arXiv:2406.00927 · Physical Review A

Double, triple, and quadruple magic wavelengths for cesium ground, excited, and Rydberg states

Anal Bhowmik, Marius Gaudesius, Grant W. Biedermann, D. Blume

Published Oct 23, 2024• 5 citations

Abstract

Dynamic polarizabilities of cesium Rydberg states, explicitly $n{S}_{1/2}, n{P}_{1/2}, n{P}_{3/2}, n{D}_{3/2}$, and $n{D}_{5/2}$, where the principal quantum number $n$ is 40--70, are presented for linearly polarized light. The dynamic polarizability is calculated using the sum-over-state approach. We identify double magic wavelengths in the range of $1000--2000$ nm for simultaneous trapping of the ground state and a Rydberg state, which are red detuned and blue detuned, respectively, with respect to a low-lying excited auxiliary state. Based on calculations of the radiative lifetime, blackbody-radiation-induced transitions, and population transfer out of the Rydberg and auxiliary states (estimated within two-state and master-equation models), we conclude that magic wavelength trapping is particularly promising experimentally for the $n{D}_{J,|{M}_{J}|}$ Rydberg series with angular momentum $J=3/2$ and projection quantum numbers ${M}_{J}=\ifmmode\pm\else\textpm\fi{}1/2$ (auxiliary state $8{P}_{1/2}$) and ${M}_{J}=\ifmmode\pm\else\textpm\fi{}3/2$ (auxiliary state $8{P}_{3/2}$), using trap depths as large as $10\phantom{\rule{0.28em}{0ex}}\textmu{}\mathrm{K}$. Moreover, by tuning the angle between the quantization axis and the polarization vector of the light, we identify triple and quadruple magic wavelengths, for which the polarizabilities of the ground state, a Rydberg state, and, respectively, one and two low-lying excited states are equal. Our comprehensive theoretical study provides much needed guidance for ongoing experimental efforts on cesium Rydberg-state-based quantum simulations that operate on timescales up to several microseconds.

DOI: 10.1103/physreva.110.043114

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arXiv:2406.00927 · Physical Review A

Double, triple, and quadruple magic wavelengths for cesium ground, excited, and Rydberg states

Anal Bhowmik, Marius Gaudesius, Grant W. Biedermann, D. Blume

Published Oct 23, 2024• 5 citations

arXiv HTML PDF

Abstract

Dynamic polarizabilities of cesium Rydberg states, explicitly

n{S}_{1/2}, n{P}_{1/2}, n{P}_{3/2}, n{D}_{3/2}

, and

n{D}_{5/2}

, where the principal quantum number

n

is 40--70, are presented for linearly polarized light. The dynamic polarizability is calculated using the sum-over-state approach. We identify double magic wavelengths in the range of

1000--2000

nm for simultaneous trapping of the ground state and a Rydberg state, which are red detuned and blue detuned, respectively, with respect to a low-lying excited auxiliary state. Based on calculations of the radiative lifetime, blackbody-radiation-induced transitions, and population transfer out of the Rydberg and auxiliary states (estimated within two-state and master-equation models), we conclude that magic wavelength trapping is particularly promising experimentally for the

n{D}_{J,|{M}_{J}|}

Rydberg series with angular momentum

J=3/2

and projection quantum numbers

{M}_{J}=\ifmmode\pm\else\textpm\fi{}1/2

(auxiliary state

8{P}_{1/2}

) and

{M}_{J}=\ifmmode\pm\else\textpm\fi{}3/2

(auxiliary state

8{P}_{3/2}

), using trap depths as large as

10\phantom{\rule{0.28em}{0ex}}\textmu{}\mathrm{K}

. Moreover, by tuning the angle between the quantization axis and the polarization vector of the light, we identify triple and quadruple magic wavelengths, for which the polarizabilities of the ground state, a Rydberg state, and, respectively, one and two low-lying excited states are equal. Our comprehensive theoretical study provides much needed guidance for ongoing experimental efforts on cesium Rydberg-state-based quantum simulations that operate on timescales up to several microseconds.

DOI: 10.1103/physreva.110.043114

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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

Yan-Min Wang, Qing-Yi Liu, Yong-Bo Tang +4 more

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 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.

arXiv:2512.23326Dec 29, 20250 citations

Magic wavelengths for the State-insensitive Optical Trapping of Cs Atoms: case studies using the linearly and circularly polarized lights

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

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.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.

Jan 4, 20160 citations

Dynamic polarizabilities of cesium Rydberg states, explicitly

n{S}_{1/2}, n{P}_{1/2}, n{P}_{3/2}, n{D}_{3/2}

, and

n{D}_{5/2}

, where the principal quantum number

n

is 40--70, are presented for linearly polarized light. The dynamic polarizability is calculated using the sum-over-state approach. We identify double magic wavelengths in the range of

1000--2000

n{D}_{J,|{M}_{J}|}

Rydberg series with angular momentum

J=3/2

and projection quantum numbers

{M}_{J}=\ifmmode\pm\else\textpm\fi{}1/2

(auxiliary state

8{P}_{1/2}

) and

{M}_{J}=\ifmmode\pm\else\textpm\fi{}3/2

(auxiliary state

8{P}_{3/2}

), using trap depths as large as

10\phantom{\rule{0.28em}{0ex}}\textmu{}\mathrm{K}

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.

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.