Coulomb Crystallization in Expanding Laser-Cooled Neutral Plasmas

We present long-time simulations of expanding ultracold neutral plasmas, including a full treatment of the strongly coupled ion dynamics. Thereby, the relaxation of the expanding laser-cooled plasma is studied, taking into account elastic as well as inelastic collisions. It is demonstrated that, depending on the initial conditions, the ionic component of the plasma may exhibit short-range order or even a superimposed long-range order resulting in concentric ion shells. In contrast to ionic plasmas confined in traps, the shell structures build up from the center of the plasma cloud rather than from the periphery.

Figure 1

The size of a laser-cooled plasma as compared to that of a freely expanding plasma of the same initial-state parameters (dotted line). The solution of Eq. (2) (dashed line) matches the particle-in-cell treatment (circles), showing that the difference to the hybrid-MD simulation (solid line) comes from the ionic correlations. The inset shows a comparison of the numerical solution with the analytical approximation [Eq. (3)].

Figure 2

Distribution of scaled interionic distances after a time of $t=52\mu \mathrm{s}$ (${\omega }_{p0}t=240$) compared to the calculated pair-correlation function of an OCP at ${\Gamma }_i=700$. The inset shows the ionic CCP calculated by different methods (see text).

Figure 3

Radial density after a time of $t=24\mu \mathrm{s}$ (${\omega }_{p0}t=110$). The inset shows a two-dimensional cut through the plasma cloud, clearly revealing the formation of concentric shells. (For better contrast, cuts with $x=0$, $y=0$, and $z=0$, respectively, have been overlayed.)

Figure 4

The fifth shell of Fig. 3, demonstrating significant intrashell ordering.