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Cooling the motion of trapped ions to near the quantum ground state is crucial for many applications in quantum information processing and quantum metrology. However, certain motional modes of trapped-ion crystals can be difficult to cool due to weak or zero interaction between the modes and the cooling radiation, typically laser beams. We overcome this challenge by coupling a mode with weak cooling radiation interaction to one with strong cooling radiation interaction using parametric modulation of the trapping potential, thereby enabling indirect cooling of the former. In this way, we demonstrate near-ground-state cooling of motional modes with weak or zero cooling radiation interaction in multi-ion crystals of the same and mixed ion species, specifically $^9$Be$^+$-$^9$Be$^+$, $^9$Be$^+$-$^{25}$Mg$^+$, and $^9$Be$^+$-$^{25}$Mg$^+$-$^9$Be$^+$ crystals. This approach can be generally applied to any Coulomb crystal where certain motional modes cannot be directly cooled efficiently, including crystals containing molecular ions, highly-charged ions, charged fundamental particles, or charged macroscopic objects., Comment: 16 pages, 8 figures

Precise quantum control and measurement of several harmonic oscillators, such as the modes of the electromagnetic field in a cavity or of mechanical motion, are key for their use as quantum platforms. The motional modes of trapped ions can be individually controlled and have good coherence properties. However, achieving high-fidelity two-mode operations and nondestructive measurements of the motional state has been challenging. Here we demonstrate the coherent exchange of single motional quanta between spectrally separated harmonic motional modes of a trapped-ion crystal. The timing, strength, and phase of the coupling are controlled through an oscillating electric potential with suitable spatial variation. Coupling rates that are much larger than decoherence rates enable demonstrations of high fidelity quantum state transfer and beamsplitter operations, entanglement of motional modes, and Hong-Ou-Mandel-type interference. Additionally, we use the motional coupling to enable repeated non-destructive projective measurement of a trapped-ion motional state. Our work enhances the suitability of trapped-ion motion for continuous-variable quantum computing and error correction and may provide opportunities to improve the performance of motional cooling and motion-mediated entangling interactions., Comment: 27 pages, 12 figures

We demonstrate a simplified method for dissipative generation of an entangled state of two trapped-ion qubits. Our implementation produces its target state faster and with higher fidelity than previous demonstrations of dissipative entanglement generation and eliminates the need for auxiliary ions. The entangled singlet state is generated in $\sim$7 ms with a fidelity of 0.949(4). The dominant source of infidelity is photon scattering. We discuss this error source and strategies for its mitigation., Comment: 12 pages, 6 figures

We describe the design, commissioning and operation of an ultra-low-vibration closed-cycle cryogenic ion trap apparatus. One hundred lines for low-frequency signals and eight microwave / radio frequency coaxial feed lines offer the possibility of implementing a small-scale ion-trap quantum processor or simulator. With all supply cables attached, more than 1.3 W of cooling power at 5 K is still available for absorbing energy from electrical pulses introduced to control ions. The trap itself is isolated from vibrations induced by the cold head using a helium exchange gas interface. The performance of the vibration isolation system has been characterized using a Michelson interferometer, finding residual vibration amplitudes on the order of 10 nm rms. Trapping of $^9$Be$^+$ ions has been demonstrated using a combination of laser ablation and photoionization., Comment: 10 figures

We demonstrate the experimental realization of a two-qubit M{\o}lmer-S{\o}rensen gate on a magnetic field-insensitive hyperfine transition in $^9$Be$^+$ ions using microwave-near fields emitted by a single microwave conductor embedded in a surface-electrode ion trap. The design of the conductor was optimized to produce a high oscillating magnetic field gradient at the ion position. The measured gate fidelity is determined to be $98.2\pm1.2\,\%$ and is limited by technical imperfections, as is confirmed by a comprehensive numerical error analysis. The conductor design can potentially simplify the implementation of multi-qubit gates and represents a self-contained, scalable module for entangling gates within the quantum CCD architecture for an ion-trap quantum computer., Comment: 4 figures, 1 table

We present a multilayer surface-electrode ion trap with embedded 3D microwave circuitry for implementing entangling quantum logic gates. We discuss the electromagnetic full-wave simulation procedure that has led to the trap design and the characterization of the resulting microwave field-pattern using a single ion as a local field probe. The results agree with simulations within the uncertainty; compared to previous traps, this design reduces detrimental AC Zeeman shifts by three orders of magnitude. The design presented here can be viewed as an entangling gate component in a library for surface-electrode ion traps intended for quantum logic operations.

We present a novel ion trap fabrication method enabling the realization of multilayer ion traps scalable to an in principle arbitrary number of metal-dielectric levels. We benchmark our method by fabricating a multilayer ion trap with integrated three-dimensional microwave circuitry. We demonstrate ion trapping and microwave control of the hyperfine states of a laser cooled $\,^{9}$Be$^{+}$ ion held at a distance of 35$\,\mu$m above the trap surface. This method can be used to implement large-scale ion trap arrays for scalable quantum information processing and quantum simulation., Comment: 11 pages, 4 figures