States of an Ensemble of Two-Level Atoms with Reduced Quantum Uncertainty: Auxiliary Material

The parameters of the near-confocal Fabry-Pérot resonator at the wavelengths of trap light (851 nm) and probe light (780 nm) are summarized in table A1. Both trap laser and probe laser are locked to the resonator via Pound-Drever-Hall locks of 1 MHz loop bandwidth. Another feedback loop stabilizes the resonator frequency to an atomic transition in Rb. The atoms are loaded into the standing-wave optical trap from a microchip-based magnetic trap described elsewhere [1]. After polarization gradient cooling in the linearly polarized optical trap, we apply a 5.6 G magnetic field along the resonator axis and a circular polarization fraction of 0.5(1) to the trap light. This combination yields a first-order cancellation of the vector and scalar light shifts, minimizing inhomogeneous broadening of the clock transition. Table A2 summarizes the characteristics of the atomic cloud in the optical dipole trap.