Laser manipulation of spin-exchange interaction between alkaline-earth atoms in 1S0 and 3P2 states

Abstract

Ultracold gases of fermionic alkaline-earth(-like) atoms are hopeful candidates for the quantum simulation of many-body physics induced by magnetic impurities (e.g., the Kondo physics), because there are spin-exchange interactions (SEIs) between two atoms in the electronic ground ($^{1}\mathrm{S}_{0}$) and metastable ($^{3}\mathrm{P}$) state, respectively. Nevertheless, this SEI cannot be tuned via magnetic Feshbach resonance. In this paper, we propose three methods to control the SEI between one atom in the $^{1}\mathrm{S}_{0}$ state and another atom in the $^{3}\mathrm{P}_{2}$ states or $^{3}\mathrm{P}_{2}\text{\ensuremath{-}}^{3}\mathrm{P}_{0}$ dressed states, with one or two laser beams. These methods are based on the spin-dependent ac-Stark shifts of the $^{3}\mathrm{P}_{2}$ states or the $^{3}\mathrm{P}_{2}\text{\ensuremath{-}}^{3}\mathrm{P}_{0}$ Raman coupling. We show that due to the structure of alkaline-earth (like) atoms, the heating effects induced by the laser beams of our methods are very weak. For instance, for ultracold Yb atoms, ac-Stark-shift difference of variant spin states of the $^{3}\mathrm{P}_{2}(F=3/2)$ level, or the strength of the $^{3}\mathrm{P}_{2}\text{\ensuremath{-}}^{3}\mathrm{P}_{0}$ Raman coupling, could be of the order of $(2\ensuremath{\pi})\phantom{\rule{0.28em}{0ex}}\mathrm{MHz}$, while the heating rate (photon scattering rate) is only of the order of Hz. As a result, the Feshbach resonances, with which one can efficiently control the SEI by changing the laser intensity, may be induced by the laser beams with a low-enough heating rate, even if the scattering lengths of the bare interatomic interaction are so small that they are comparable with the length scale associated with the van der Waals interaction.