Ultracold Fermi gases with tuneable interactions represent a unique test bed to explore the many-body physics of strongly interacting quantum systems [1-4]. In the past decade, experiments have investigated a wealth of intriguing phenomena, and precise measurements of groundstate properties have provided exquisite benchmarks for the development of elaborate theoretical descriptions. Metastable states in Fermi gases with strong repulsive interactions [5-11] represent an exciting new frontier in the field. The realization of such systems constitutes a major challenge since a strong repulsive interaction in an atomic quantum gas implies the existence of a weakly bound molecular state, which makes the system intrinsically unstable against decay. Here, we exploit radio-frequency spectroscopy to measure the complete excitation spectrum of fermionic 40 K impurities resonantly interacting with a Fermi sea of 6 Li atoms. In particular, we show that a welldefined quasiparticle exists for strongly repulsive interactions. For this "repulsive polaron" [9, 12, 13] we measure its energy and its lifetime against decay. We also probe its coherence properties by measuring the quasiparticle residue. The results are well described by a theoretical approach that takes into account the finite effective range of the interaction in our system. We find that a non-zero range of the order of the interparticle spacing results in a substantial lifetime increase. This major benefit for the stability of the repulsive branch opens up new perspectives for investigating novel phenomena in metastable, repulsively interacting fermion systems.Landau's theory of a Fermi liquid [14] and the underlying concept of quasiparticles lay at the heart of our understanding of interacting Fermi systems over a wide range of energy scales, including liquid 3 He, electrons in metals, atomic nuclei, and the quark-gluon plasma. In the field of ultracold Fermi gases, the normal (non-superfluid) phase of a strongly interacting system can be interpreted in terms of a Fermi liquid [15][16][17][18]. In the population-imbalanced case, quasiparticles coined Fermi polarons are the essential building blocks and have been studied in detail experimentally [16] for attractive interactions. Recent theoretical work [9,12,13] has suggested a novel quasiparticle associated with repulsive interactions. The properties of this repulsive polaron are of fundamental importance for the prospects of repulsive many-body states. A crucial question for the feasibility of future experiments is the stability against decay into molecular excitations The vertical lines at 1/(κ F a) = ±1 indicate the width of the strongly interacting regime. The inset illustrates our rf spectroscopic scheme where the impurity is transferred from a noninteracting spin state |0 to the interacting state |1 . [11,12,19]. Indeed, whenever a strongly repulsive interaction is realized by means of a Feshbach resonance [20], a weakly bound molecular state is present into which the system may rapidly decay.Our system consi...

The fastest possible collective response of a quantum many-body system is related to its excitations at the highest possible energy. In condensed-matter systems, the corresponding timescale is typically set by the Fermi energy. Taking advantage of fast and precise control of interactions between ultracold atoms, we report on the observation of ultrafast dynamics of impurities coupled to an atomic Fermi sea. Our interferometric measurements track the non-perturbative quantum evolution of a fermionic many-body system, revealing in real time the formation dynamics of quasiparticles and the quantum interference between attractive and repulsive states throughout the full depth of the Fermi sea. Ultrafast time-domain methods to manipulate and investigate strongly interacting quantum gases open up new windows on the dynamics of quantum matter under extreme nonequilibrium conditions.Non-equilibrium dynamics of fermionic systems is at the heart of many problems in science and technology, from the physics of neutron stars and heavy ion collisions to the operation of electronic devices. The wide range of energy scales, spanning the low energies of excitations near the Fermi surface up to high energies of excitations from deep within the Fermi sea, challenges our understanding of the quantum dynamics in such fundamental systems. The Fermi energy E F sets the shortest response time for the collective response of a fermionic many-body system through the Fermi time τ F =h/E F , whereh is the reduced Planck constant. In a metal, i.e. a Fermi sea of electrons, E F is in the range of a few electronvolts, which corresponds to τ F on the order of 100 attoseconds. Dynamics in condensed matter systems on this timescale can be recorded by attosecond streaking techniques [1] and the initial applications were demonstrated by probing photoelectron emission from a surface [2]. However, despite these spectacular advances, the direct observation of the coherent evolution of a fermionic many-body system on the Fermi timescale has remained beyond reach.In atomic quantum gases, the fermions are much heavier and the densities far lower, which brings τ F into the experimentally accessible range of typically a few microseconds. Furthermore, the powerful techniques of atom interferometry [3] now offer the exciting opportunity to probe and manipulate the real-time coherent evolution of a fermionic quantum many-body system. Such techniques have been successfully used, e.g. to measure bosonic Hanbury-Brown-Twiss correlations [4], demonstrate topological bands [5], probe quantum and thermal fluctuations in low-dimensional condensates [6,7], and to measure demagnetization dynamics of a fermionic gas [8,9]. Impurities coupled to a quantum gas provide a novel and unique probe of the many-body state. Strikingly, they allow direct access to the system's wave function when the internal states of the impurities are manipulated using a Ramsey atom-interferometric technique [10,11].We employ dilute 40 K atoms in a 6 Li Fermi sea to measure the response of the ...