Scale Invariance and Viscosity of a Two-Dimensional Fermi Gas

Abstract

We investigate collective excitations of a harmonically trapped two-dimensional Fermi gas from the collisionless (zero sound) to the hydrodynamic (first sound) regime. The breathing mode, which is sensitive to the equation of state, is observed with an undamped amplitude at a frequency 2 times the dipole mode frequency for a large range of interaction strengths and different temperatures. This provides evidence for a dynamical SO(2,1) scaling symmetry of the two-dimensional Fermi gas. Moreover, we investigate the quadrupole mode to measure the shear viscosity of the two-dimensional gas and study its temperature dependence.

Lattice Boltzmann simulations of a strongly interacting two-dimensional Fermi gas

“…The behavior of the frequencies and damping rates are qualitatively similar to the case of the idealized, harmonic trap case, but shifted to lower values. Since in the experimental setup the sloshing mode frequency is used to calibrate ω ⊥ , such a frequency shift is not apparent in the experimental measurements [10]. Moreover, one finds that in the Gaussian potential trap both the breathing mode and sloshing mode damping rates Γ B , Γ S are no longer consistent with zero, but found to be a small but non-vanishing value, similar to what has been found in experiment [10].…”

“…While we aim to implement this in a follow-up study, for the present work we chose a reference value V0 T0 = 10 that is comparable to experimental values in Ref. [10].…”

“…(31), finding T TF = 0.37 − 0.9 for an average number of atoms of N ≃ 2000 per 2D cloud [10]. Once the temperature and the number of atoms is known, the chemical potential µ 0 at the center of an arbitrary trapping potential can be obtained by numerically inverting Eq.…”

“…[5][6][7][8][9][10][11]. So far, theoretical descriptions of the collective behavior observed in these experiments has mostly been based on (analytic) linear or scaling solutions to hydrodynamic or kinetic equations, see e.g.…”

Path-integral Fujikawa’s approach to anomalous virial theorems and equations of state for systems with SO(2,1) symmetry

“…Hofmann speculates that the experimental negative anomaly findings of the authors of [22] may be explained as a consequence of finite-temperature corrections. The interconnection between zero and finite-temperature effects is indeed non-trivial.…”