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...

Thermodynamic properties of matter are conveniently expressed as functional relations between variables known as equations of state. Here we experimentally determine the compressibility, density, and pressure equations of state for an attractive 2D Fermi gas in the normal phase as a function of temperature and interaction strength. In 2D, interacting gases exhibit qualitatively different features to those found in 3D. This is evident in the normalized density equation of state, which peaks at intermediate densities corresponding to the crossover from classical to quantum behavior.

Ultracold Fermi gases subject to tight transverse confinement offer a highly controllable setting to study the two-dimensional (2D) BCS to Berezinskii-Kosterlitz-Thouless superfluid crossover. Achieving the 2D regime requires confining particles to their transverse ground state which presents challenges in interacting systems. Here, we establish the conditions for an interacting Fermi gas to behave kinematically 2D. Transverse excitations are detected by measuring the transverse expansion rate which displays a sudden increase when the atom number exceeds a critical value N2D signifying a density driven departure from 2D kinematics. For weak interactions N2D is set by the aspect ratio of the trap. Close to a Feshbach resonance, however, the stronger interactions reduce N2D and excitations appear at lower density.PACS numbers: 03.75. Ss, 03.75.Hh, 05.30.Fk, 67.85.Lm Fermions confined to two-dimensional (2D) planes represent an important paradigm in many-body physics in settings ranging from thin films of superfluid helium-3 [1, 2] to the superconducting planes in high-T c cuprates [3]. Ultracold atomic gases confined in oblate potentials allow access to the 2D regime [4][5][6][7][8][9][10][11][12][13][14][15] where interactions between particles can be controlled using a Feshbach resonance [16]. In 2D Fermi gases, one can realize the BCS to Berezinskii-Kosterlitz-Thouless (BKT) superfluid crossover [17][18][19][20][21][22][23][24][25] by tuning the attractive interaction between particles in different spin states. Of particular interest is the enhanced pairing due to the transverse confinement [26][27][28][29][30] and the consequences this has for the phase diagram of the crossover [15,[31][32][33].Theoretical studies of the BCS-BKT crossover generally assume only two spatial dimensions, however, all atomic gases exist in 3D environments. Lower dimensional behaviour can be realized by freezing out dynamics along one or more directions. For atoms in a harmonic potential, with frequencies ω x , ω y and ω z , the 2D regime is achieved when the transverse (z) confinement is strong enough that occupation of transverse excited states is energetically forbidden. When a gas is frozen in the transverse ground state, dynamics in the x-y plane become decoupled from z and the gas is kinematically 2D. In an ideal gas this requires the thermal energy and chemical potential be much smaller than the transverse confinement energy k B T, µ ω z , where k B is Boltzmann's constant, T is the temperature and µ the chemical potential. When interactions are present, however, these can provide another means for generating transverse excitations which go beyond purely 2D models.In this Rapid Communication, we examine the criteria for an interacting Fermi gas to behave kinematically 2D.By measuring the transverse cloud width after time of flight we observe a rapid growth in the expansion rate when transverse excitations are present. Both the trap geometry and interaction strength are seen to limit the parameter space where interacting sys...