Qian Yu

We demonstrate the operation of a dual-frequency Paul trap and characterize its performance by storing either electrons or calcium ions while applying two quadrupole fields simultaneously which oscillate at $Ω_\textrm{fast} = 2π\times 1.6$ GHz and $Ω_\textrm{slow} = 2π\times 2$ MHz. The particles are loaded and stored in the trap under various conditions followed by detection employing an electron multiplier tube. We find that tens of electrons or ions can be trapped for up to ten milliseconds and a small fraction remains trapped even after hundreds of milliseconds. During dual-frequency operation we find that while the number of trapped electrons rapidly decreases with increase of the $Ω_\textrm{slow}$ field amplitude, the number of trapped ions shows no dependence on the $Ω_\textrm{fast}$ field amplitude as supported by our extensive numerical simulations. We aim to use a similar trap for synthesising antihydrogen from antiprotons and positrons. Accordingly, we discuss open challenges such as the co-trapping of oppositely charged species and particle trap duration.

Trapped-ion applications, such as in quantum information, precision measurements, optical clocks, and mass spectrometry, rely on specialized high-performance ion traps. The latter applications typically employ traditional machining to customize macroscopic 3D Paul traps, while quantum information processing experiments usually rely on photo-lithographic techniques to miniaturize the traps and meet scalability requirements. Using photolithography, however, it is challenging to fabricate the complex three-dimensional electrode structures required for optimal confinement. Here we address these limitations by adopting a high-resolution 3D printing technology based on two-photon polymerization supporting fabrication of large arrays of high-performance miniaturized 3D traps. We show that 3D-printed ion traps combine the advantages of traditionally machined 3D traps with the miniaturization provided by photolithography by confining single calcium ions in a small 3D-printed ion trap with radial trap frequencies ranging from 2 MHz to 24 MHz. The tight confinement eases ion cooling requirements and allows us to demonstrate high-fidelity coherent operations on an optical qubit after only Doppler cooling. With 3D printing technology, the design freedom is drastically expanded without sacrificing scalability and precision so that ion trap geometries can be optimized for higher performance and better functionality.

In this work, we derive analytic formulae that determine the effect of error mechanisms on one- and two-qubit gates in trapped ions and electrons. First, we analyze, and derive expressions for, the effect of driving field inhomogeneities on one-qubit gate fidelities. Second, we derive expressions for two-qubit gate errors, including static motional frequency shifts, trap anharmonicities, field inhomogeneities, heating, and motional dephasing. We show that, for small errors, each of our expressions for infidelity converges to its respective numerical simulation; this shows our formulae are sufficient for determining error budgets for high-fidelity gates, obviating numerical simulations in future projects. All of the derivations are general to any internal qubit state, and any mixed state of the ion crystal's motion that is diagonal in the Fock state basis. Our treatment of static motional frequency shifts, trap anharmonicities, heating, and motional dephasing apply to both laser-based and laser-free gates, while our treatment of field imhomogenieties applies to laser-free systems.