Polarizability of ultracold ${\text{Rb}}_2$ molecules in the rovibrational ground state of ${\mathrm{a}}^3{\Sigma }_u^{+}$

Abstract

We study, both theoretically and experimentally, the dynamical polarizability $\alpha (\omega )$ of ${\text{Rb}}_2$ molecules in the rovibrational ground state of ${\mathrm{a}}^3{\Sigma }_u^{+}$. Taking all relevant excited molecular bound states into account, we compute the complex-valued polarizability $\alpha (\omega )$ for wave numbers up to $20000{\text{cm}}^{-1}$. Our calculations are compared to experimental results at $1064.5\text{nm}$ ($\sim 9400{\text{cm}}^{-1}$) as well as at $830.4\text{nm}$ ($\sim 12000{\text{cm}}^{-1}$). Here, we discuss the measurements at $1064.5\text{nm}$. The ultracold ${\text{Rb}}_2$ molecules are trapped in the lowest Bloch band of a 3D optical lattice. Their polarizability is determined by lattice modulation spectroscopy which measures the potential depth for a given light intensity. Moreover, we investigate the decay of molecules in the optical lattice, where lifetimes of more than $2\text{s}$ are observed. In addition, the dynamical polarizability for the ${\mathrm{X}}^1{\Sigma }_g^{+}$ state is calculated. We provide simple analytical expressions that reproduce the numerical results for $\alpha (\omega )$ for all vibrational levels of ${\mathrm{a}}^3{\Sigma }_u^{+}$ as well as ${\mathrm{X}}^1{\Sigma }_g^{+}$. Precise knowledge of the molecular polarizability is essential for designing experiments with ultracold molecules as lifetimes and lattice depths are key parameters. Specifically the wavelength at $\sim 1064\text{nm}$ is of interest, since here, ultrastable high power lasers are available.

22 pages, 10 figures

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• Lattice model parameters for ultracold nonreactive molecules: chaotic scattering and its limitations
• Pendular trapping conditions for ultracold polar molecules enforced by external electric fields
• A low-cost four-component relativistic coupled cluster linear response theory based on perturbation sensitive natural spinors
• Limitations of coupled cluster approximations for highlyaccurate investigations of Rb${}_2^{+}$
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