Scattering amplitude and two-body loss of ultracold alkaline-earth atoms in a shaking synthetic magnetic field

Abstract

The idea of manipulating the interaction between ultracold fermionic alkaline-earth (like) atoms via a laser-induced periodical synthetic magnetic field was proposed in [Phys. Rev. B {\bf 97}, 155156 (2018)]. In that work it was shown that in the presence of the shaking synthetic magnetic field, two atoms in $^1$S$_0$ and $^3$P$_0$ states experiences a periodical interaction in a rotated frame, and the effective inter-atomic interaction was approximated as the time-averaged operator of this time-dependent interaction. This technique is supposed to be efficient for $^{173}$Yb atoms which has large natural scattering length. Here we exam this time-averaging approximation and derive the rate of the two-body loss induced by the shaking of the synthetic magnetic field, by calculating the zero-energy inter-atomic scattering amplitude corresponding to the explicit periodical interaction. We find that for the typical cases with shaking angular frequency $\lambda$ of the synthetic magnetic field being of the order of $(2\pi)$kHz, the time-averaging approximation is applicable only when the shaking amplitude is small enough. Moreover, the two-body loss rate increases with the shaking amplitude, and is of the order of $10^{-10}$${\rm cm}^{3}{\rm s}^{-1}$ or even larger when the time-averaging approximation is not applicable. Our results are helpful for the quantum simulations with ultracold gases of fermionic alkaline-earth (like) atoms.