Rydberg-Rydberg interaction profile from the excitation dynamics of ultracold atoms in lattices

We propose a method for the determination of the interaction potential of Rydberg atoms. Specifically, we consider a laser-driven Rydberg gas confined in a one-dimensional lattice and demonstrate that the Rydberg atom number after a laser excitation cycle as a function of the laser detuning provides a measure for the Rydberg interaction coefficient. With the lattice spacing precisely known, the proposed scheme only relies on the measurement of the number of Rydberg atoms and thus circumvents the necessity to map the interaction potential by varying the interparticle separation.

Figure 1

Schematics of the considered setup. Ultracold atoms in a lattice are excited from the ground-state $|g\rangle$ (blue/dark gray) to their Rydberg state $\left|e\right.〉$ (red/light gray). The Rydberg-Rydberg interaction shifts the excitation from its single atom resonance (top of the figure). This dipole blockade effect can be compensated for by the laser detuning $\Delta$. In this particular example, the excitation is resonant to the many-body state $|geegeeg\rangle$.

Figure 2

(a) Total number of Rydberg atoms and (b) number of neighboring Rydberg excitations after the laser excitation of an $N=8$ lattice of ground-state atoms as a function of the detuning from the single atom resonance; a laser coupling strength of $\Omega =0.15V$ is considered. The thin gray lines correspond to excitation durations of $T=15,18,21,24,$ and $27{\Omega }^{-1}$. The thick red line is an average over many different laser cycle times. (c) Energy spectrum for the same setup. The dashed line represents the canonical ground-state $|G\rangle$ for $\Omega =0$. The peaks of panels (a) and (b) occur at the points where $|G\rangle$ crosses many-body states possessing different numbers of Rydberg excitations, as described by Eq. (6).