Low-Cost and High-Performance Multi-Frequency Lock-In Amplifier to Dramatically Improve Spectroscopy Speed*

Scanning tunneling spectroscopy (STS) and quasiparticle interference (QPI) measurements allow the study of the electronic structure of materials by measuring the local density of states. Conventional methods require many serial measurements per spectrum, taking up to 72 hours for a 512x512 pixel map. Using just one measurement, multi-frequency lock-in amplifiers (MFLIAs) simultaneously measure higher harmonics of the base modulation to acquire each spectrum, accelerating STS and QPI by an order of magnitude.

This technique has been demonstrated before [1], but current commercial MFLIA solutions are expensive, while providing too few harmonics for sufficient reconstruction. We demonstrate an MFLIA implemented on a low-cost, off-the-shelf FPGA board. Our system costs less than $1000 while demodulating at twice the number of harmonics of commercial solutions.

Idealized tests reconstruct spectra of superconducting Bi₂Sr₂Ca_n−1Cu_nO_2n+4+x with a maximum error of 2% at 2 kHz modulation. We present further results benchmarking our MFLIA implementation for QPI measurements.

[1] B. Zengin et. al., PRR, 3 L042025 (2021)