Homodyne Quadrature Laser Interferometry for the Characterization of Low-Frequency Residual Vibrational Noise in Cryogenic Trapped-Ion Systems

Cryogenic trapped-ion systems (CTISs) have emerged as indispensable platforms for the advancement of quantum computation and precision measurement techniques. However, the sensitivity of these systems to vibrational noise, especially during the compression and expansion cycles of the cold head in a Gifford-McMahon cycle refrigerator (GMCR), poses a significant challenge. To mitigate this, we have crafted an innovative methodology for characterizing low-frequency residual vibrational noise in closed-cycle cryogenic trapped-ion systems. Our methodology is underpinned by a compact homodyne quadrature laser interferometer (HQLI) vibrometer system that boasts nanometer-scale accuracy. This state-of-the-art system leverages elliptic curve fitting to rectify nonlinear noise artifacts and applies an inverse tangent function to demodulation phase techniques, enabling accurate vibrational displacement measurements. Unlike the conventional approach, our scheme circumvents the introduction of extraneous vibrational noise associated with piezoelectric ceramic mirrors, which are conventionally employed to track target vibrations for locking the interference signal intensity in the reference arm. This innovation not only improves the overall CTIS performance but is also significantly applied to characterize the practical realization of quantum computation and precision measurement.