A degenerate Fermi gas is rapidly quenched into the regime of strong effective repulsion near a Feshbach resonance. The spin fluctuations are monitored using speckle imaging and, contrary to several theoretical predictions, the samples remain in the paramagnetic phase for an arbitrarily large scattering length. Over a wide range of interaction strengths a rapid decay into bound pairs is observed over times on the order of 10ℏ/E(F), preventing the study of equilibrium phases of strongly repulsive fermions. Our work suggests that a Fermi gas with strong short-range repulsive interactions does not undergo a ferromagnetic phase transition.

Spin fluctuations and density fluctuations are studied for a two-component gas of strongly interacting fermions along the BEC-BCS crossover. This is done by in-situ imaging of dispersive speckle patterns. Compressibility and magnetic susceptibility are determined from the measured fluctuations. This new sensitive method easily resolves a tenfold suppression of spin fluctuations below shot noise due to pairing, and can be applied to novel magnetic phases in optical lattices.PACS numbers: 03.75. Ss, 05.30.Fk, 67.85.Lm One frontier in the field of ultracold atoms is the realization of quantum systems with strong interactions and strong correlations. Many properties of strongly correlated systems cannot be deduced from mean density distributions. This has drawn interest toward novel ways of probing cold atoms, e.g. via RF spectroscopy [1,2], Bragg and Raman scattering [3], interferometric methods [4,5] and by recording density correlations [6][7][8]. Further insight into quantum systems is obtained by looking not only at expectation values, but also at fluctuations. Several recent studies looked at density fluctuations, either of bosons around the superfluid-to-Mott insulator transition [9-11], or of a gas of non-interacting fermions [12,13].In this paper, we extend the study of fluctuations of ultracold gases in several ways. First, we apply it to a two-component Fermi gas across the BEC-BCS crossover. Second, we implement a very sensitive way to measure fluctuations in the magnetization, i.e. the difference of the densities in the two different states. Third, we introduce the technique of speckle imaging as a simple and highly sensitive method to characterize fluctuations.Our work is motivated by the prospect of realizing wide classes of spin Hamiltonians using a two-component gas of ultracold atoms in an optical lattice [14,15]. An important thermodynamic quantity to characterize twocomponent systems is the spin susceptibility, which provides a clear signature of phase transitions or crossovers involving the onset of pairing or magnetic order [16,17]. At a ferromagnetic phase transition the susceptibility diverges, whereas in a transition to a paired or antiferromagnetic phase the susceptibility becomes exponentially small in the ratio of the pair binding energy (or antiferromagnetic gap) to the temperature. The fluctuationdissipation theorem relates response functions to fluctuations, consequently the spin susceptibility can be determined by measuring the fluctuations in the relative density of the two spin components.In our experiment spin fluctuations create phase shifts of (detuned) imaging light that vary randomly in space; we measure them by imaging the resulting speckle patterns. When imaging atom clouds, one usually relates the transmitted light intensity with absorption and its phase with dispersion [18]. This is different in our method. Spin and density fluctuations occur on all spatial scales down to the interatomic separation, and their observation is limited by the maximum resolution of the imagin...

We study density profiles of an ideal Fermi gas and observe Pauli suppression of density fluctuations (atom shot noise) for cold clouds deep in the quantum degenerate regime. Strong suppression is observed for probe volumes containing more than 10,000 atoms. Measuring the level of suppression provides sensitive thermometry at low temperatures. After this method of sensitive noise measurements has been validated with an ideal Fermi gas, it can now be applied to characterize phase transitions in strongly correlated many-body systems.PACS numbers: 03.75. Ss, 05.30.Fk, 67.85.Lm Systems of fermions obey the Pauli exclusion principle. Processes that would require two fermions to occupy the same quantum state are suppressed. In recent years, several classic experiments have directly observed manifestations of Pauli suppression in Fermi gases. Antibunching and the suppression of noise correlations are a direct consequence of the forbidden double occupancy of a quantum state. Such experiments were carried out for electrons [1][2][3], neutral atoms [4,5], and neutrons [6]. In principle, such experiments can be done with fermions at any temperature, but in practice low temperatures increase the signal. A second class of (two-body) Pauli suppression effects, the suppression of collisions, requires a temperature low enough such that the de Broglie wavelength of the fermions becomes larger than the range of the interatomic potential and p-wave collisions freeze out. Experiments observed the suppression of elastic collisions [7,8] and of clock shifts in radio frequency spectroscopy [9,10].Here we report on the observation of Pauli suppression of density fluctuations, a many-body phenomenon which occurs only at even lower temperatures in the quantum degenerate regime, where the Fermi gas is cooled below the Fermi temperature and the low lying quantum states are occupied with probabilities close to one. In contrast, an ideal Bose gas close to quantum degeneracy shows enhanced density fluctuations [11].The development of a technique to sensitively measure density fluctuations was motivated by the connection between density fluctuations and compressibility through the fluctuation dissipation theorem. In this paper, we validate our technique for determining the compressibility by applying it to the ideal Fermi gas. In future work, it could be extended to interesting many-body phases in optical lattices which are distinguished by their incompressibility [12]. These include the band insulator, Mott insulator, and also the antiferromagnet for which spin fluctuations, i.e. fluctuations of the difference in density between the two spin states, are suppressed.Until now, sub-Poissonian number fluctuations of ultracold atoms have been observed only for small clouds of bosons with typically a few hundred atoms [13][14][15][16] and directly [17,18] or indirectly [19] for the bosonic Mott in-