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We report the experimental measurement of the equation of state of atwo-dimensional Fermi gas with attractive s-wave interactions throughout thecrossover from a weakly coupled Fermi gas to a Bose gas of tightly bound dimersas the interaction strength is varied. We demonstrate that interactions lead toa renormalization of the density of the Fermi gas by several orders ofmagnitude. We compare our data near the ground state and at finite temperatureto predictions for both fermions and bosons from Quantum Monte Carlosimulations and Luttinger-Ward theory. Our results serve as input forinvestigations of close-to-equilibrium dynamics and transport in thetwo-dimensional system.

Equation of State of Ultracold Fermions in the 2D BEC-BCS Crossover Region