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Physica Scripta

Probing the effects of dynamic E2 polarizabilities and electric field gradients in magic wavelength calculations for clock transitions in singly ionized Ca, Sr and Ba

Mandeep Kaur, Jyoti, Jingbiao Chen

Published Aug 24, 2026• 0 citations
Publisher

Abstract

Abstract In present work, we have investigated the roles of dynamic quadrupole polarizabilities and the effect of electric field gradient in the accurate determination of magic wavelengths of the clock transitions for Ca + , Sr + and Ba + ions for linearly polarized light. We have employed relativistic all-order method for the evaluation of matrix elements for accurate determination of polarizability. The effect of gradient of electric field on magic wavelengths is analyzed with reference to small and large values of applied electric field-gradients in context to the experiments. Additional magic wavelengths have been revealed when the ratio of the electric field-gradient to electric field strength ( η = ‖ ( ∇ ε ∗ ⊗ ∇ ε ) ( k ) ‖ ‖ ( ε ∗ ⊗ ε ) ( k ) ‖ ) exceeds 0.1 a.u.. It is also observed that the characteristics of the trap can be switched with alteration in η . We have also estimated additional parameters such as trap depths, photon scattering rates and sensitivity to laser linewidths for these newly emerged magic wavelengths. Therefore, we believe that it is crucial to consider the spatial variation of any electric field while determining magic wavelengths for better understanding and implementation of laser trapping techniques.

DOI
10.1088/1402-4896/ae9e02

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Abstract In present work, we have investigated the roles of dynamic quadrupole polarizabilities and the effect of electric field gradient in the accurate determination of magic wavelengths of the clock transitions for Ca + , Sr + and Ba + ions for linearly polarized light. We have employed relativistic all-order method for the evaluation of matrix elements for accurate determination of polarizability. The effect of gradient of electric field on magic wavelengths is analyzed with reference to small and large values of applied electric field-gradients in context to the experiments. Additional magic wavelengths have been revealed when the ratio of the electric field-gradient to electric field strength ( η = ‖ ( ∇ ε ∗ ⊗ ∇ ε ) ( k ) ‖ ‖ ( ε ∗ ⊗ ε ) ( k ) ‖ ) exceeds 0.1 a.u.. It is also observed that the characteristics of the trap can be switched with alteration in η . We have also estimated additional parameters such as trap depths, photon scattering rates and sensitivity to laser linewidths for these newly emerged magic wavelengths. Therefore, we believe that it is crucial to consider the spatial variation of any electric field while determining magic wavelengths for better understanding and implementation of laser trapping techniques.
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