An inverted crossover resonance within one Zeeman manifold

We carry out investigations of inverted crossover resonances in $\pi$-driven four-level systems where $\Delta F$ can be zero. Through the use of sub-Doppler frequency modulation spectroscopy of the $(6s^{2})$ $^{1}S_{0}$ $-$ $(6s6p)$ $^{3}P_{1}$ transition in $^{171}$Yb the resonance becomes manifest. The centre-frequency is inherently insensitive to first-order Zeeman shifts and equates to the two-level resonance frequency in the absence of a magnetic field. A rate equation model is used to help validate the nature of the resonance. Optical frequency measurements of the $F'=1/2$ hyperfine line recorded over two months demonstrate a statistical uncertainty of $2\times10^{-11}$. The inverted crossover resonance found with the $F'=3/2$ line is used for 556 nm laser frequency stabilization, which is an alternative means when applied to magneto-optical trapping of $^{171}$Yb.