Phase-Stable Free-Space Optical Lattices for Trapped Ions

Breaking the Entangling Gate Speed Limit for Trapped-Ion Qubits Using a Phase-Stable Standing Wave

All laser-driven entangling operations for trapped-ion qubits have hitherto been performed without control of the optical phase of the light field, which precludes independent tuning of the carrier and motional coupling. By placing ^{88}Sr^{+} ions in a λ=674  nm standing wave, whose relative position is controlled to ≈λ/100, we suppress the carrier coupling by a factor of 18, while coherently enhancing the spin-motion coupling. We experimentally demonstrate that the off-resonant carrier coupling imposes a speed limit for conventional traveling-wave Mølmer-Sørensen gates; we use the standing wave to surpass this limit and achieve a gate duration of 15  μs, restricted by the available laser power.

Control of an Atomic Quadrupole Transition in a Phase-Stable Standing Wave

Using a single calcium ion confined in a surface-electrode trap, we study the interaction of electric quadrupole transitions with a passively phase-stable optical standing wave field sourced by photonics integrated within the trap. We characterize the optical fields through spatial mapping of the Rabi frequencies of both carrier and motional sideband transitions as well as ac Stark shifts. Our measurements demonstrate the ability to engineer favorable combinations of sideband and carrier Rabi frequency as well as ac Stark shifts for specific tasks in quantum state control and metrology.

Coherent Transfer of Transverse Optical Momentum to the Motion of a Single Trapped Ion

Using a structured light beam carrying orbital angular momentum, we demonstrate excitation of the center-of-mass motion of a single atom in the transverse direction to the beam's propagation. This interaction enables quantum control of atomic motion in all axes with a single beam direction, which leads to applications in quantum computing and simulations with ion crystals. Here we demonstrate all the key features required for these applications, namely, coherent dynamics and strong carrier suppression in a configuration with the ion centered in the beam, which allows for single ion addressing and also provides robustness against pointing instabilities. To quantify transverse momentum transfer, we observe coherent dynamics on the sidebands of the S_{1/2} to D_{5/2} transition near 729 nm of a singly charged ^{40}Ca^{+} ion, cooled near the ground state of motion in the 3D harmonic potential of a Paul trap, and placed at the center of a first-order Laguerre-Gaussian beam. Exchange of quanta in the perpendicular direction to the beam's wave vector k is observed with a centered vortex shaped beam, together reduction of the parasitic carrier excitation by a factor of 40. This is in sharp contrast to the vanishing spin-motion coupling at the center of the Gaussian beam. Further, we characterize the coherent interaction by an effective transverse Lamb-Dicke factor η_{⊥}^{exp}=0.0062(5) which is in agreement with our theoretical prediction η_{⊥}^{theo}=0.0057(1).

Optical Superresolution Sensing of a Trapped Ion's Wave Packet Size

We demonstrate superresolution optical sensing of the size of the wave packet of a single trapped ion. Our method extends the well-known ground state depletion (GSD) technique to the coherent regime. Here, we use a hollow beam to strongly saturate a coherently driven dipole-forbidden transition around a subdiffraction limited area at its center and observe state dependent fluorescence. By spatially scanning this laser beam over a single trapped ^{40}Ca^{+} ion, we are able to measure the wave packet sizes of cooled ions. Using a depletion beam waist of 4.2(1)  μm we reach a spatial resolution which allows us to determine a wave packet size of 39(9) nm for a near ground state cooled ion. This value matches an independently deduced value of 32(2) nm, calculated from resolved sideband spectroscopy measurements. Finally, we discuss the ultimate resolution limits of our adapted GSD imaging technique in view of applications to direct quantum wave packet imaging.

Spin Heat Engine Coupled to a Harmonic-Oscillator Flywheel

We realize a heat engine using a single-electron spin as a working medium. The spin pertains to the valence electron of a trapped ^{40}Ca^{+} ion, and heat reservoirs are emulated by controlling the spin polarization via optical pumping. The engine is coupled to the ion's harmonic-oscillator degree of freedom via spin-dependent optical forces. The oscillator stores the work produced by the heat engine and, therefore, acts as a flywheel. We characterize the state of the flywheel by reconstructing the Husimi Q function of the oscillator after different engine run times. This allows us to infer both the deposited energy and the corresponding fluctuations throughout the onset of operation, starting in the oscillator ground state. In order to understand the energetics of the flywheel, we determine its ergotropy, i.e., the maximum amount of work which can be further extracted from it. Our results demonstrate how the intrinsic fluctuations of a microscopic heat engine fundamentally limit performance.

Trapped Ion Quantum Information Processing with Squeezed Phonons

Trapped ions offer a pristine platform for quantum computation and simulation, but improving their coherence remains a crucial challenge. Here, we propose and analyze a new strategy to enhance the coherent interactions in trapped ion systems via parametric amplification of the ions' motion-by squeezing the collective motional modes (phonons), the spin-spin interactions they mediate can be significantly enhanced. We illustrate the power of this approach by showing how it can enhance collective spin states useful for quantum metrology, and how it can improve the speed and fidelity of two-qubit gates in multi-ion systems, important ingredients for scalable trapped ion quantum computation. Our results are also directly relevant to numerous other physical platforms in which spin interactions are mediated by bosons.

Visibility of Young's Interference Fringes: Scattered Light from Small Ion Crystals

We observe interference in the light scattered from trapped ^{40}Ca^{+} ion crystals. By varying the intensity of the excitation laser, we study the influence of elastic and inelastic scattering on the visibility of the fringe pattern and discriminate its effect from that of the ion temperature and wave-packet localization. In this way we determine the complex degree of coherence and the mutual coherence of light fields produced by individual atoms. We obtain interference fringes from crystals consisting of two, three, and four ions in a harmonic trap. Control of the trapping potential allows for the adjustment of the interatomic distances and thus the formation of linear arrays of atoms serving as a regular grating of microscopic scatterers.