UCLA

The highly popular ytterbium-171 ($^{171} \mathrm{Yb}^+$) ion is commonly employed in quantum information research as a qubit whose excellent coherence time and fast, simple state preparation has allowed cutting edge work in quantum computation and simulation. Despite these large benefits, the demonstrated measurement fidelity of this ion has lagged the state preparation and gate fidelity achieved to date.

In this thesis we investigate and realize methods of increasing the measurement fidelity of $^{171} \mathrm{Yb}^+$ in a scaleable way for large quantum systems. Using methods of coherent control, we implement a pulsed state detection scheme using a mode-locked laser to perform background-free spectroscopy of the ``bright'' state of the qubit. The small hyperfine splitting of the ion necessitates the use of multiple (two) pulses to manipulate time dynamics of the ion to excite a single transition. A Mach-Zehnder interferometer is constructed to control these pulse separations both coarsely ($\sim$ 237 ps) and on a fine sub-femtosecond scale. These pulses cause destructive/constructive interference of the electron wave packet of a single ion levitated in vacuum and are engineered to state-selectively excite the qubit. This allows measurement of the qubit whose transition frequency is much smaller than the bandwidth of the interrogation laser.

During this spectroscopy, mechanical forces from the mode-locked laser frequency comb can drive the ion into large coherent states of motion. This motion has been dubbed ``phonon lasing''. We investigate the phonon lasing affect and how the ion interacts with multiple comb teeth. The large number of teeth leads to a protection mechanism from runaway energy gain by near-by blue detuned teeth, allowing ions to be trapped and cooled by the mode-locked laser, regardless of its detuning. We further explore these discrete amplitude coherent states by injecting energy into the ion's motion and exciting higher-order oscillations.

We, for the first time, implement an ``electron shelving'' of the hyperfine qubit, and incoherently transfer the bright state population in the extremely long-lived ($\approx$5 yr) $^2$F$_{7/2}$ state of $^{171}$Yb$^+$, functionally disconnected state. This is accomplished via narrow-band optical pumping on the $^2$S$_{1/2}$ to the $^2$D$_{5/2}$ quadrupole which has a leaky dipole channel into the $^2$F$_{7/2}$. Narrow-band optical pumping is again used to rescue the ion at the end of the experiment with the aid of a 760 nm E2 transition back into the cooling cycle. Measurement with this scheme is no longer limited by off-resonant effects from the main cycling transition. Limits of this novel technique, as well as further directions using the F state as a utility for quantum information are explored.

Finally, we combine the pulsed background-free spectroscopy with shelving and demonstrate high-fidelity, background free detection of a single trapped $^{171}\mathrm{Yb}^+$ qubit.