  Pairing is the fundamental requirement for fermionic superfluidity and
superconductivity. To understand the mechanism behind pair formation is an
ongoing challenge in the study of many strongly correlated fermionic systems.
Cooper pairs are the key ingredient to BCS theory as the microscopic
explanation of conventional superconductivity. They form between particles of
opposite spin and momentum at the Fermi surface of the system. Here, we
directly observe Cooper pairs in a mesoscopic two-dimensional Fermi gas. We
apply an imaging scheme that enables us to extract the full in-situ momentum
distribution of a strongly interacting Fermi gas with single particle and spin
resolution. Our ultracold gas allows us to freely tune between a completely
non-interacting, unpaired system and weak attractions, where we find Cooper
pair correlations at the Fermi surface. When increasing the attractive
interactions even further, the pairs gradually turn into deeply bound molecules
breaking up the Fermi surface. Our mesoscopic system is closely related to the
physics of nuclei, superconducting grains or quantum dots. With the precise
control over interactions, particle number and potential landscape in our
experiment, the observables we establish in this work provide a new approach to
longstanding questions concerning not only such mesoscopic systems but also
their connection to the macroscopic world.
