Rapid crystallization of externally produced ions in a Penning trap

We have studied the cooling dynamics, formation process, and geometric structure of mesoscopic crystals of externally produced magnesium ions in a Penning trap. We present a cooling model and measurements for a combination of buffer gas cooling and laser cooling which has been found to reduce the ion kinetic energy by eight orders of magnitude from several hundreds of eV to $\mu \mathrm{eV}$ and below within seconds. With ion numbers of the order of $1\times {10}^3$ to $1\times {10}^5$, such cooling leads to the formation of ion Coulomb crystals which display a characteristic shell structure in agreement with the theory of non-neutral plasmas. We show the production and characterization of two-species ion crystals as a means of sympathetic cooling of ions lacking a suitable laser-cooling transition.

Figure 1

Sectional view of the SpecTrap setup: A, Penning trap; B, magnet; C, LHe dewar; D, ${\mathrm{LN}}_2$ dewar; E, pulsed drift tubes; F, nondestructive ion detector; and G, CCD camera. For details see text.

Figure 2

Schematic of the SpecTrap Penning trap.

Figure 3

Ion energy (black dashed curve, left axis) and scaled fluorescence rate (red curve, right axis) as a function of time during the cooling process.

Figure 4

Phase diagram of the plasma parameter ${\mathrm{\Gamma }}_{\text{p}}$ for the present conditions. Dotted line, Doppler limit of ${\mathrm{Mg}}^{+}$ ions of 1 mK; shaded area, possible ion number densities in thermal equilibrium. For details see text.

Figure 5

Planar-shell model geometry and the involved quantities. This model does not account for correlations in ion position between different shells.

Figure 6

Correlation energy per particle as a function of $\overline{\sigma }=\sigma a_{\text{WS}}^2$ given for various numbers of shells, $S$ (red curve, left-hand scale) and the distance $D$ for which the energy per particle has a minimum as a function of the normalized area (straight blue lines, right-hand scale).

Figure 7

Planar-shell model prediction of the crystal shell structure as a function of $\overline{\sigma }=\sigma a_{\text{WS}}^2$.

Figure 8

Time evolution of the fluorescence signal for three different values of the laser cooling parameters. Blue curves, data; red curves, theory. In all cases, $E=400$ eV and ${\epsilon }_1{E}_0=k_{\text{B}}\times 4$ K.

Figure 9

Left: Appearance time of the fluorescence peak as a function of the initial laser detuning for a constant scan rate of ${\mathrm{\Delta }}_m=2\pi \times 8$ MHz/s. Right: Same as a function of the laser scan rate for constant initial detuning ${\mathrm{\Delta }}_i=-2\pi \times 208$ MHz.

Figure 10

Top: Detected fluorescence during ion cooling and crystal formation extracted from fluorescence images. Bottom: Selected images of the ion cloud during cooling. All images shown are false-color images of the UV fluorescence with light color representing the highest intensity.

Figure 11

(a) CCD image of an ion crystal with scale given. The circle indicates the trapping region visible to the camera. (b) Cross section of the fluorescence, showing four shells.

Figure 12

Images of a ${\mathrm{Mg}}^{+}$ ion crystal with the number of ions and hence shells decreasing with time. For details see text.

Figure 13

Left: Temporal evolution of the ion crystal cross section depicted in Fig. 12. Red dots are theoretical values from the planar-shell model; for details see text. Right: The corresponding residual cross sections. Up to 11 crystal shells can be seen.

Figure 14

Fluorescence signal (bottom left) of a ${\mathrm{Mg}}^{+}$ cloud during the consecutive injection of three bunches of ${\mathrm{CO}}_2{}^{+}$ ions ($m=44$ u) and four capture switching cycles without ion loading (red “X”). Three crystal images (right) show the crystal structure at different times (blue dots in fluorescence signal). The temporal evolution of the cross section for each video frame (top left) reveals the temporal evolution of the crystal structure.