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arXiv:1703.08969 · Physical Review A

Annexing magic and tune-out wavelengths to the clock transitions of the alkaline-earth-metal ions

Jasmeet Kaur, Sukhjit Singh Sehra, Bindiya Arora, B. K. Sahoo

Published Apr 6, 2017• 17 citations
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Abstract

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.

DOI
10.1103/physreva.95.042501

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We present additional magic wavelengths (\ensuremathλmagic{\ensuremath{\lambda}}_{\mathrm{magic}}\ensuremathλmagic​) 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 [\ensuremathαd(\ensuremathω)][{\ensuremath{\alpha}}_{d}(\ensuremath{\omega})][\ensuremathαd​(\ensuremathω)] of the atomic states associated with the clock transitions play major roles in the evaluation of these \ensuremathλmagic{\ensuremath{\lambda}}_{\mathrm{magic}}\ensuremathλmagic​, 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 \ensuremathλmagic{\ensuremath{\lambda}}_{\mathrm{magic}}\ensuremathλmagic​ values in these hyperfine transitions are estimated and found to be different from \ensuremathλmagic{\ensuremath{\lambda}}_{\mathrm{magic}}\ensuremathλmagic​ for the atomic transitions due to different contributions coming from the vector and tensor parts of \ensuremathαd(\ensuremathω){\ensuremath{\alpha}}_{d}(\ensuremath{\omega})\ensuremathαd​(\ensuremathω). Importantly, we also present \ensuremathλmagic{\ensuremath{\lambda}}_{\mathrm{magic}}\ensuremathλmagic​ values that depend only on the scalar component of \ensuremathαd(\ensuremathω){\ensuremath{\alpha}}_{d}(\ensuremath{\omega})\ensuremathαd​(\ensuremathω) 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 \ensuremathαd(\ensuremathω){\ensuremath{\alpha}}_{d}(\ensuremath{\omega})\ensuremathαd​(\ensuremathω) 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.
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.
Light shift in a state due to the applied laser in an atomic system vanishes at tune-out wavelengths (λTs). Similarly, differential light shift in a transition vanishes at the magic wavelengths (λmagics). In many of the earlier studies, values of the electric dipole (E1) matrix elements were inferred precisely by combining measurements and calculations of λmagic. Similarly, the λT values of an atomic state can be used to infer the E1 matrix element, as it involves dynamic electric dipole (α) values of only one state whereas the λmagic values require evaluation of α values for two states. However, both the λmagic and λT values depend on angular momenta and their magnetic components (M) of states. Here, we report the λmagic and λT values of many S1/2 and D3/2,5/2 states, and transitions among these states of the Mg+, Ca+, Sr+ and Ba+ ions that are independent of M values. It is possible to infer a large number of E1 matrix elements of the above ions accurately by measuring these values and combining with our calculations.
The circular polarized laser beam of the ``magic'' wavelength may be used for mixing the 3P1^{3}P_{1}3P1​ state into the long-living metastable state 3P0^{3}P_{0}3P0​, thus enabling the strictly forbidden $^{1}S_{0}\text{\ensuremath{-}}^{3}P_{0}$ ``clock'' transition in even isotopes of alkaline-earth-metal-like atoms, without a change of the transition frequency. In odd isotopes the laser beam may adjust to an optimum value the linewidth of the clock transition, originally enabled by the hyperfine mixing. We present a detailed analysis of various factors influencing resolution and uncertainty for an optical frequency standard based on atoms exposed simultaneously to the lattice standing wave and an additional ``state-mixing'' wave, including estimations of the ``magic'' wavelengths, Rabi frequencies for the clock and state-mixing transitions, ac Stark shifts for the ground and metastable states of divalent atoms.
The present paper determines the precise values of magic wavelengths corresponding to the clock transitions 52S–42D{5}^{2}S\text{--}{4}^{2}D52S–42D of the Y2+{\mathrm{Y}}^{2+}Y2+ ion at the levels of both fine and hyperfine structures due to the external light beams having linear as well as circular polarization. To calculate the dynamic polarizabilities of the associated states of the transitions, we employ the sum-over-states technique, where the dominating and correlation sensitive part of the sum is evaluated using a highly correlated relativistic coupled-cluster theory. The estimated magic wavelengths of the light beams have substantial importance to cool and trap the ion using a blue-detuned trapping scheme. We also present the tune-out wavelengths, which are useful in state-insensitive trapping and cooling. The vector component of a total polarizability, which is induced by a circularly polarized light only, can provide additional magic wavelengths. Considerable effects of hyperfine interaction on the values of polarizabilities and number of magic wavelengths divulge the importance of precise estimations of hyperfine-structure splitting.
Magic-wave-induced 1S0−3P0^1S_0-^3P_01S0​−3P0​ transition in even isotopes of alkaline-earth-like atoms
The circular polarized laser beam of the ``magic'' wavelength may be used for mixing the 3P1^3P_13P1​ state into the long-living metastable state 3P0^3P_03P0​, thus enabling the strictly forbidden 1S0^1S_01S0​−-−3P0^3P_03P0​ ''clock'' transition in even isotopes of alkaline-earth-like atoms, without change of the transition frequency. In odd isotopes the laser beam may adjust to an optimum value the line width of the "clock" transition, originally enabled by the hyperfine mixing. We present a detailed analysis of various factors influencing resolution and uncertainty for an optical frequency standard based on atoms exposed simultaneously to the lattice standing wave and an additional "state-mixing" wave, including estimations of the "magic" wavelengths, Rabi frequencies for the ''clock'' and state-mixing transitions, ac Stark shifts for the ground and metastable states of divalent atoms.
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.