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arXiv:1411.4703 · Physical Review A

Criteria for two-dimensional kinematics in an interacting Fermi gas

Paul Dyke, Kristian Fenech, Tyson Peppler, Marcus Lingham, Sascha Hoinka, W. Zhang, Shi-Guo Peng, Brendan C. Mulkerin, Hui Hu, Xia-Ji Liu, Chris J. Vale

Published Jan 14, 2016• 30 citations
arXivHTMLPDF

Abstract

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 display 2D kinematics. 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.

DOI
10.1103/physreva.93.011603

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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 display 2D kinematics. Transverse excitations are detected by measuring the transverse expansion rate which displays a sudden increase when the atom number exceeds a critical value N2D{N}_{2D}N2D​ signifying a density driven departure from 2D kinematics. For weak interactions N2D{N}_{2D}N2D​ is set by the aspect ratio of the trap. Close to a Feshbach resonance, however, the stronger interactions reduce N2D{N}_{2D}N2D​ and excitations appear at lower density.
Spatial profiles of the pressure have been measured in atomic Fermi gases with primarily two-dimensional (2D) kinematics. The in-plane motion of the particles is confined by a Gaussian-shape potential. The two-component deeply degenerate Fermi gases are prepared at different values of the sss-wave attraction. The pressure profile is found using the force-balance equation, from the measured density profile and the trapping potential. The pressure is compared to zero-temperature models within the local density approximation. In the weakly interacting regime, the pressure lies above a Landau Fermi-liquid theory and below the ideal-Fermi-gas model, whose prediction coincides with that of the Cooper-pair mean-field theory. The values closest to the data are provided by the approach where the mean field of Cooper pairs is supplemented with fluctuations. In the regime of strong interactions, in response to the increasing attraction, the pressure shifts below this model reaching lower values calculated within Monte Carlo methods. Comparison to models shows that interaction-induced departure from 2D kinematics is either small or absent. In particular, comparison with a lattice Monte Carlo suggests that kinematics is two dimensional in the strongly interacting regime.
This work studies zero-temperature Fermi gases with short-ranged and attractive interactions with focus on the dimensionality aspects by confining the system from three to two dimensions. Interacting Fermi gases are superfluids characterized as being strongly correlated if the scattering length is much larger than the other scales present. In the many-body context, this category of systems requires a careful treatment since mean-field approaches are not expected to hold under the conditions which define the strong pairing. For this reason, we employ quantum Monte Carlo methods to study the dimensionality effects in two-component Fermi gases in the Bardeen-Cooper-Schrieffer to Bose-Einstein condensate (BCS-BEC) crossover. To be able to investigate such aspects, we consider a three-dimensional gas with periodic boundary conditions in the xy plane and a confining potential in the z direction capable of reducing the dimensionality of the system, which defines a dimensional BCS-BEC crossover. We calculate the equation of state as the energy per particle as a function of the dimensionality and as a function of the interaction parameter, which are characterized by the oscillator length in the z direction and the scattering length respectively. The greater confinement in the system lowers the interparticle distances, which increases the effects of the attractive interactions between antiparallel-spin fermions.We also calculate the density profile in the z direction over the crossover for different confinements and different interaction parameters to quantify their influence on the spatial distribution of the particles. This study connects the perspectives between theoretical and experimental works in low-dimensional ultracold Fermi gases by utilizing an approach that is similar to what it is realized in modern experiments.
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.
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We investigate the properties of a spin-orbit coupled quasi-two-dimensional Fermi gas with tunable sss-wave interaction between the two spin species. By analyzing the two-body bound state, we find that the population of the excited states in the tightly confined axial direction can be significant when the two-body binding energy becomes comparable to or exceeds the axial confinement. Since the Rashba spin-orbit coupling that we study here tends to enhance the two-body binding energy, this effect can become prominent at unitarity or even on the BCS side of the Feshbach resonance. To study the impact of these excited modes along the third dimension, we adopt an effective two-dimensional Hamiltonian in the form of a two-channel model, where the dressed molecules in the closed channel consist of the conventional Feshbach molecules as well as the excited states occupation in the axial direction. With properly renormalized interactions between atoms and dressed molecules, we find that both the density distribution and the phase structure in the trap can be significantly modified near a wide Feshbach resonance. In particular, the stability region of the topological superfluid phase is increased. Our findings provide a proper description for a quasi-two-dimensional Fermi gas under spin-orbit coupling, and are helpful for the experimental search for the topological superfluid phase in ultracold Fermi gases.
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