Collective oscillations in ultracold atomic gas

Using both fluid and kinetic descriptions, with repulsive forces between nearby atoms included, we discuss the basic oscillations and waves of a cloud of ultracold atoms confined in a magneto-optical trap. The existence of a hybrid mode, with properties similar to both plasma and acoustic waves, is described in detail. Tonks-Dattner resonances for confined hybrid modes in a spherical cloud are discussed, and the prediction of a nonlinear coupling between the dipole resonance and the hybrid modes is considered. Landau damping processes and quasilinear diffusion in velocity space are also discussed.

Figure 1

(Color online) Normalized dispersion relation $\omega /{\omega }_P$ plotted against $k{\lambda }_D$. The red dashed line represents the acoustic asymptotic behavior of the hybrid waves.

Figure 2

(Color online) Normalized modes ${\omega }_{\nu ,l}^2/{\omega }_P^2$ plotted against the nodes $r_{\nu ,l}/a$ of the radial solution for the density perturbation $\tilde{n}$, for ${\lambda }_D/a=0.1$ and $1<\nu <10$. Blue squares $\left(l=0\right)$, red circles $\left(l=1\right)$, violet stars $\left(l=2\right)$, yellow triangles $\left(l=3\right)$, and green open circles $\left(l=4\right)$. The full line is plotted at $l=0$ and scales as $1/{\nu }^2$.

Figure 3

(Color online) Normalized roots of Eq. (39) in terms of the dimensionless quantities $\Omega =\omega /{\omega }_p$, $K=\vec{k}\cdot {\vec{v}}_1/{\omega }_p$, and $N=n_1/n_0$. (a) Dimensionless growth rate $\Gamma \left(K\right)=+{\Omega }_i\left(K\right)$ (unstable solutions) and (b) dimensionless modes ${\Omega }_r\left(K\right)$ (stable solutions). In both plots, $N=1$ (full black line), 1/2 (dashed violet line), and 1/3 (dotted blue line).