  Two vertical-external-cavity surface-emitting laser (VECSEL) systems
producing ultraviolet (UV) radiation at 235 nm and 313 nm are demonstrated. The
systems are suitable for quantum information processing applications with
trapped beryllium ions. Each system consists of a compact, single-frequency,
continuous-wave VECSEL producing high-power near-infrared light, tunable over
tens of nanometers. One system generates 2.4 W at 940 nm, using a gain mirror
based on GaInAs/GaAs quantum wells, which is converted to 54 mW of 235 nm light
for photoionization of neutral beryllium atoms. The other system uses a novel
gain mirror based on GaInNAs/GaAs quantum-wells, enabling wavelength extension
with manageable strain in the GaAs lattice. This system generates 1.6 W at 1252
nm, which is converted to 41 mW of 313 nm light that is used to laser cool
trapped $^{9}$Be$^{+}$ ions and to implement quantum state preparation and
detection. The 313 nm system is also suitable for implementing high-fidelity
quantum gates, and more broadly, our results extend the capabilities of VECSEL
systems for applications in atomic, molecular, and optical physics.
