Rydberg Molecule-Induced Remote Spin Flips

We have performed high resolution photoassociation spectroscopy of rubidium ultralong-range Rydberg molecules in the vicinity of the $25P$ state. Because of the hyperfine interaction in the ground state perturber atom, the emerging mixed singlet-triplet potentials contain contributions from both hyperfine states. We show that this can be used to induce remote spin flips in the perturber atom upon excitation of a Rydberg molecule. Furthermore, when the spin-orbit splitting of the Rydberg state is comparable to the hyperfine splitting in the ground state, the orbital angular momentum of the Rydberg electron is entangled with the nuclear spin of the perturber atom. Our results open new possibilities for the implementation of spin-dependent interactions for ultracold atoms in bulk systems and in optical lattices.

Figure 1

(a) The contact interaction between the Rydberg electron $e^{-}$ and the ground state atom Rb leads to a spin-dependent interaction over distances up to 50 nm in the $25P$ state. (b) The angular momentum coupling scheme shows how the spin-spin interaction (SS) couples the fine structure (FS) of the Rydberg atom with the hyperfine structure (HFS) of the perturber. The color of the arrows corresponds to the colors used in (a). (c) Transition scheme. When the sample is in the $F=2$ ground state, only the atomic transitions to states adiabatically connecting to $F=2$ states are possible (red arrows). Because of the hyperfine mixing of the molecular interaction (see text), transitions to molecular states in the $F=1$ spectrum are also possible (purple arrows).

Figure 2

(a) Adiabatic PECs for ultralong-range Rydberg molecules of rubidium 87. The PECs adiabatically connect to the four different $25P$ states. The blue PECs are of pure triplet type and do not mix the hyperfine states, the orange PECs are of mixed singlet-triplet character and contain both hyperfine states. The red numbers give the admixture of opposite spin to the states in the respective wells of the potential. (b) and (c) show the measured TOF spectrum for a BEC prepared in a pure $F=2$ and $F=1$ state, respectively. The energy scale coincides with the one of (a). The time of flight is $58\mu \mathrm{s}$ for the ${\mathrm{Rb}}^{+}$ ions and $82\mu \mathrm{s}$ for the ${\mathrm{Rb}}_2^{+}$. The deep blue regions were not measured. The white lines show the flight-time integrated spectrum. The insets (d) and (e) show zoom ins on highlighted parts of the $F=2$ spectrum, illustrating the entanglement and the spin-flip regime, respectively. The employed TOF measurement technique allows us to extract the lifetime of the observed molecular resonances to an accuracy of $1\mu \mathrm{s}$ by fitting the temporal decay of the signal with an exponential function.

Figure 3

Comparison of the molecular spectra in the region between the $25P_{3/2}$, $F=1$ state (0 MHz) and the $25P_{1/2}$, $F=2$ state ($-929\mathrm{MHz}$) in a sample with all atoms in the $F=1$ state (blue) and all atoms in the $F=2$ state (red). Since, in the $F=2$ spectrum, we only observe the mixed type PEC (see text) that also appears in the $F=1$ spectrum, every line in the $F=2$ spectrum has a corresponding line in the $F=1$ spectrum (orange lines). The calculated energies of the lowest bound states in each well of the mixed type PEC (green bars) agree with the observed resonances. Compared to the $F=1$ spectrum, the $F=2$ spectrum is magnified by a factor of 16. Because of an uncertainty in the frequency calibration, the $F=2$ measurement was stretched by 2% in accordance with the frequency mismatch observed in comparable measurements.