Two-photon polarizability of Ba$^+$ ion: Control of spin-mixing process in an ultracold $^{137}$Ba$^+$--$^{87}$Rb mixture

Abstract

Ionic clocks exhibit one of the most promising candidates for the frequency standards. Recent investigations show the profound advantages of interrogating two laser lights with different frequencies in developing the frequency standards. Here, we present a scheme of a two-photon excitation process to calculate the dynamic polarizabilities of a few low-lying states of 137 Ba + by employing highly correlated relativistic many-body theory. We demonstrate the Stark shift cancellation for the clock states of 137 Ba + at the two-photon magic wavelengths, which would be an essential input to achieve better accuracy for the ionic clock experiments. We also calculate the magic wavelengths under the single-photon process to serve as the reference and for a comparative study. The calculated single-and two-photon magic wavelengths lie in the optical regime and are thus significant for future state-of-the-art experiments. Further, as an application, we investigate the impact of the two-photon polarizability on the spin-mixing process of an ultra-cold spin-1 mixture 137 Ba + − 87 Rb.We demonstrate the flexibility of the spin-exchange mechanism in the mixture in the presence of a tunable magnetic field and highlight the two-photon process-specific spin-oscillation protocol.