Single Ion as a Three-Body Reaction Center in an Ultracold Atomic Gas

We report on three-body recombination of a single trapped ${\mathrm{Rb}}^{+}$ ion and two neutral Rb atoms in an ultracold atom cloud. We observe that the corresponding rate coefficient $K_3$ depends on collision energy and is about a factor of 1000 larger than for three colliding neutral Rb atoms. In the three-body recombination process large energies up to several 0.1 eV are released leading to an ejection of the ion from the atom cloud. It is sympathetically recooled back into the cloud via elastic binary collisions with cold atoms. Further, we find that the final ionic product of the three-body processes is again an atomic ${\mathrm{Rb}}^{+}$ ion suggesting that the ion merely acts as a catalyzer, possibly in the formation of deeply bound ${\mathrm{Rb}}_2$ molecules.

Figure 1

Decay of the atom cloud under influence of a single trapped ion. (a) Remaining atom numbers after interaction time $\tau$ for an ion with $E_{\mathrm{ion}}\approx 35\mathrm{mK}·k_{\mathrm{B}}$ [18] and $n_{\mathrm{at}}\approx {10}^{11}{\mathrm{cm}}^{-3}$. The solid line indicates the decay of the mean atom number. (b) Same as (a) but $E_{\mathrm{ion}}\approx 0.5\mathrm{mK}·k_{\mathrm{B}}$ [18] and $n_{\mathrm{at}}\approx 1.1\times {10}^{12}{\mathrm{cm}}^{-3}$. (c) Histograms containing the data shown in (b).

Figure 2

(a) Illustration of an atom-atom-ion collision. (I) Two atoms simultaneously enter the interaction radius of the ion and a three-body process takes place. (II) The three-body reaction ejects the ion onto a trajectory much larger than the atom cloud. (b) Illustration of our simple model. Left: Various possible time traces for the atom number. If only binary atom-ion collisions occur the atomic sample decays exponentially (Trace $T_1$). Three-body events ($E_2$, $E_3$) interrupt the atom loss until the atom is recooled and reenters the sample at point $R_2$ (Traces $T_2$ and $T_3$). Right: Atom number histogram from Fig. 1c ($\tau =8\mathrm{s}$) and the corresponding simulation result (solid black line). (c) Plot of the probability $P_{\mathrm{three}\mathrm{\text{−}}\mathrm{body}}$ for initial atomic densities $(1.8,1.1,0.7,0.3)\times {10}^{12}{\mathrm{cm}}^{-3}$ and atom numbers $(6.5,4.0,2.8,1.6)\times {10}^4$, respectively. The solid lines are results of the numerical simulation.

Figure 3

(a) Probing the ion’s presence using an atom cloud. A low (high) remaining atom number $N_{\mathrm{at}}$ signals the presence (absence) of an ion. For better visibility, we have slightly offset in energy the black squares corresponding to ions that have participated in a three-body process from the grey circles corresponding to ions where purely binary collisions were detected. (b) Ion loss probability $P_{\mathrm{loss}}$ calculated from the data in (a). The continuous lines are fits to the data using a broadened step function. The trap depths $U_{\mathrm{red}}$ are determined for our Paul trap geometry using methods detailed in Ref. 22 for both ${\mathrm{Rb}}^{+}$ (bottom abscissa scale) and ${\mathrm{Rb}}_2^{+}$ (top). A trap with negative trap depth value is nontrapping.

Figure 4

(a) $P_{\mathrm{three}\mathrm{\text{−}}\mathrm{body}}$ as a function of the external electric field. (b) Double-logarithmic plot of $P_{\mathrm{three}\mathrm{\text{−}}\mathrm{body}}$ as a function of the ion energy $E_{\mathrm{ion}}$ [18]. A scale for the three-body coefficients $K_3$ as derived from the simulation is also given (see text for details).