Stochastic multi-channel lock-in detection

TL;DR

This paper extends lock-in detection to multiple channels using orthogonal waveforms, improving noise rejection and systematic error mitigation, enabling high-precision measurements like the electron's electric dipole moment.

Contribution

It introduces a multi-channel lock-in detection scheme with orthogonal waveforms and strategies to reject background drifts and systematic errors.

Findings

Effective noise rejection for random and correlated noise

Systematic error reduction by changing waveforms between runs

Successful application in measuring the electron's electric dipole moment

Abstract

High-precision measurements benefit from lock-in detection of small signals. Here we discuss the extension of lock-in detection to many channels, using mutually orthogonal modulation waveforms, and show how the the choice of waveforms affects the information content of the signal. We also consider how well the detection scheme rejects noise, both random and correlated. We address the particular difficulty of rejecting a background drift that makes a reproducible offset in the output signal and we show how a systematic error can be avoided by changing the waveforms between runs and averaging over many runs. These advances made possible a recent measurement of the electron's electric dipole moment.