We present a solid-state laser system that generates 750 mW of continuous-wave single-frequency output at 313 nm. Sum-frequency generation with fiber lasers at 1550 nm and 1051 nm produces up to 2 W at 626 nm. This visible light is then converted to UV by cavity-enhanced second-harmonic generation. The laser output can be tuned over a 495 GHz range, which includes the 9 Be + laser cooling and repumping transitions. This is the first report of a narrow-linewidth laser system with sufficient power to perform fault-tolerant quantum-gate operations with trapped 9 Be + ions by use of stimulated Raman transitions. IntroductionTwo of the primary objectives in quantum information processing and computing, are scaling to large numbers of quantum gates, and achieving fault-tolerant gate operation [1][2]. A promising approach to achieving both objectives is to use trapped ions, in which the quantum information is encoded on internal atomic states [3]. Efforts to improve ion-trap scalability have focused on multizone arrays [4][5], with complex surface-electrode geometries that provide multiple trapping zones [6]. These traps include control electrodes that enable the shuttling of ions between zones that are used to perform gate operations, state detection, and information storage. For fault-tolerant two-qubit (quantum bit) gate operations, error-correction protocols have been proposed [7][8], but these require a sufficiently low error per gate (typically assumed to be less that 10 -4 ), and this threshold has not yet been achieved. In one approach, qubits are encoded into ground-state hyperfine states, since these are very well isolated from environmental effects that cause memory error. However, gate operations are usually performed via optical transitions with laser beams, leading to spontaneous emission that dominates gate error. Spontaneous emission is reduced by a large detuning from atomic resonance, but then higher laser powers required to maintain the gate speed. For example, Ozeri et al. calculate that with the commonly trapped ion species of 9 Be + , 25 Mg + , and 43 Ca + , in order to reach the fault-tolerant regime for a two-qubit phase gate, one needs narrow-linewidth, continuous-wave (cw) laser power in the range of 140 mW to 540 mW (and detuning from atomic resonance on the THz scale) [9].The most challenging aspect of developing laser sources for this purpose is that most of the wavelengths are in the UV region. For trapped 43 Ca + ions, the required 729 nm or 397 nm light can be generated directly with semiconductor lasers; but for the shorter wavelengths needed for most other trapped-ion species, the traditional approach has been to frequency-double the visible output from a ring dye laser. While solid-state lasers have replaced gas and dye lasers in many spectral regions, some wavelengths have remained difficult to produce. [11]. Their setup includes a frequencydoubled Nd:YAG laser at 532 nm, a titanium sapphire laser at 760 nm, and sum-frequency generation (SFG) in an enhancement cavity resona...

We cool the fundamental mode of a miniature cantilever by capacitively coupling it to a driven rf resonant circuit. Cooling results from the rf capacitive force, which is phase shifted relative to the cantilever motion. We demonstrate the technique by cooling a 7 kHz cantilever from room temperature to 45 K, obtaining reasonable agreement with a model for the cooling, damping, and frequency shift. Extending the method to higher frequencies in a cryogenic system could enable ground state cooling and may prove simpler than related optical experiments in a low temperature apparatus. PACS numbers: 05.40.Jc,85.85.+j Stimulated by the early work of Braginsky and collaborators [1,2], the quantum-limited measurement and control of mechanical oscillators continues to be a subject of great interest. If one can cool to the ground state of the oscillator, the generation of nonclassical states of motion also becomes feasible. For an atom bound in a harmonic well, laser cooling in a room-temperature apparatus can cool the modes of mechanical motion to a level with mean occupation numbers n < 0.1 for oscillation frequencies ∼1−10 MHz [3,4]. This has made it possible to generate nonclassical mechanical oscillator states such as squeezed, Fock [5], multiparticle entangled [6], and (in principle) arbitrary superposition states [7].For more macroscopic systems, smaller and smaller micromechanical resonators have approached the quantum limit through thermal contact with a cryogenic bath (for a summary, see [8]). Small mechanical resonators, having low-order mode frequencies of 10−1000 MHz, can come close to the quantum regime at low temperature ( < 1 K), and mean occupation numbers of approximately 25 have been achieved [9]. Cooling of macroscopic mechanical oscillators also has been achieved with optical forces. The requisite damping can be implemented by use of active external electronics to control the applied force [10,11,12,13] (see also [14]). Passive feedback cooling has been realized in which a mirror attached to a mechanical oscillator forms an optical cavity with another stationary mirror. For appropriate tuning of radiation incident on the cavity, a delay in the optical force on the oscillator as it moves gives cooling. This delay can result from a photothermal effect [15,16] or from the stored energy response time of the cavity [17,18,19]. Closely related passive cooling has been reported in [9,20].We demonstrate a similar cooling mechanism where the damping force is the electric force between capacitor plates [21] that here contribute to a resonant rf circuit [2,22]. This approach has potential practical advantages over optical schemes: eliminating optical components simplifies fabrication and integration into a cryogenic system, and the rf circuit could be incorporated on-chip with the mechanical oscillator.A conducting cantilever of mass density ρ is fixed at one end [ Fig. 1(a)]. One face is placed a distance d from a rigidly mounted plate of area w × h, forming a parallel-plate capacitor C c = ε 0 wh/d, where ε ...

Microwave near-field quantum control of spin and motional degrees of freedom of 25 Mg + ions can be used to generate two-ion entanglement, as recently demonstrated in Ospelkaus et al. [Nature 476, 181 (2011)]. Here, we describe additional details of the setup and calibration procedures for these experiments. We discuss the design and characteristics of the surface-electrode trap and the microwave system, and compare experimental measurements of the microwave near-fields with numerical simulations. Additionally, we present a method that utilizes oscillating magnetic-field gradients to detect micromotion induced by the ponderomotive radio-frequency potential in linear traps. Finally, we discuss the present limitations of microwave-driven two-ion entangling gates in our system.

We present a microfabricated surface-electrode ion trap with a pair of integrated waveguides that generate a standing microwave field resonant with the 171 Yb + hyperfine qubit. The waveguides are engineered to position the wave antinode near the center of the trap, resulting in maximum field amplitude and uniformity along the trap axis. By calibrating the relative amplitudes and phases of the waveguide currents, we can control the polarization of the microwave field to reduce off-resonant coupling to undesired Zeeman sublevels. We demonstrate single-qubit π -rotations as fast as 1 µs with less than 6% variation in Rabi frequency over an 800 µm microwave interaction region. Fully compensating pulse sequences further improve the uniformity of X -gates across this interaction region.

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