We show that short-range pair correlations in a strongly interacting Fermi gas follow a simple universal law described by Tan's relations. This is achieved through measurements of the static structure factor which displays a universal scaling proportional to the ratio of Tan's contact to the momentum C/q. Bragg spectroscopy of ultracold 6Li atoms from a periodic optical potential is used to measure the structure factor for a wide range of momenta and interaction strengths, providing broad confirmation of this universal law. We calibrate our Bragg spectra using the f-sum rule, which is found to improve the accuracy of the structure factor measurement.

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 use collective oscillations of a two-component Bose-Einstein condensate (2CBEC) of 87 Rb atoms prepared in the internal states |1 ≡ |F = 1, mF = −1 and |2 ≡ |F = 2, mF = 1 for the precision measurement of the interspecies scattering length a12 with a relative uncertainty of 1.6 × 10 −4 . We show that in a cigar-shaped trap the three-dimensional (3D) dynamics of a component with a small relative population can be conveniently described by a one-dimensional (1D) Schrödinger equation for an effective harmonic oscillator. The frequency of the collective oscillations is defined by the axial trap frequency and the ratio a12/a11, where a11 is the intraspecies scattering length of a highly populated component 1, and is largely decoupled from the scattering length a22, the total atom number and loss terms. By fitting numerical simulations of the coupled Gross-Pitaevskii equations to the recorded temporal evolution of the axial width we obtain the value a12 = 98.006(16) a0, where a0 is the Bohr radius. Our reported value is in a reasonable agreement with the theoretical prediction a12 = 98.13(10) a0 but deviates significantly from the previously measured value a12 = 97.66 a0 [1] which is commonly used in the characterisation of spin dynamics in degenerate 87 Rb atoms. Using Ramsey interferometry of the 2CBEC we measure the scattering length a22 = 95.44(7) a0 which also deviates from the previously reported value a22 = 95.0 a0 [1]. We characterise two-body losses for the component 2 and obtain the loss coefficients γ12 = 1.51(18) × 10 −14 cm 3 /s and γ22 = 8.1(3) × 10 −14 cm 3 /s.