Strong Coupling of Rydberg Atoms and Surface Phonon Polaritons on Piezoelectric Superlattices

We propose a hybrid quantum system where the strong coupling regime can be achieved between a Rydberg atomic ensemble and propagating surface phonon polaritons on a piezoelectric superlattice. By exploiting the large electric dipole moment and long lifetime of Rydberg atoms as well as tightly confined surface phonon polariton modes, it is possible to achieve a coupling constant far exceeding the relevant decay rates. The frequency of the surface mode can be selected so that it is resonant with a Rydberg transition by engineering the piezoelectric superlattice. We describe a way to observe the Rabi splitting associated with the strong coupling regime under realistic experimental conditions. The system can be viewed as a new type of optomechanical system.

Figure 1

(a) Schematic picture of Rydberg atoms coupled to a SPhP propagating on a PPLN crystal. The laser beams parallel to the surface excite the atoms into Rydberg states. (b) The rubidium atomic energy level scheme used in this work. The SPhPs are resonant with the Rydberg state transition.

Figure 2

Coupling constants for parallel ($\parallel$), perpendicular ($\perp$), and isotropic (iso) orientations of Rydberg atoms at distances of (a) 1 mm, (b) 30 mm, and (c) 100 mm from the PSL surface, respectively. (d) The dispersion curve for the SPhP with parameters as described in the text. $k_y$ is the propagation constant along the $y$ direction of the crystal that is shown in Fig. 1.

Figure 3

Absorption spectrum for the atoms at different distances away from the surface. The probe and coupling laser Rabi frequencies are 1 and 10 MHz, respectively. The PSL and the SPhP are the same as for the other calculations.

Figure 4

$G$ as a function of SPhP frequency. (Inset) $G$ as a function of the distance away from the surface at a SPhP frequency of around 5 GHz. The red line is a guide for the eye.