electrodes can be independently DC-biased to create various aspect ratio trap geometries. We trap and Doppler cool 2D crystals of up to 30 Ba+ ions and demonstrate the tunability of the trapping potential both in the plane of the crystal and in the transverse direction.
We propose a scheme to realize scalable quantum computation in a planar ion crystal confined by a Paul trap. We show that the inevitable in-plane micromotion affects the gate design via three separate effects: renormalization of the equilibrium positions, coupling to the transverse motional modes, and amplitude modulation in the addressing beam. We demonstrate that all of these effects can be taken into account and high-fidelity gates are possible in the presence of micromotion. This proposal opens the prospect to realize large-scale fault-tolerant quantum computation within a single Paul trap.
A Coulomb crystal formed in a linear Paul trap by Doppler cooling with a single axial laser often shows undesired oscillatory behavior in the direction perpendicular to the trap axis. This transverse oscillation is found to include two distinct coherent motions; in addition to the well-known micromotion driven by external error fields, there exists another natural oscillatory component. The latter oscillation is a kind of statistical phenomenon that takes place even in the absence of any mechanical errors. A detailed theoretical study is performed to clarify the basic characteristics of these overlapping coherent motions. A simple cooling scheme is proposed to minimize the transverse oscillation amplitude of a Coulomb crystal without use of extra lasers. The validity of theoretical predictions made in the present paper is confirmed through molecular dynamics simulations assuming the three-dimensional electrode geometry of a typical Paul trap.
Monolithic three-dimensional (3D) Paul traps combine the high-precision microfabrication of two-dimensional (2D) chip traps with the deep trapping potentials and low heating rates characteristic of macroscopic 3D Paul traps, which are typically machined by traditional means and mechanically assembled. However, achieving low motional heating rates and optical access with a high numerical aperture (NA) while maintaining the high radio-frequency (RF) voltages required for trapping heavy ionic species, such as Yb
+ and Ba
+, remains a significant technical challenge. In this work, we present a fused-silica, monolithic segmented 3D Paul trap with an ion-electrode distance of 250
μm, and stable operation at high RF voltages. We benchmark the performance of the trap using Yb
+ ions, demonstrating axially homogeneous trapping potentials spanning over 200
μm about the axial center of the trap, high multi-directional optical access (up to 0.7 NA), and radial motional heating as low as $\dot{\bar n}=1.1 \pm 0.1 $ quanta/s at radial trap frequencies about 3 MHz near room temperature. Furthermore, we observe a motional Ramsey coherence time,
T2, of about 95 ms for the radial center-of-mass mode. We demonstrate the generation of a two-qubit Bell state with a parity contrast of
99.3−1.5+0.7% with state preparation and measurement correction. These results establish fused-silica monolithic 3D Paul traps as a scalable, modular platform for quantum simulation, computation, metrology, and networking with heavy ionic species.