  Detection of weak electromagnetic waves and hypothetical particles aided by
quantum amplification is important for fundamental physics and applications.
However, demonstrations of quantum amplification are still limited; in
particular, the physics of quantum amplification is not fully explored in
periodically driven (Floquet) systems, which are generally defined by
time-periodic Hamiltonians and enable observation of many exotic quantum
phenomena such as time crystals. Here we investigate the magnetic-field signal
amplification by periodically driven $^{129}$Xe spins and observe signal
amplification at frequencies of transitions between Floquet spin states. This
"Floquet amplification" allows to simultaneously enhance and measure multiple
magnetic fields with at least one order of magnitude improvement, offering the
capability of femtotesla-level measurements. Our findings extend the physics of
quantum amplification to Floquet systems and can be generalized to a wide
variety of existing amplifiers, enabling a previously unexplored class of
"Floquet amplifiers".
