Novel Multi-Frequency Scanning Probe Microscopy Technique for Quantum Metrology

Quantum sensing technologies are at the forefront of achieving unparalleled sensitivities in measuring various physical quantities, which are crucial for advancements in various scientific fields, ranging from fundamental physics to biomedical research. In particular, new scanning probe modalities based on the Atomic Force Microscope (AFM) continue to emerge, allowing for highly controlled and precise operation, excitation, and manipulation of both the microcantilever probe and a specific sample region. Here, we present a novel multi-frequency AFM technique that leverages the nanomechanical interaction between the AFM tip and the sample surface in the quantum regime of the sample deformation states. We use this technique to image the vibrational modes of suspended carbon nanotube resonators. Specifically, we realize nanomechanical resonators consisting of arrays of single walled carbon nanotubes (SWCNTs) clamped between metallic contact electrodes and suspended above trenches etched in SiO2 substrates. TheSWCNTs are excited in various vibration states by applying controllable voltages to an underlying back-gate electrode patterned on the substrate. The bending mode vibrations of these mesoscopic quantum oscillators are detected by means of a novel multi-frequency AFM approach that enables the measurement of vibrational states across a wide range of frequencies, from 0.1 – 1 GHz. We quantify the dynamics of these systems and measure the fundamental parameters that describe the system-environment interactions, including the sample quality factor, damping rates, and relaxation timescales. We demonstrate that this measurement technique is minimally invasive, involving sub-pN interaction forces, and thus it is optimal for a variety of quantum sensing and quantum metrology applications.