Digital stabilization of an IQ modulator in the carrier suppressed single side-band (CS-SSB) mode for atom interferometry

We present an all-digital method for stabilising the phase biases in an electro-optic I/Q modulator for carrier-suppressed single-sideband modulation. Building on the method presented in S. Wald \ea, Appl. Opt. \textbf{62}, 1-7 (2023), we use the Red Pitaya STEMlab 125-14 platform to digitally generate and demodulate an auxiliary radio-frequency tone whose beat with the optical carrier probes the I/Q modulator's phase imbalances. We implement a multiple-input, multiple-output integral feedback controller which accounts for unavoidable cross-couplings in the phase biases to lock the error signals at exactly zero where optical power fluctuations have no impact on phase stability. We demonstrate $>23\,\rm dB$ suppression of the optical carrier relative to the desired sideband at $+3.4\,\rm GHz$ over a period of $15$ hours and over temperature variations of $20^\circ\rm C$.