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Physical Review A

Mean-field analysis of dimensional crossover from two dimensions to three dimensions in a weakly interacting Fermi gas

Hui Hu

Published Nov 21, 2011• 3 citations
Publisher

Abstract

We investigate theoretically the transition from two to three dimensions in a weakly interacting ultracold Fermi gas. This transition was recently observed by Dyke et al. [Phys. Rev. Lett. 106, 105304 (2011)] in a cloud of fermionic ${}^{6}$Li atoms trapped in an oblate harmonic potential. We calculate the density distribution and cloud size of the Fermi cloud by numerically solving three-dimensional Hartree-Fock mean-field equations. Local density approximation is used to ease the calculations in the weakly confined radial direction. Our theoretical results are shown to be in good agreement with the experimental measurements.

DOI
10.1103/physreva.84.053624

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We calculated and measured the density distribution and cloud size of a trapped two-dimensional (2D) 6 Li Fermi gas near a Feshbach resonance at low temperatures. Density distributions and cloud sizes were calculated for a wide range of interaction parameters using a local density approximation (LDA) and a zero-temperature equation of state obtained from quantum Monte Carlo simulations reported by Bertaina and Giorgini (2011 Phys. Rev. Lett. 106 110403). We found that LDA predictions agree well with experimental measurements across a Feshbach resonance. Theoretical results for Tan's contact parameter in a trapped gas are reported here along with predictions for the static structure factor at large momentum which could be measured in future Bragg spectroscopy experiments on 2D Fermi gases.
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We address the interplay between dimension and quantum anomaly on the breathing mode frequency of a strongly interacting Fermi gas harmonically trapped at zero temperature. Using a beyond-mean-field Gaussian pair fluctuation theory, we employ periodic boundary conditions to simulate the dimensionality of the system and impose a local-density approximation, with two different schemes, to model different trapping potentials in the tightly confined axial direction. By using a sum-rule approach, we compute the breathing mode frequency associated with a small variation of the trapping frequency along the weakly confined transverse direction and describe its behavior as a function of the dimensionality, from two to three dimensions, and of the interaction strength. We compare our predictions with previous calculations on the two-dimensional breathing mode anomaly and discuss their possible observation in ultracold Fermi gases of 6Li^{6}\mathrm{Li}6Li and 40K^{40}\mathrm{K}40K atoms.