Non-Abelian topological order and anyons on a trapped-ion processor.

Non-Abelian topological order is a coveted state of matter with remarkable properties, including quasiparticles that can remember the sequence in which they are exchanged. These anyonic excitations are promising building blocks of fault-tolerant quantum computers. However, despite extensive efforts, non-Abelian topological order and its excitations have remained elusive, unlike the simpler quasiparticles or defects in Abelian topological order.

High Fidelity State Preparation and Measurement of Ion Hyperfine Qubits with I>1/2.

We present a method for achieving high fidelity state preparation and measurement (SPAM) using trapped ion hyperfine qubits with nuclear spins higher than I=1/2. The ground states of these higher nuclear spin isotopes do not afford a simple frequency-selective state preparation scheme. We circumvent this limitation by stroboscopically driving strong and weak transitions, blending fast optical pumping using dipole transitions, and narrow microwave or optical quadrupole transitions.

Phonon Lasing from Optical Frequency Comb Illumination of Trapped Ions.

We demonstrate the use of a frequency-doubled optical frequency comb to load, cool, and crystallize trapped atomic ions as an alternative to ultraviolet (UV) or even deep UV continuous-wave lasers. We find that the Doppler shift from the atom's oscillation in the trap, driven by the blue-detuned comb teeth, introduces additional cooling and amplification which gives rise to steady-state phonon lasing of the ion's harmonic motion in the trap. The phonon laser's gain saturation keeps the optical frequency comb from continually adding energy without bound.

Realization of Translational Symmetry in Trapped Cold Ion Rings.

We crystallize up to 15 ^{40}Ca^{+} ions in a ring with a microfabricated silicon surface Paul trap. Delocalization of the Doppler laser-cooled ions shows that the translational symmetry of the ion ring is preserved at millikelvin temperatures. By characterizing the collective motion of the ion crystals, we identify homogeneous electric fields as the dominant symmetry-breaking mechanism at this energy scale.