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arXiv:1212.1814 · Physical Review A

Magic wavelengths for trapping the alkali-metal atoms with circularly polarized light

B. K. Sahoo, Bindiya Arora

Published Feb 5, 2013• 25 citations
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Abstract

Magic wavelengths for the Li, Na, and K alkali-metal atoms are determined using the circularly polarized light for the $ns$-$n{p}_{1/2,3/2}$ transitions, with $n$ denoting their ground-state principal quantum numbers, by studying their differential ac dynamic polarizabilities. These wavelengths for all possible sublevels are given linearly as well as circularly polarized lights and are further compared with the available results for the linearly polarized light. The present study suggests that it is possible to carry out state-insensitive trapping of different alkali-metal atoms using the circularly polarized light.

DOI
10.1103/physreva.87.023402

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Magic wavelengths for the Li, Na, and K alkali-metal atoms are determined using the circularly polarized light for the nsnsns-np1/2,3/2n{p}_{1/2,3/2}np1/2,3/2​ transitions, with nnn denoting their ground-state principal quantum numbers, by studying their differential ac dynamic polarizabilities. These wavelengths for all possible sublevels are given linearly as well as circularly polarized lights and are further compared with the available results for the linearly polarized light. The present study suggests that it is possible to carry out state-insensitive trapping of different alkali-metal atoms using the circularly polarized light.
We demonstrate magic wavelengths for the 6s 2S1/2−6p 2P3/2,1/26s ~ {^2}S_{1/2}-6p ~ {^2}P_{3/2,1/2}6s 2S1/2​−6p 2P3/2,1/2​ transitions in the Cs atom due to the circularly polarized light. In addition, we also obtain magic wavelengths using the linearly polarized light in order to verify the previously reported values and make a comparative study with the values obtained for the circularly polarized light. Most of these wavelengths are found to be in the optical region and could be of immense interest to the experimentalists for carrying out high precision measurements. To obtain these wavelengths, we have calculated dynamic dipole polarizabilities of the ground, 6p 2P1/26p ~{^2}P_{1/2}6p 2P1/2​ and 6p 2P3/26p ~{^2}P_{3/2}6p 2P3/2​ states. We use the available precise values of the electric dipole (E1) matrix elements for the most dominantly contributing transitions from the lifetime measurements of the above excited states and obtain other relevant important E1 matrix elements by employing a relativistic coupled-cluster method approximating at the singles and doubles level. Accuracies in these quantities are substantiated by comparing our evaluated scalar polarizability values with the corresponding experimental results.
We study the cancellation of differential ac Stark shifts in the 5s5s5s and 5p5p5p states of the rubidium atom using the linearly and circularly polarized lights by calculating their dynamic polarizabilities. Matrix elements were calculated using a relativistic coupled-cluster method at the single and double excitations and at the important valence triple excitation approximation including all possible nonlinear correlation terms. Some of the important matrix elements were further optimized using the experimental results available for the lifetimes and static polarizabilities of atomic states. ``Magic wavelengths'' are determined from the differential Stark shifts and results for the linearly polarized light are compared with the previously available results. The possible scope of facilitating state-insensitive optical trapping schemes using the magic wavelengths for circularly polarized light is discussed. Using the optimized matrix elements, the lifetimes of the 4d4d4d and 6s6s6s states of this atom are ameliorated.
We present magic wavelengths for the $n{S}_{1/2}\text{\ensuremath{-}}n{P}_{1/2,3/2},$ and $n{S}_{1/2}\text{\ensuremath{-}}m{D}_{3/2,5/2}$ transitions in Mg+,{\mathrm{Mg}}^{+},Mg+, Ca+,{\mathrm{Ca}}^{+},Ca+, Sr+,{\mathrm{Sr}}^{+},Sr+, and Ba+{\mathrm{Ba}}^{+}Ba+ alkaline-earth-metal ions, for the principal quantum numbers nnn and mmm for the ground and first excited DDD states, respectively. These wavelengths are presented for linearly polarized light by plotting the dynamic polarizabilities of the nS,nP1/2,3/2,nS,n{P}_{1/2,3/2},nS,nP1/2,3/2​, and mD3/2,5/2m{D}_{3/2,5/2}mD3/2,5/2​ states of the considered ions. Required dynamic polarizabilities are evaluated by employing a relativistic all-order perturbative method and their accuracies are ratified by comparing their static values with available high-precision experimental or other theoretical results. Moreover, some of the magic wavelengths identified by us in Ca+{\mathrm{Ca}}^{+}Ca+ concur with the recent measurements reported by Liu et al. [Phys. Rev. Lett. 114, 223001 (2015)]. Knowledge of these magic wavelengths is propitious to carry out many proposed high-precision measurements trapping the above ions in electric fields with the corresponding frequencies.
Extensive calculations of the electric-dipole matrix elements in alkali-metal atoms are conducted using the relativistic all-order method. This approach is a linearized version of the coupled-cluster method, which sums infinite sets of many-body perturbation theory terms. All allowed transitions between the lowest nsnsns, np1∕2n{p}_{1∕2}np1∕2​, np3∕2n{p}_{3∕2}np3∕2​ states and a large number of excited states are considered in these calculations and their accuracy is evaluated. The resulting electric-dipole matrix elements are used for the high-precision calculation of frequency-dependent polarizabilities of the excited states of alkali-metal atoms. We find ``magic'' wavelengths in alkali-metal atoms for which the nsnsns and np1∕2n{p}_{1∕2}np1∕2​ and np3∕2n{p}_{3∕2}np3∕2​ atomic levels have the same ac Stark shifts, which facilitates state-insensitive optical cooling and trapping.
We present additional magic wavelengths (${\ensuremath{\lambda}}_{\mathrm{magic}}$) for the clock transitions in the alkaline-earth-metal ions, considering circular polarized light, aside from our previously reported values [Kaur et al., Phys. Rev. A 92, 031402(R) (2015)] for linearly polarized light. Contributions from the vector component to the dynamic dipole polarizabilities $[{\ensuremath{\alpha}}_{d}(\ensuremath{\omega})]$ of the atomic states associated with the clock transitions play major roles in the evaluation of these ${\ensuremath{\lambda}}_{\mathrm{magic}}$, hence facilitating choosing circular polarization of lasers in the experiments. Moreover, the actual clock transitions in these ions are carried out among the hyperfine levels. The ${\ensuremath{\lambda}}_{\mathrm{magic}}$ values in these hyperfine transitions are estimated and found to be different from ${\ensuremath{\lambda}}_{\mathrm{magic}}$ for the atomic transitions due to different contributions coming from the vector and tensor parts of ${\ensuremath{\alpha}}_{d}(\ensuremath{\omega})$. Importantly, we also present ${\ensuremath{\lambda}}_{\mathrm{magic}}$ values that depend only on the scalar component of ${\ensuremath{\alpha}}_{d}(\ensuremath{\omega})$ for their uses in a specially designed trap geometry for these ions so that they can be used unambiguously among any hyperfine levels of the atomic states of the clock transitions. We also present ${\ensuremath{\alpha}}_{d}(\ensuremath{\omega})$ values explicitly at 1064 nm for the atomic states associated with the clock transitions, which may be useful for creating high-field-seeking traps for the above ions using the Nd:YAG laser. The tune-out wavelengths at which the states would be free from the Stark shifts are also presented. Accurate values of the electric dipole matrix elements required for these studies are given and trends of electron correlation effects in determining them are also highlighted.