Non-equilibrium dynamics of strongly correlated systems constitutes a fascinating problem of condensed matter physics with many open questions. Here we investigate the relaxation dynamics of Landau-quantized electron system into spin-valley polarized ground state in a gate-tunable MoSe$_2$ monolayer subjected to a strong magnetic field. The system is driven out of equilibrium with optically injected excitons that depolarize the electron spins and the subsequent electron spin-valley relaxation is probed in time-resolved experiments. We demonstrate that the relaxation rate at millikelvin temperatures sensitively depends on the Landau level filling factor: it becomes faster whenever the electrons form an integer quantum Hall liquid and slows down appreciably at non-integer fillings. Our findings evidence that valley relaxation dynamics may be used as a tool to investigate the interplay between the effects of disorder and strong interactions in the electronic ground state.
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