Fig. 1: Key elements of the experimental setup, timing sequence, level scheme, and level occupation probability.

a Schematic of the experimental setup and generic timing sequence used in the measurements. The microwave generator (OSC) drives the horn antenna, used to excite and sense the atoms as represented here, through a bidirectional coupler (CPL). The atoms are detected via a modification of the antenna’s radiation impedance caused by their presence. This modification is observed in the reflected microwave power picked-up at the CPL reverse coupled port and measured with a detector (D), here a spectrum analyzer in zero span mode. The step “Microwave” in the sequence corresponds to driving and/or detection of the atomic populations. b Relevant energy levels of the hyperfine ground states of ⁸⁷Rb atoms under a quantization field of 2 Gauss. The microwave at a frequency ω couples to the clock transition with an adjustable detuning. c Fractional state 2 population as a function of the horn detuning observed via the reflected wave power. d Spectrum of the fractional state 2 population as measured by absorption imaging. The blue solid lines are fits to the spectra using the two-level atom excited state population equation (see Supplementary Note 2). The error bars correspond to the standard deviation of repeated measurements.