Sympathetic Cooling of ${ \rm 139BaH^{+}}$ Using Laser-Cooled ${ \rm 138Ba^{+}}$ in Linear RF Traps

We present the results of simulating sympathetic cooling of ${\rm 139BaH^{+}}$ ions using laser-cooled ${\rm 138Ba^{+}}$ ions in linear RF quadrupole and octupole traps. We show that it is possible to bring ions to a crystal state and obtain $0.1-100$ mK hydrogen. First, ${\rm Ba^{+}}$ and ${\rm BaH^{+}}$ ions are laser ablated from the surface of the barium hydride salt target. Subsequently, these ions can be captured in a linear radio-frequency trap. Once the charged ions are hung in electric fields, ${\rm Ba^{+}}$ ions can be laser cooled using the $493$ nm transition line. Cool ${\rm Ba^{+}}$ ions then interact with hotter ${\rm BaH^{+}}$ ions via Coulomb forces and the ion ensemble cools down as a whole. Finally, hydrogen is photodissociated from the ${\rm BaH^{+}}$ ions using a $\sim 415$ nm laser beam and becomes $\sim 139$ times colder than its parent ion before photodissociation.