Polyatomic Trilobite Rydberg Molecules in a Dense Random Gas

Trilobites are exotic giant dimers with enormous dipole moments. They consist of a Rydberg atom and a distant ground-state atom bound together by short-range electron-neutral attraction. We show that highly polar, polyatomic trilobite states unexpectedly persist and thrive in a dense ultracold gas of randomly positioned atoms. This is caused by perturbation-induced quantum scarring and the localization of electron density on randomly occurring atom clusters. At certain densities these states also mix with an $s$ state, overcoming selection rules that hinder the photoassociation of ordinary trilobites.

Figure 1

Electron density of a highly polar $n=50$ rubidium trilobite state at atom density $\rho ={10}^{16}{\mathrm{cm}}^{-3}$. The electron density is visualized using a contour surface (in blue) that contains 42% of the total probability mass. The small (red) spheres denote the locations of the perturbing atoms. For visibility, their radius is approximately twice the electron-atom scattering length. The electron density is localized around the highlighted cluster of three atoms (in yellow). The Rydberg core (in green) is at the origin, and the radius of the spherical cloud of atoms is the classically allowed radius $r_{\mathrm{c}}=5000$. For comparison, the inset shows an equal visualization of the ordinary trilobite state [1] with $n=30$ and a single atom at $R=1232$. The visualization was done with Mayavi [25].

Figure 2

Probability distribution of the dipole moment of the $n=50$ trilobite state as a function of the atom density $\rho$. The solid line shows the median value and the edges of the two shaded regions denote the 5th, 25th, 75th, and 95th percentiles. The dashed line denotes the mean value. The dotted line shows the probability that a snapshot of $\{R_p\}$ contains at least one cluster where three atoms are located within 300 a.u. of each other. The values are estimated from an ensemble of $10^4$ snapshots of the atom locations.

Figure 3

Probability distribution of the energy of the $n=50$ trilobite state and the $53s$ state as a function of the atom density $\rho$. The zero of energy is chosen at the degenerate $n=50$ hydrogen manifold. The probability distribution is visualized through its mean and percentile curves and estimated from an ensemble as in Fig. 2.

Figure 4

Distribution of the magnitude of $l=0$ character in the $n=50$ trilobite state, i.e., the squared overlap between the unperturbed $53s$ state and the trilobite state, as a function of the atom density $\rho$. The probability distribution is visualized through its mean and percentile curves and is estimated from an ensemble as in Fig. 2.