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arXiv:1905.03842 · Physical Review A

Scalar, tensor, and vector polarizability of Tm atoms in a 532-nm dipole trap

V. V. Tsyganok, D. A. Pershin, E. T. Davletov, Vladimir Khlebnikov, Alexey V. Akimov

Published Oct 4, 2019• 17 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.100.042502

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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±\else\textpm\fi53a.u.\ensuremath{-}145\ifmmode\pm\else\textpm\fi{}53\phantom{\rule{0.16em}{0ex}}\phantom{\rule{0.16em}{0ex}}\mathrm{a}.\mathrm{u}.\ensuremath−145\ifmmode±\else\textpm\fi53a.u. and vector polarizability was 680\ifmmode±\else\textpm\fi240a.u.680\ifmmode\pm\else\textpm\fi{}240\phantom{\rule{0.16em}{0ex}}\phantom{\rule{0.16em}{0ex}}\mathrm{a}.\mathrm{u}.680\ifmmode±\else\textpm\fi240a.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.
Recently, thulium has been condensed to Bose-Einstein condensate. Machine learning was used to avoid a detailed study of all obstacles, making cooling difficult. This paper analyzes the atomic loss mechanism for the 532-nm optical trap, used in the Bose-condensation experiment, and compares it with the alternative and more traditional micrometer-range optical dipole trap. We also measured the scalar and tensor polarizability of thulium at 1064 nm, which were found to be $167\ifmmode\pm\else\textpm\fi{}25$ a.u. ($275\ifmmode\pm\else\textpm\fi{}41\phantom{\rule{0.55542pt}{0ex}}\phantom{\rule{0.55542pt}{0ex}}\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}41}\mathrm{F}\phantom{\rule{0.16em}{0ex}}{\mathrm{m}}^{2}$) and $\ensuremath{-}4\ifmmode\pm\else\textpm\fi{}1$ a.u. ($7\ifmmode\pm\else\textpm\fi{}2\phantom{\rule{0.55542pt}{0ex}}\phantom{\rule{0.55542pt}{0ex}}\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}41}\phantom{\rule{0.28em}{0ex}}\mathrm{F}\phantom{\rule{0.16em}{0ex}}{\mathrm{m}}^{2}$), respectively.
We report the theoretical prediction and measurement of a tune-out wavelength for the ground state of the thulium atom in a linearly polarized optical dipole trap with a wavelength of approximately 576 nm. The measurements were conducted using a combination of trap frequency and RF loss spectroscopy, thus making it possible to separate the scalar and tensor parts of the total polarizability without measurements in the range of negative total polarizability. The calculated tune-out wavelength is consistent with the measured one of 575.646−0.014+0.016575.646_{-0.014}^{+0.016}575.646−0.014+0.016​ nm in air. The existence of the zero in the polarizability for the Tm ground state was confirmed by the trap loss experiment, which also made it possible to refine the tune-out wavelength to 575.646−0.004+0.004575.646_{-0.004}^{+0.004}575.646−0.004+0.004​. Despite the presence of an imaginary part of the polarizability at some wavelengths, it was experimentally demonstrated that, with a proper choice of the dipole trap polarization, it was possible to achieve Bose-Einstein condensation of thulium atoms in the range from 575.348 to 575.689 nm, covering the tune-out wavelength.
We report on the determination of the dynamical polarizability of ultracold erbium atoms in the ground and in one excited state at three different wavelengths, which are particularly relevant for optical trapping. Our study combines experimental measurements of the light shift and theoretical calculations. In particular, our experimental approach allows us to isolate the different contributions to the polarizability, namely, the isotropic scalar and anisotropic tensor part. For the latter contribution, we observe a clear dependence of the atomic polarizability on the angle between the laser-field-polarization axis and the quantization axis, set by the external magnetic field. Such an angle dependence is particularly pronounced in the excited-state polarizability. We compare our experimental findings with the theoretical values, based on semiempirical electronic structure calculations, and we observe a very good overall agreement. Our results pave the way to exploit the anisotropy of the tensor polarizability for spin-selective preparation and manipulation.
Neutral-atom quantum simulation is susceptible to entanglement between the atom's internal electronic state and its center-of-mass position. In many alkali Rydberg platforms, the 'spin-motion coupling' is exacerbated by the free expansion required to avoid ponderomotive anti-trapping from optical fields. A recent proposal (arXiv:2505.01071) claims sufficiently excited Rydberg states could be trapped in a monochromatic, far-detuned, circularly polarized optical field by harnessing a large vector polarizability. We disprove the proposal through analytic calculation and measurement of the vector polarizability of the 54S54S54S, 54P54P54P, and 53D53D53D orbitals of Cesium. Regarding the optical angular frequency ωωω, we analytically derive that the scalar, vector, and tensor polarizabilities scale as ω−2ω^{-2}ω−2, ω−3ω^{-3}ω−3, and ω−4ω^{-4}ω−4, as opposed to the proposed scaling of ω−2ω^{-2}ω−2, ω−1ω^{-1}ω−1, and ω−2ω^{-2}ω−2. We refine the sum-over-states expression for vector and tensor polarizability to be numerically stable and predict negligible vector and tensor polarizabilities far detuned from resonances, in agreement with our measurements. However, we find vector polarizability can enhance a recent proposal for near-detuned attractive trapping. Furthermore, we evaluate the breakdown of the electric-dipole approximation and derive no effect stronger than ponderomotive repulsion. We conclude that an attractive, monochromatic, far-detuned optical trap for alkali Rydberg states is not possible, regardless of the beam geometry.
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.
We report experimental measurements of the dynamical polarizability of dysprosium, at a wavelength of 532 nm. We measure all three components (scalar, vector, and tensor) of the anisotropic polarizability for the ground and the excited manifolds of the intercombination transition of Dy at 626 nm. The apparatus on which the measurements are performed is presented. We obtain with this setup imaging of single Dy atoms with fidelity above 99% and losses below 2.5% induced by imaging. We then describe the methods used to extract the polarizability. In particular, we combine a measurement of trap frequency and trap depth on single atoms in optical tweezers, allowing us to obtain a measurement of the ground-state polarizability free of errors in trap waist calibration. The obtained values give a magic condition between two Zeeman states in the ground and excited manifolds, which is used to image single atoms in optical tweezer arrays. The scalar polarizability of the ground state is in disagreement with theoretical expectations, calling for future investigations to resolve the discrepancy.