Collective excitations of a harmonically trapped, two-dimensional, spin-polarized dipolar Fermi gas in the hydrodynamic regime

The collective excitations of a zero-temperature, spin-polarized, harmonically trapped, two-dimensional dipolar Fermi gas are examined within the Thomas-Fermi–von Weizsäcker hydrodynamic theory. We focus on repulsive interactions and investigate the dependence of the excitation frequencies on the strength of the dipolar interaction and particle number. We find that the mode spectrum can be classified according to bulk modes, whose frequencies are shifted upward as the interaction strength is increased, and an infinite ladder of surface modes, whose frequencies are independent of the interactions in the large particle limit. We argue quite generally that it is the local character of the two-dimensional energy density that is responsible for the insensitivity of surface excitations to the dipolar interaction strength and not the precise form of the equation of state. This property will not be found for the collective excitations of harmonically trapped, dipolar Fermi gases in one and three dimensions, where the energy density is manifestly nonlocal.

Figure 1

Collective excitation frequencies ${\omega }_{m,n}$ for $N={10}^3$ atoms. Here $C_{dd}$ is dimensionless, as defined in Eq. (14), and the curves are labeled by $(m,n)$. Note that for this particle number, the ${\omega }_{m,0}$ modes appear to be independent of the interaction strength on the scale of the plot.

Figure 2

Collective excitation frequencies ${\omega }_{m,0}$ for $N={10}^2$ (solid curves) and $N={10}^5$ (dashed curves) atoms. This figure illustrates that for large particle numbers, the ${\omega }_{m,0}$ modes become independent of the interaction strength. As shown in Eq. (47), the dashed curves have the frequency ${\omega }_{m,0}=\sqrt{m}$.

Figure 3

Same as in Fig. 1 but for $N={10}^5$ atoms.

Figure 4

Collective excitation frequencies ${\omega }_{m,n}$ at fixed $C_{dd}=2.6$ as a function of the particle number. We have not displayed the ${\omega }_{m,0}$ modes here as they exhibit no dispersion on the scale of the plot.

Figure 5

Density fluctuations corresponding to the ${\omega }_{1,0}$ dipolar (Kohn) mode. The left panel corresponds to $N={10}^2$ particles and the right panel to $N={10}^5$ particles. Within each panel, from left to right, we have $C_{dd}=0,5,10,20,40$, respectively.

Figure 6

Same as in Fig. 5 but for the ${\omega }_{5,0}$ mode.