We report the measurement of the anisotropic ac polarizability of ultracold polar (40)K(87)Rb molecules in the ground and first rotationally excited states. Theoretical analysis of the polarizability agrees well with experimental findings. Although the polarizability can vary by more than 30%, a "magic" angle between the laser polarization and the quantization axis is found where the polarizability of the |N=0,m(N)=0> and the |N=1,m(N)=0> states match. At this angle, rotational decoherence due to the mismatch in trapping potentials is eliminated, and we observe a sharp increase in the coherence time. This paves the way for precise spectroscopic measurements and coherent manipulations of rotational states as a tool in the creation and probing of novel quantum many-body states of polar molecules.
Ultracold atoms confined in a dipole trap are submitted to a potential whose depth is proportional to the real part of their dynamic dipole polarizability. The atoms also experience photon scattering whose rate is proportional to the imaginary part of their dynamic dipole polarizability. In this article we calculate the complex dynamic dipole polarizability of ground-state erbium, a rare-earth atom that was recently Bose condensed. The polarizability is calculated with the sum-over-state formula inherent to second-order perturbation theory. The summation is performed on transition energies and transition dipole moments from ground-state erbium, which are computed using the Racah-Slater least-squares fitting procedure provided by the cowan codes. This allows us to predict nine unobserved odd-parity energy levels of total angular momentum
J=5, 6, and 7, in the range 25 000--31 000 cm${}^{\ensuremath{-}1}$ above the ground state. Regarding the trapping potential, we find that ground-state erbium essentially behaves like a spherically symmetric atom, in spite of its large electronic angular momentum. We also find a mostly isotropic van der Waals interaction between two ground-state erbium atoms, characterized by a coefficient
C6iso=1760 a.u. To the contrary, the photon-scattering rate shows a pronounced anisotropy since it strongly depends on the polarization of the trapping light.
Abstract The efficiency of the optical trapping of ultracold atoms depends on the atomic dynamic dipole polarizability governing the atom-field interaction. In this article, we have calculated the real and imaginary parts of the dynamic dipole polarizability of dysprosium in the ground and first excited levels. Due to the high electronic angular momentum of those two states, the polarizabilities possess scalar, vector and tensor contributions that we have computed, on a wide range of trapping wavelengths, using the sum-over-state formula. Using the same formalism, we have also calculated the C 6 coefficients characterizing the van der Waals interaction between two dysprosium atoms in the two lowest levels. We have computed the energies of excited states and the transition probabilities appearing in the sums, using a combination of ab initio and least-square-fitting techniques provided by the Cowan codes and extended in our group. Regarding the real part of the polarizability, for field frequencies far from atomic resonances, the vector and tensor contributions are two-orders-of-magnitude smaller than the scalar contribution, whereas for the imaginary part, the vector and tensor contributions represent a noticeable fraction of the scalar contribution. Finally, our anisotropic C 6 coefficients are much smaller than those published in the literature.
Dipolar atoms have unique properties, making them interesting for laser cooling and quantum simulations. But, due to relatively large orbital momentum in the ground state these atoms may have large dynamic tensor and vector polarizabilities in the ground state. This enables the formation of spin-dependent optical traps. In this paper the real part of tensor and vector dynamic polarizability was experimentally measured and compared to a theoretical simulation. For an optical dipole trap operating around 532.07 nm, tensor polarizability was found to be $\ensuremath{-}145\ifmmode\pm\else\textpm\fi{}53\phantom{\rule{0.16em}{0ex}}\phantom{\rule{0.16em}{0ex}}\mathrm{a}.\mathrm{u}.$ and vector polarizability was $680\ifmmode\pm\else\textpm\fi{}240\phantom{\rule{0.16em}{0ex}}\phantom{\rule{0.16em}{0ex}}\mathrm{a}.\mathrm{u}.$ The measurements were compared with simulations, which were done based on the known set of levels from a thulium atom. The simulations are in good agreement with experimental results. In addition, losses of atoms from the dipole trap were measured for different trap configurations and compared to the calculated imaginary part of vector and tensor polarizabilities.
The efficiency of optical trapping is determined by the atomic dynamic dipole polarizability, whose real and imaginary parts are associated with the potential energy and photon-scattering rate, respectively. In this article we develop a formalism to calculate analytically the real and imaginary parts of the scalar, vector, and tensor polarizabilities of lanthanide atoms. We assume that the sum-over-state formula comprises only transitions involving electrons in the valence orbitals like
6s,5d,6p, and
7s, while transitions involving
4f core electrons are neglected. Applying this formalism to the ground level of configuration
4fq6s2, we restrict the sum to transitions implying the
4fq6s6p configuration, which yields polarizabilities depending on two parameters: an effective transition energy and an effective transition dipole moment. Then, by introducing configuration-interaction mixing between
4fq6s6p and other configurations, we demonstrate that the imaginary part of the scalar, vector, and tensor polarizabilities is very sensitive to configuration-interaction coefficients, whereas the real part is not. The magnitude and anisotropy of the photon-scattering rate are thus strongly related to the details of the atomic electronic structure. Those analytical results agree with our detailed electronic-structure calculations of the energy levels, Land\'e
g factors, transition probabilities, polarizabilities, and van der Waals
C6 coefficients, previously performed on erbium and dysprosium and presently performed on holmium. Our results show that, although the density of states decreases with increasing
q, the configuration interaction between $4{f}^{q}6s6p,\phantom{\rule{0.16em}{0ex}}4{f}^{q\ensuremath{-}1}5d6{s}^{2}$, and $4{f}^{q\ensuremath{-}1}5{d}^{2}6s$ is surprisingly stronger in erbium (
q=12) than in holmium (
q=11), itself stronger than in dysprosium (
q=10).
We report measurements of the AC polarizabilities of ultracold ground-state
23Na87Rb molecules. While the polarizability of the ground rotational state
J=0 is isotropic, that of the first excited rotational state
J=1 is anisotropic and depends strongly on the light polarization angle. We obtain both polarizabilities precisely by combining trap oscillation frequency measurement and high-resolution rotational spectroscopy driven by microwave. With the optimized light polarization angle and intensity combination, the nonuniformity of the differential AC Stark shift between the two rotational states is minimized and the rotational coherence time is observed to be the longest.