Measuring impurity-induced shifts in Coulomb crystallization

Abstract

We report a laboratory measurement of how impurities shift Coulomb crystallization in a strongly interacting ionic system. This is achieved by using laser cooled Ca$^+$ crystals doped with a controlled number of Xe$^{12+}$ highly charged ions. We find that the crystallization threshold is unchanged at low impurity concentration, but shows a clear crossover once the impurity content becomes sufficiently large, after which the shift grows approximately linearly. Complementary measurements reveal that this global effect originates from a local pinning of the crystal around the impurities. We further show how the measured shift could impact standard models of crystallization in white dwarfs and neutron stars. Our results provide an experimental route to incorporating impurity effects into models of multicomponent Coulomb matter, relevant to stellar crystallization and strongly coupled plasmas.

Figures (7)

• Figure 1: a) Fluorescence images of samples of 50 $\pm$ 5 Ca$^+$ ions across the liquid-to-crystal crossover. The observable voids are caused by Xe$^{12+}$ ions, acting as dopants. The number of Xe HCIs increases from left to right (the first column is the undoped reference). The trapping frequencies in the first row are $(\omega_x,\omega_y,\omega_z)=2\pi\times(192,262,164)$ kHz. By increasing the radial confinement (from top to bottom), corresponding to increasing the Coulomb parameter $\Gamma$, we observe the progressive onset of crystallization. The radial frequencies in the last row are $(\omega_x,\omega_y)=2\pi\times(888,897)$ kHz. Each image is $\simeq330\times110$$\mu$m, and the exposure time is 300 ms. b) The same as a) but with 191 $\pm$ 23 Ca$^+$ ions.
• Figure 2: The purple line is the measured value of the normalized critical Coulomb parameter $\gamma=\Gamma_c(Q_{imp})/\Gamma_c(0)$ as a function of the impurity parameter $Q_{imp}$. The shaded area corresponds to the standard deviation SM. The color scale of the underlying contour plot is the normalized Tenengrad deviation $\delta=\Delta\langle \mathcal{T}\rangle/\langle \mathcal{T}(0)\rangle$.
• Figure 3: Lindemann parameter $\mathcal{L}$ as a function of the normalized radial pressure $\Pi$ and the impurity parameter $Q_{imp}$. The green line corresponds to the condition $\mathcal{L}=0.1$, which approximately sets the boundary between the liquid and the crystal phases.
• Figure 4: Evaluation of the potential impact of the impurity-induced shift of crystallization measured in this work on stellar models. a) Relative shift in the luminosity at crystallization onset in white dwarfs. b) Corresponding shift in the crystallization age. (c) Shift in the crystallization density in the neutron-star crust at fixed temperature. The shaded areas correspond to the average uncertainty in $\gamma$SM.
• Figure S1: Average Tenengrad $\langle\mathcal{T}\rangle$ for a sample of 250 $\pm$ 30 (left) and 21 $\pm$ 2 (right) Ca$^+$ ions containing a variable number of Xe$^{12+}$ impurity ions. The horizontal dashed lines are the threshold $\langle\mathcal{T}\rangle_{ thr}$, calculated as explained in the text.