Inelastic collision dynamics of a single cold ion immersed in a Bose-Einstein condensate

We investigate inelastic collision dynamics of a single cold ion in a Bose-Einstein condensate. We observe rapid ion-atom-atom three-body recombination leading to the formation of weakly bound molecular ions followed by secondary two-body molecule-atom collisions quenching the rovibrational states towards deeper binding energies. In contrast to previous studies exploiting hybrid ion traps, we work in an effectively field-free environment and generate a free low-energy ionic impurity directly from the atomic ensemble via Rydberg excitation and ionization. This allows us to implement an energy-resolved field-dissociation technique to trace the relaxation dynamics of the recombination products. Our observations are in good agreement with numerical simulations based on Langevin capture dynamics and provide a complementary means to study stability and reaction dynamics of ionic impurities in ultracold quantum gases.

Figure 1

(a)–(c) Low-energy ion production and subsequent inelastic collision dynamics. (a) A single low-energy ${\mathrm{Rb}}^{+}$ ionic impurity is implanted in a BEC via fast electric field ionization (inset indicates the two-pulse ionization sequence) of a precursor Rydberg atom. (b) Ion-atom-atom three-body recombination causes the formation of a weakly bound ${\mathrm{Rb}}_2^{+}$ molecular ion. (c) Secondary molecule-atom collisions lead to ${\mathrm{Rb}}_2^{+}$ rovibrational quenching. (d) ${\mathrm{Rb}}_2^{+}$ molecular potential $V$ as a function of internuclear distance $R$ near the dissociation limit. Binding energies of the most weakly bound vibrational states are denoted as horizontal lines together with three exemplary vibrational wave functions. Black arrows indicate vibrational quenching. An adjustable external electric field $E_{\mathrm{ex}}$ modifies the total potential (gray lines) and allows for energy-resolved dissociation of the molecular ion. (e) Time of flight distribution of ion counts on the MCP after $t=21\mu \mathrm{s}$ and for $E_{\mathrm{ex}}=89\mathrm{V}/\mathrm{cm}$. ${\mathrm{Rb}}^{+}$ ions (${\mathrm{Rb}}_2^{+}$ molecular ions) arrive around $10.1\mu \mathrm{s}$ ($12\mu \mathrm{s}$).

Figure 2

Three-body recombination and molecular ion rovibrational quenching. (a) ${\mathrm{Rb}}^{+}$ (blue squares) and ${\mathrm{Rb}}_2^{+}$ (red diamonds) signal as a function of evolution time $t$ measured with the ${\mathrm{Rb}}_2^{+}$ dissociation field set to $E_{\mathrm{ex}}=89\mathrm{V}/\mathrm{cm}$. Black triangles show the sum of the ${\mathrm{Rb}}^{+}$ and ${\mathrm{Rb}}_2^{+}$ signals. (b) Fraction $\eta$ of detected ${\mathrm{Rb}}_2^{+}$ as a function of the dissociation electric field $E_{\mathrm{ex}}$. Data sets are for $t=6\mu \mathrm{s}$ (diamonds) and $t=21\mu \mathrm{s}$ (squares). ($\mathrm{c}$) $\eta$ as a function of critical molecular binding energy $E_{\mathrm{b}}^{\mathrm{crit}}$, which is the threshold value beyond which molecules are dissociated in the electric field $E_{\mathrm{ex}}$ (see text). The shaded regions are results from numerical simulations of the inelastic collision dynamics.

Figure 3

Distribution $P\left(\nu \right)$ of the most weakly bound states for three different evolution times obtained from the numerical simulations. The data for $t=1\mu \mathrm{s}$ reflect the initial distribution of vibrational states occupied as a result of TBR, whereas data for $t=10\mu \mathrm{s}$ and $t=21\mu \mathrm{s}$ illustrate redistribution to more deeply bound states via atom-molecule collisions.