Simultaneous two-photon resonant optical laser locking (STROLLing) in the hyperfine Paschen--Back regime

We demonstrate a technique to lock simultaneously two laser frequencies to each step of a two-photon transition in the presence of a magnetic field sufficiently large to gain access to the hyperfine Paschen-Back regime. A ladder configuration with the 5S${}_{1\mathrm{/}2}$, 5P${}_{3\mathrm{/}2}$ and 5D${}_{5\mathrm{/}2}$ terms in a thermal vapour of ${}^{87}$Rb atoms is used. The two lasers remain locked for more than 24 hours. For the sum of the laser frequencies, which represents the stability of the two-photon lock, we measure a frequency instability of less than the Rb D${}_2$ natural linewidth of 6 MHz for nearly all measured time scales