Ionic Impurity in a Bose-Einstein Condensate at Submicrokelvin Temperatures

Rydberg atoms immersed in a Bose-Einstein condensate interact with the quantum gas via electron-atom and ion-atom interaction. To suppress the typically dominant electron-neutral interaction, Rydberg states with a principal quantum number up to $n=190$ are excited from a dense and tightly trapped micron-sized condensate. This allows us to explore a regime where the Rydberg orbit exceeds the size of the atomic sample by far. In this case, a detailed line shape analysis of the Rydberg excitation spectrum provides clear evidence for ion-atom interaction at temperatures well below a microkelvin. Our results may open up ways to enter the quantum regime of ion-atom scattering for the exploration of charged quantum impurities and associated polaron physics.

Figure 1

Concept of the experiment. (a) Potential energy $U_{i,e}$ (black) and $U_e$ (red) as a function of internuclear distance $R$ in the vicinity of the $190S_{1/2}+5S_{1/2}$ asymptote ($U=0$). While $U_e$ only accounts for the electron-neutral interaction, $U_{i,e}$ also includes the interaction with the Rydberg core ion. In the lower panel, nearest (solid), next-nearest (dashed), and next-next-nearest (dash-dotted) neighbor distributions are depicted for a typical density of $3\times {10}^{15}{\mathrm{cm}}^{-3}$. (b) Full spatial range of $U_{i,e}$ shown for three principal quantum numbers for comparison with the spatial extent of the BEC Thomas-Fermi profile (green) along the short trap axis. (c) Illustration of the BEC dimension (green), trapped in the optical tweezer (red), and the size of the $nS$ Rydberg electron orbit (blue) for the Rydberg states in (b).

Figure 2

Rydberg spectroscopy in the BEC. The normalized ion count rate is shown as a function of laser detuning $\delta$ with respect to the bare $|n{S}_{1/2}⟩$ Rydberg resonance ($\delta =0$) for a set of principal quantum numbers $n$ as indicated. Solid lines are Gaussian fits to the data to extract the spectral width $\sigma$. The data sets are offset for better readability and zero count rate is denoted by the dotted lines. The data for $n=40$, 71 are scaled by a factor of 2. Error bars show $1\sigma$ statistical uncertainty. The filled diamonds indicate the center of the excitation spectra predicted from a full numerical simulation (see text). Inset: Spectral width $\sigma$ as a function of principal quantum number. Error bars indicate the confidence interval from the fitting procedure to extract $\sigma$. The solid black (dashed red) line shows the prediction from our numerical simulation with (without) taking the ion-atom interaction into account. Shaded regions indicate the experimental uncertainty in atom number ($\pm 10\%$) and trapping parameters.

Figure 3

Contribution of ion-atom interaction to Rydberg spectra for high-$n$ Rydberg states ($n=160$, 175; inset $n=71$). The normalized ion count rate is shown as a function of laser detuning $\delta$ in the vicinity of the bare $|n{S}_{1/2}⟩$ Rydberg resonance ($\delta =0$). The solid black (dashed red) line shows the result of our full numerical line shape simulation with (without) taking the ion-atom interaction into account. The shaded areas indicate experimental uncertainty dominated by a $\pm 10\%$ error on the atom number [$N=4.8\times {10}^4$ ($71S$); $N=5.1\times {10}^4$ ($160S$); $N=4.6\times {10}^4$ ($175S$)]. Error bars show $1\sigma$ statistical uncertainty.

Figure 4

Collisional lifetime $\tau$ of the Rydberg excitation in the BEC as a function of principal quantum number $n$. The solid line is a fit to the data based on a $\sim n^3$ scaling.