Direct Laser Cooling of Rydberg Atoms with an Isolated-Core Transition

We propose a scheme to directly laser cool Rydberg atoms by laser cooling the residual ion core within the Rydberg-electron orbit. The scheme is detailed for alkaline-earth-metal Rydberg atoms, whose ions can be easily laser cooled. We demonstrate that a closed optical cooling cycle can be found despite the perturbations caused by the Rydberg electron and that this cycle can be driven over more than $100\mathrm{\mu }\mathrm{s}$ to achieve laser cooling. The cooling dynamics with and without the presence of magnetic fields are discussed in detail.

Figure 1

(a) Schematic representation of Rydberg-atom laser cooling with an isolated-core transition. (b) Schematic view of the energy-level structure of $4s_{1/2}nl$, $4p_{1/2}nl$, and $3d_{3/2}nl$ Rydberg series. (c) Energy-level structure of the relevant ${}^{40}\mathrm{Ca}$ Rydberg states ($n=55$, $l=12$), without ($E^0$) and with ($E^0+\mathrm{\Delta }{E}^{(1)}+\mathrm{\Delta }{E}^{(2)}$) residual electron interaction. Energy splittings are in units of $h·\mathrm{MHz}$.

Figure 2

Time evolution of the populations of Rydberg states ($n=55$, $l=12$) with $4s_{1/2}$ (orange line), $3d_{3/2}$ (red line), and $4p_{1/2}$ (green line) ion-core states, obtained by summing the populations of states with different values of $K$ and $M_K$ but identical values of $n_c$, $l_c$, and $j_c$. The photon-scattering rate $\mathrm{\Gamma }$ for the cooling transition is shown as the black line. The dynamics for the isolated ion are shown by the pale gray lines.

Figure 3

(a) Energy levels of the $4s_{1/2}n{l}_{K{M}_K}$, $3d_{3/2}n{l}_{K{M}_K}$, and $4p_{1/2}n{l}_{K{M}_K}$ states in the presence of a $20\mathrm{\mu }\mathrm{T}$ magnetic field ($n=55$, $l=12$). (b) Top graph: time evolution of the ion-core populations and photon-scattering rate (the same as Fig. 2). Lower graphs: time evolution of the population of each of the 200 sublevels involved in the cooling.