High-resolution, high-accuracy spectroscopy of trapped ions

Microwave spectroscopy using trapped and cooled ions can achieve precision and accuracy comparable to the best cesium frequency standards. We discuss standards based on ${}^{\mathrm{199}}{\mathrm{Hg}}^{\mathrm{+}}$ ions trapped in linear Paul traps: the Jet Propulsion Laboratory (JPL) standard, which uses up to ${10}^7$ atoms confined near the trap axis, and the recently evaluated NIST standard, which uses approximately ten ions laser cooled and crystalized on the trap axis. We consider future directions in trapped ion frequency standard work, including the use of entangled states for achieving higher precision, and progress on trapped ion optical frequency standards. Finally, we discuss scientific and technical applications of extremely stable frequency standards.