Criteria for 2D kinematics in an interacting Fermi gas

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 $N_{2D}$ signifying a density driven departure from 2D kinematics. For weak interactions $N_{2D}$ is set by the aspect ratio of the trap. Close to a Feshbach resonance, however, the stronger interactions reduce $N_{2D}$ and excitations appear at lower density.

Temperature dependence of the contact in a unitary Fermi gas

The contact ${cal I}$, introduced by Tan, has emerged as a key parameter characterizing universal properties of strongly interacting Fermi gases. For ultracold Fermi gases near a Feshbach resonance, the contact depends upon two quantities: the interaction parameter $1/(k_F a)$, where $k_F$ is the Fermi wave-vector and $a$ is the $s$-wave scattering length, and the temperature $T/T_F$, where $T_F$ is the Fermi temperature. We present the first measurements of the temperature dependence of the contact in a unitary Fermi gas using Bragg spectroscopy. The contact is seen to follow the predicted decay with temperature and shows how pair-correlations at high momentum persist well above the superfluid transition temperature.

Crossover from 2D to 3D in a weakly interacting Fermi gas

We have studied the transition from two to three dimensions in a low temperature weakly interacting $^6$Li 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.

Bragg spectroscopy of a strongly interacting Fermi gas

We present a comprehensive study of the Bose-Einstein condensate to Bardeen-Cooper-Schrieffer (BEC-BCS) crossover in fermionic $^6$Li using Bragg spectroscopy. A smooth transition from molecular to atomic spectra is observed with a clear signature of pairing at and above unitarity. These spectra probe the dynamic and static structure factors of the gas and provide a direct link to two-body correlations. We have characterised these correlations and measured their density dependence across the broad Feshbach resonance at 834 G.

A self-interacting partially directed walk subject to a force

We consider a directed walk model of a homopolymer (in two dimensions) which is self-interacting and can undergo a collapse transition, subject to an applied tensile force. We review and interpret all the results already in the literature concerning the case where this force is in the preferred direction of the walk. We consider the force extension curves at different temperatures as well as the critical-force temperature curve. We demonstrate that this model can be analysed rigorously for all key quantities of interest even when there may not be explicit expressions for these quantities available. We show which of the techniques available can be extended to the full model, where the force has components in the preferred direction and the direction perpendicular to this. Whilst the solution of the generating function is available, its analysis is far more complicated and not all the rigorous techniques are available. However, many results can be extracted including the location of the critical point which gives the general critical-force temperature curve. Lastly, we generalise the model to a three-dimensional analogue and show that several key properties can be analysed if the force is restricted to the plane of preferred directions.

Binding Energies of 6Li p-wave Feshbach Molecules

We present measurements of the binding energies of $^6$Li p-wave Feshbach molecules formed in combinations of the (F = 1/2, m_F = +1/2), (1), and (F = 1/2, m_F = -1/2), (2), states. The binding energies scale linearly with magnetic field detuning for all three resonances. The relative molecular magnetic moments are found to be $113 pm 7 mu$K/G, $111 pm 6 mu$K/G and $118 pm 8 mu$K/G for the (1)-(1), (1)-(2) and (2)-(2) resonances, respectively, in good agreement with theoretical predictions. Closed channel amplitudes and the size of the p-wave molecules are obtained theoretically from full closed-coupled calculations.