Abstract
The role of fluctuations is enhanced in lower dimensionality systems: in a two dimensions off- diagonal long-range order is destroyed by the fluctuations at any finite temperature, drastically modifying the critical properties with respect to the three-dimensional counterpart. Recently two-dimensional systems of interacting fermions have been the subject of Montecarlo studies and experimental investigations, in particular an ultracold gas of attractive fermions with a widely tunable interaction due to a Feshbach resonance has been realized and the Berezinskii- Kosterlitz-Thouless transition has been observed. The present work deals with the theoretical description of an ultracold Fermi gas: we discuss the role of Gaussian fluctuations of the order parameter in the equation of state, in particular we take into account the first sound velocity, showing that the inclusion of order parameter fluctuations is needed in order to get the correct composite-boson limit in the strong-coupling regime. The theory is also compared with experimental data. Finally we focus on the superfluid density in the weak-coupling, intermediate and strong-coupling regimes at finite temperature, through which the Berezinskii-Kosterlitz-Thouless critical temperature is obtained.
Highlights
The present work deals with the theoretical description of an ultracold Fermi gas: we discuss the role of Gaussian fluctuations of the order parameter in the equation of state, in particular we take into account the first sound velocity, showing that the inclusion of order parameter fluctuations is needed in order to get the correct composite-boson limit in the strong-coupling regime
It has been reported that in two dimensions at T = 0 an ultracold Fermi gas is correctly described by the mean-field theory only in the weakcoupling limit, the correct composite boson equation of state of the strong coupling limit being correctly recovered only when the order parameter fluctuations are taken into account [9]
In this work, using a one-loop equation of state, we have calculated the first sound speed and the superfluid density, showing that the Gaussian fluctuations are needed in order to recover the correct composite boson limit even in the zero-temperature case
Summary
The recent experimental realization of an attractive quasi-two-dimensional ultracold Fermi gas with widely tunable interactions [1, 2, 3, 4], the experimental observation of the critical properties [5], along with many Montecarlo investigations [6, 7] renovated the interested in the twodimensional BCS-BEC crossover and motivate further theoretical pursuits in this field. It has been reported that in two dimensions at T = 0 an ultracold Fermi gas is correctly described by the mean-field theory only in the weakcoupling limit, the correct composite boson equation of state of the strong coupling limit being correctly recovered only when the order parameter fluctuations are taken into account [9]. The superfluid density as a function of the crossover allows one to determine the BerezinskiiKosterlitz-Thouless critical temperature [12, 13] through the Kosterlitz-Nelson condition [14]
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