UCLA

Trapped atomic ions are among the most capable platforms for quantum computation, yet leading architectures using laser-based gates suffer photon-scattering errors, demanding cooling requirements, and optical delivery challenges that grow more burdensome at scale. Electric-field-gradient gates (EGGS) bypass these obstacles by driving qubit transitions with radio-frequency fields applied directly to easily scalable trap electrodes - the transitions addressed render photon scattering negligible and tolerate thermal motion. The low-lying, electric-dipole transitions necessary for EGGS are found only in molecules, and this dissertation details the pursuit of EGGS-based quantum-logic spectroscopy of the lambda-doublet qubit in H35Cl+ with a co-trapped 40Ca+ ion in a cryogenic system built to that end. This pursuit required wideband calibration of the EGGS field gradients across the 10 MHz to 1000 MHz band of the molecular transitions - for which no suitably wideband interaction existed. We resolve this with our discovery of motional Raman transitions, which downconvert an arbitrary-frequency drive into a near-resonant motional displacement, and apply them toward quantum vector signal analysis, a protocol for complete waveform sensing of an electric field, which we demonstrate from 100 kHz to 1 GHz, a range 800× wider than prior work. The protocol is compatible with quantum amplification, which we use to reach an amplitude sensitivity 3.4(20) dB below the standard quantum limit. We then extend this family of interactions toward sensing beyond conventional limits. We use subharmonic motional Raman transitions to achieve nonlinearity-enhanced frequency sensitivity, surpassing the Fourier-transform limit with classical states alone to reach a frequency uncertainty of 0.56(32) Hz at 80 MHz - to our knowledge, the most precise frequency measurement of a radio-frequency signal on a quantum harmonic oscillator. Separately, we demonstrate broadband frequency super-resolution: a phase-reversal sequence encodes the separation between two conventionally unresolvable tones into a displacement, resolving a 5 Hz splitting near 80 MHz to 1.6 Hz, 200x below the spectral limit. Finally, combining Fock-state enhancement with synchronized readout recovers a quantum advantage that persists to long timescales, improving the ultimate frequency precision to 2 uHz.