Emergence of Fermi's Golden Rule in the Spectroscopy of a Strongly Correlated Fermi Gas

Connecting experimental observables to many-body quantities often relies on linear-response theory via Fermi's Golden Rule. However, its range of applicability is not always straightforward, especially when probing a strongly interacting system. Here, we explore the radio-frequency spectroscopic response of a homogeneous, balanced spin-½ Fermi gas of ⁶Li, where we drive one of the two components into a third unoccupied level and measure the transfer fraction rate. We observe three distinct regimes. First, at early stages, the transfer fraction scales quadratically with pulse duration. At intermediate times, the 'Fermi’s Golden Rule' regime emerges. For long enough pulse duration, we observe the saturation of the transfer fraction, beyond linear response. This clarifies the validity of linear-response theory in many-body spectroscopy.