Chinese Physics B

Magic wavelengths for 6s1/2 → 5d3/2,5/2 transitions of Yb+ ions

Ting Chen, Lei Wu, Ru-Kui Zhang, Yongbo Tang, Jun Jiang, Chenzhong Dong

Published Feb 16, 2023• 1 citation

Abstract

The wave functions, energy levels and matrix elements of Yb+ ions are calculated using the relativistic configuration interaction plus core polarization (RCICP) method. The static and dynamic electric dipole polarizabilities of the ground state and low-lying excited states are determined. Then, the magic wavelengths of the magnetic sublevel 6s1/2,m = 1/2 → 5d3/2,m = ±3/2,±1/2 and 6s1/2,m = 1/2 → 5d5/2,m = ±5/2,±3/2,±1/2 transitions in the linearly, right-handed, and left-handed polarized light are further determined. The dependence of the magic wavelengths upon the angle between the direction of magnetic field and the direction of laser polarization is analyzed.

DOI: 10.1088/1674-1056/acbc6c

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Chinese Physics B

Magic wavelengths for 6s1/2 → 5d3/2,5/2 transitions of Yb+ ions

Ting Chen, Lei Wu, Ru-Kui Zhang, Yongbo Tang, Jun Jiang, Chenzhong Dong

Published Feb 16, 2023• 1 citation

Publisher

Abstract

DOI: 10.1088/1674-1056/acbc6c

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Magic wavelengths of Ca+ ion for linearly and circularly polarized light

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arXiv:1703.09950Journal of Physics Conference SeriesJul 1, 20172 citations

Magic wavelengths and triple magic trapping conditions for $5s^2~^1\!S_0$ and $5s5p~^3\!P_{0,2}$ states of Sr atomsMagic wavelengths and triple magic trapping conditions for $5s^2~^1\!S_0$ and $5s5p~^3\!P_{0,2}$ states of Sr atoms

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Sukhjit Singh Sehra, Kiranpreet Kaur, B. K. Sahoo +1 more

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Jan 4, 20160 citations

Magic wavelengths and triple magic trapping conditions for

5s^2~^1\!S_0

and

5s5p~^3\!P_{0,2}

states of Sr atoms

The static and dynamic electric dipole polarizabilities of the

5s^2~^1\!S_0

and

5s5p~^3\!P_{0,2}

states of Sr atoms are calculated using the relativistic configuration interaction plus the many-body perturbation theory (RCI+MBPT) method. Magic wavelengths are determined for the transitions

5s^2~^1\!S_0\rightarrow 5s5p~^3\!P_{0}

5s^2~^1\!S_0\rightarrow 5s5p~^3\!P_{2}

, and

5s5p~^3\!P_0\rightarrow 5s5p~^3\!P_{2}

. A comprehensive study is conducted on the dependence of magic wavelengths on the angle between the laser polarization and the magnetic field. Furthermore, the conditions for realizing triple magic trapping at 813.4~nm for the

5s^2~^1\!S_0

5s5p~^3\!P_{0}

and

5s5p~^3\!P_{2}

states are investigated. In the case of linearly polarized light, when the angle (

θ_p

) between the laser polarization direction and the magnetic field is

79.1(0.7)^\circ

, triple magic trapping for the

5s^2~^1\!S_0

5s5p~^3\!P_{0}

, and

5s5p~^3\!P_{2}~M=0

states can be achieved. This result agrees well with the recent experimental measurement (78.49(3)

^\circ

)[Phys. Rev. Lett. 135, 143401 (2025)]. Meanwhile, triple magic trapping involving the

5s5p~^3\!P_{2}~M=2

state can be achieved when

θ_p= 37.4(0.3)^\circ

. The conditions for achieving triple magic trapping with circularly and arbitrarily elliptically polarized light are also presented.

The dynamic polarizabilities of the atomic states with angular momentum

j>1/2

are sensitive to the angle between the quantization axis ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{e}}_{z}$ and the polarization vector $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\epsilon}}$ owing to the contribution of anisotropic tensor polarizabilities. The magic wavelength at which the differential Stark shift of an atomic transition nullifies depends on this angle. We identified the magic wavelengths for the $4{s}_{1/2}\ensuremath{\rightarrow}3{d}_{3/2,5/2}$ transitions of

{\mathrm{Ca}}^{+}

ions at different angles between ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{e}}_{z}$ and $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\epsilon}}$ in the case of linearly polarized light. The magic wavelengths near 395.79 nm, which lie between the $4{s}_{1/2}\ensuremath{\rightarrow}4{p}_{1/2}$ and $4{s}_{1/2}\ensuremath{\rightarrow}4{p}_{3/2}$ transition wavelengths, remain insensitive to the angle, while the longest magic wavelength, which is around 1000 nm, for each of the magnetic sublevel transitions is very sensitive to the angle. We suggest that accurate measurements on the longest magic wavelengths for the $4{s}_{1/2}\ensuremath{\rightarrow}3{d}_{5/2}$ and $4{s}_{1/2}\ensuremath{\rightarrow}3{d}_{3/2}$ transitions can be used to determine the oscillator strengths for the $4{s}_{1/2}\ensuremath{\rightarrow}4{p}_{1/2,3/2}, 3{d}_{5/2}\ensuremath{\rightarrow}4{p}_{3/2}$, and $3{d}_{3/2}\ensuremath{\rightarrow}4{p}_{1/2,3/2}$ transitions, and the difference of the static polarizabilities of the

4{s}_{1/2}

and

3{d}_{5/2}

states, and the tensor polarizability of the

3{d}_{5/2}

state.

The present paper determines the precise values of magic wavelengths corresponding to the clock transitions

{5}^{2}S\text{--}{4}^{2}D

of the

{\mathrm{Y}}^{2+}

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.

We demonstrate magic wavelengths for the

6s ~ {^2}S_{1/2}-6p ~ {^2}P_{3/2,1/2}

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 ~{^2}P_{1/2}

and

6p ~{^2}P_{3/2}

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.