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arXiv:1011.4738 · Physical Review A

Dynamic polarizabilities and magic wavelengths for dysprosium

V. A. Dzuba, V. V. Flambaum, Benjamin Lev

Published Mar 4, 2011• 39 citations
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Abstract

We theoretically study dynamic scalar polarizabilities of the ground and select long-lived excited states of dysprosium, a highly magnetic atom recently laser cooled and trapped. We demonstrate that there is a set of magic wavelengths of the unpolarized lattice laser field for each pair of states, which includes the ground state and one of these excited states. At these wavelengths, the energy shift due to laser field is the same for both states, which can be useful for resolved sideband cooling on narrow transitions and precision spectroscopy. We present an analytical formula that, near resonances, allows for the determination of approximate values of the magic wavelengths without calculating the dynamic polarizabilities of the excited states.

DOI
10.1103/physreva.83.032502

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We theoretically study dynamic scalar polarizabilities of the ground and select long-lived excited states of dysprosium, a highly magnetic atom recently laser cooled and trapped. We demonstrate that there is a set of magic wavelengths of the unpolarized lattice laser field for each pair of states, which includes the ground state and one of these excited states. At these wavelengths, the energy shift due to laser field is the same for both states, which can be useful for resolved sideband cooling on narrow transitions and precision spectroscopy. We present an analytical formula that, near resonances, allows for the determination of approximate values of the magic wavelengths without calculating the dynamic polarizabilities of the excited states.
Open-shell lanthanide atoms, and dysprosium in particular, combine a large ground-state angular momentum with dense electronic spectra, making their dynamical polarizability strongly dependent on wavelength and internal state, and therefore challenging to calculate and characterize experimentally. This issue has become especially relevant with the recent development of single-atom trapping of dysprosium in optical-tweezer arrays, where precise knowledge of the polarizability is needed to design optimized trapping architectures. Here, we exploit the strong spin-dependent light shift near the J′=J−1J'=J-1J′=J−1 intercombination line at 530.306 nm to determine the background scalar and vector polarizabilities of 162^{162}162Dy in its ground state near this wavelength. Our measurements quantitatively agree with atomic-structure calculations and provide new insight into the contributions of nearby transitions in a spectral region relevant to emerging dysprosium tweezer platforms.
For the trapped pre-cooled atoms in an optical dipole trap (ODT), the magic-wavelength ODT can eliminate the differential light shift of the transition between two atomic states, so that the transition frequency between the two states is the same as that of atoms in the free space, which is of great significance for improving the experimental repetition rate and reducing the atomic decoherence in the fields of cold atom physics, quantum optics, and precision measurement. Here we calculate the dynamic polarizabilities of cesium 6S ground state and 7P excited state by using the multi-level model for the ODT with laser wavelength from 1200 to 2000 nm. The magic wavelengths of ODT are obtained for the linearly and circularly polarized laser beams at the intersection of dynamic polarizabilities of two atomic states. Furthermore, we analyze the robustness of the magic trapping conditions and the feasibility of the experimental operation near the telecom C-band wavelength.
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 a measurement of the dynamical polarizability of dysprosium atoms in their electronic ground state at the optical wavelength of 1064 nm, which is of particular interest for laser trapping experiments. Our method is based on collective oscillations in an optical dipole trap, and reaches unprecedented accuracy and precision by comparison with an alkali atom (potassium) as a reference species. We obtain values of 184.4(2.4) and 1.7(6) a.u. for the scalar and tensor polarizability, respectively. Our experiments have reached a level that permits meaningful tests of current theoretical descriptions and provides valuable information for future experiments utilizing the intriguing properties of heavy lanthanide atoms.
We carry out a systematic study of the static and dynamic polarizabilities of the potassium atom using a first-principles high-precision relativistic all-order method in which all single, double, and partial triple excitations of the Dirac-Fock wave functions are included to all orders of perturbation theory. Recommended values are provided for a large number of electric-dipole matrix elements. Static polarizabilities of the 4s, 4p_j, 5s, 5p_j, and 3d_j states are compared with other theory and experiment where available. We use the results of the polarizability calculations to identify magic wavelengths for the 4s-np transitions for n=4,5n = 4, 5n=4,5, i.e. those wavelengths for which the two levels have the same ac Stark shifts. These facilitate state-insensitive optical cooling and trapping. The magic wavelengths for the 4s−5p4s-5p4s−5p transitions are of particular interest for attaining a quantum gas of potassium at high phase-space density. We find 20 such wavelengths in the technically interest region of 1050-1130 nm. Uncertainties of all recommended values are estimated.
We characterize the anisotropic differential ac-Stark shift for the Dy 626nm626\phantom{\rule{3.33333pt}{0ex}}\mathrm{nm}626nm intercombination transition, induced in a far-detuned 1070nm1070\phantom{\rule{3.33333pt}{0ex}}\mathrm{nm}1070nm optical dipole trap, and observe the existence of a ``magic polarization'' for which the polarizabilities of the ground and excited states are equal. From our measurements we extract both the scalar and tensorial components of the dynamic dipole polarizability for the excited state, ${\ensuremath{\alpha}}_{E}^{\text{s}}=188(12){\ensuremath{\alpha}}_{\text{0}}$ and ${\ensuremath{\alpha}}_{E}^{\text{t}}=34(12){\ensuremath{\alpha}}_{\text{0}}$, respectively, where ${\ensuremath{\alpha}}_{\text{0}}$ is the atomic unit for the electric polarizability. We also provide a theoretical model allowing us to predict the excited state polarizability and find qualitative agreement with our observations. Furthermore, we utilize our findings to optimize the efficiency of Doppler cooling of a trapped gas, by controlling the sign and magnitude of the inhomogeneous broadening of the optical transition. The resulting initial gain of the collisional rate allows us, after forced evaporation cooling, to produce a quasipure Bose-Einstein condensate of 162Dy^{162}\mathrm{Dy}162Dy with $3\ifmmode\times\else\texttimes\fi{}{10}^{4}$ atoms.