. According to Goldstone's theorem, phase transitions that break continuous symmetries lead to the existence of gapless excitations in the long-wavelength limit 5 . These Goldstone modes can become the dominant low-energy excitation, showing that symmetry breaking has a profound impact on the physical properties of matter. Here, we present a comprehensive study of the elementary excitations in a homogeneous strongly interacting Fermi gas through the crossover from a Bardeen-Cooper-Schrie er (BCS) superfluid to a Bose-Einstein condensate (BEC) of molecules using two-photon Bragg spectroscopy. The spectra exhibit a discrete Goldstone mode, associated with the broken-symmetry superfluid phase, as well as pair-breaking single-particle excitations. Our techniques yield a direct determination of the superfluid pairing gap and speed of sound in close agreement with strong-coupling theories.When a Hamiltonian is invariant with respect to a continuous symmetry, but the ground state is not, a massless bosonic mode appears in the spectrum of allowed excitations 5 . At temperatures low enough for quantum effects to become prominent, dynamical behaviours, such as superconductivity and superfluidity, are possible only due to the low-energy excitation spectrum. Superfluid and superconducting states break gauge invariance and the resultant Goldstone mode is an oscillation of the phase of the order parameter giving rise to a collective motion of particles that is distinct from single-particle excitations. In superconductors, the Coulomb interaction lifts the collective mode up to the frequency of the classical plasma oscillation 4 , present in the normal phase, such that the Goldstone mode is generally imperceptible 6 . In neutral superfluids, however, the Goldstone mode takes the form of a gapless phonon 7 and provides a dramatic signature of macroscopic order.Ultracold gases of atomic fermions have enabled the creation and study of high-transition-temperature superfluids in the smooth crossover from the BCS to BEC regimes 8 . Both first-sound 9-11 and second-sound 10 propagation have been observed in inhomogeneous Fermi gases, yet the basic elementary excitation spectrum has not been measured. Here, we present a comprehensive study of the low-temperature excitations in a homogeneous Fermi superfluid throughout the whole BCS-BEC crossover. The spectra exhibit both a dominant Goldstone mode, or Bogoliubov-Anderson (BA) phonon, and a single-particle continuum. Our study reveals how the energy and spectral weight of these excitations evolve as a function of the interaction strength. We develop a theory based on the quasiparticle random-phase approximation (QRPA), which provides a good quantitative description of the data.The starting point for our experiments is a harmonically trapped gas of fermionic 6 Li atoms in a balanced mixture of the lowest two hyperfine states with tunable s-wave interactions near a broad Feshbach resonance (see Supplementary Information). Atoms are cooled to temperatures below the superfluid transition te...

We have studied the transition from two to three dimensions in a low temperature weakly interacting 6Li Fermi gas. Below a critical atom number N(2D) only the lowest transverse vibrational state of a highly anisotropic oblate trapping potential is occupied and the gas is two dimensional. Above N(2D) the Fermi gas enters the quasi-2D regime where shell structure associated with the filling of individual transverse oscillator states is apparent. This dimensional crossover is demonstrated through measurements of the cloud size and aspect ratio versus atom number.

We present a high-precision determination of the universal contact parameter in a strongly interacting Fermi gas. In a trapped gas at unitarity we find the contact to be 3.06±0.08 at a temperature of 0.08 of the Fermi temperature in a harmonic trap. The contact governs the high-momentum (short-range) properties of these systems and this low temperature measurement provides a new benchmark for the zero temperature homogeneous contact. The experimental measurement utilises Bragg spectroscopy to obtain the dynamic and static structure factors of ultracold Fermi gases at high momentum in the unitarity and molecular Bose-Einstein condensate (BEC) regimes. We have also performed quantum Monte Carlo calculations of the static properties, extending from the weakly coupled Bardeen-Cooper-Schrieffer (BCS) regime to the strongly coupled BEC case, which show agreement with experiment at the level of a few percent. [3,4] and high-energy physics [5,6]. In this context, two-component Fermi gases near a Feshbach resonance have particular significance as they are generally stable against inelastic decay. These universal quantum systems [7][8][9] are characterized by strong coupling in the form of s-wave interactions of short range r 0 and large scattering length a, such that the only scales left are thermodynamical: the density n or chemical potential µ, and temperature T , as for an ideal gas. This situation, in particular the unitarity limit 0 ← k F r 0 1 k F a → ∞, where k F is the Fermi wavevector [10], represents a major theoretical challenge as there are no small parameters. While no exact description exists, a variety of approximate techniques have been developed; however, these often give quite different predictions.One of the key quantities characterizing these systems is the universal contact parameter C, introduced by Tan [11,12]. The contact derives from the short-range correlations in strongly interacting quantum gases and is the cornerstone of a number of exact relations describing properties such as the equation of state and dynamic response functions [13][14][15][16]. Evaluating these exact relations requires precise knowledge of C itself, which is very challenging to compute with different calculations varying by as much as 10% [17,18].In this letter we provide a new experimental benchmark measurement, with error bars at the 3% level, for the contact at unitarity. This is furnished by a precise determination of the dynamic and static structure factors using Bragg spectroscopy. In addition, we present new Quantum Monte Carlo (QMC) calculations accurate to the level of a few percent. Our results indicate that theory and experiment are approaching a new level of convergence, showing that this difficult problem is becoming tractable.Experiments. The experiments presented here use a gas of 6 Li atoms prepared in an equal mixture of the |F = 1/2, m F = ±1/2 spin states, evaporatively cooled in a single-beam optical dipole trap. Interactions are tuned to the unitarity limit by setting the magnetic field to 833.0 G, ne...