arXiv:0709.0130 · Physical Review A

Magic wavelengths for the np−ns transitions in alkali-metal atoms

Bindiya Arora, Marianna S. Safronova, Charles W. Clark

Published Nov 15, 2007• 94 citations

Abstract

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 $ns$, $n{p}_{1∕2}$, $n{p}_{3∕2}$ 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 $ns$ and $n{p}_{1∕2}$ and $n{p}_{3∕2}$ atomic levels have the same ac Stark shifts, which facilitates state-insensitive optical cooling and trapping.

DOI: 10.1103/physreva.76.052509

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arXiv:0709.0130 · Physical Review A

Magic wavelengths for the np−ns transitions in alkali-metal atoms

Bindiya Arora, Marianna S. Safronova, Charles W. Clark

Published Nov 15, 2007• 94 citations

arXiv HTML PDF

Abstract

ns

n{p}_{1∕2}

n{p}_{3∕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

ns

and

n{p}_{1∕2}

and

n{p}_{3∕2}

atomic levels have the same ac Stark shifts, which facilitates state-insensitive optical cooling and trapping.

DOI: 10.1103/physreva.76.052509

Related papers

Magic wavelengths for optical cooling and trapping of lithium

Marianna S. Safronova, Marianna S. Safronova, Charles W. Clark

Using first-principles calculations, we identify magic wavelengths ${\ensuremath{\lambda}}_{\mathrm{magic}}$ for the $2s$ - $2p$ and $2s$ - $3p$ transitions in lithium. The $ns$ and $np$ atomic levels have the same ac Stark shifts at the corresponding magic wavelength, which facilitates state-insensitive optical cooling and trapping. Tune-out wavelengths for which the ground-state frequency-dependent polarizability vanishes are also calculated. Differences of these wavelengths between ${}^{6}$ Li and ${}^{7}$ Li are reported. Our approach uses high-precision, relativistic all-order methods in which all single, double, and partial triple excitations of the Dirac-Fock wave functions are included to all orders of perturbation theory. Recommended values are provided for a large number of Li electric-dipole matrix elements. Static polarizabilities for the $2s$ , $2p$ , $3s$ , $3p$ , and $3d$ levels are compared with other theory and experiment where available. Uncertainties of all recommended values are estimated. The magic wavelengths for the uv $2s$ - $3p$ transition are of particular interest for the production of a quantum gas of lithium [Duarte et al., Phys. Rev. A 84, 061406R (2011)].Using first-principles calculations, we identify magic wavelengths ${\ensuremath{\lambda}}_{\mathrm{magic}}$ for the $2s$-$2p$ and $2s$-$3p$ transitions in lithium. The $ns$ and $np$ atomic levels have the same ac Stark shifts at the corresponding magic wavelength, which facilitates state-insensitive optical cooling and trapping. Tune-out wavelengths for which the ground-state frequency-dependent polarizability vanishes are also calculated. Differences of these wavelengths between ${}^{6}$Li and ${}^{7}$Li are reported. Our approach uses high-precision, relativistic all-order methods in which all single, double, and partial triple excitations of the Dirac-Fock wave functions are included to all orders of perturbation theory. Recommended values are provided for a large number of Li electric-dipole matrix elements. Static polarizabilities for the $2s$, $2p$, $3s$, $3p$, and $3d$ levels are compared with other theory and experiment where available. Uncertainties of all recommended values are estimated. The magic wavelengths for the uv $2s$-$3p$ transition are of particular interest for the production of a quantum gas of lithium [Duarte et al., Phys. Rev. A 84, 061406R (2011)].

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Magic wavelengths for optical cooling and trapping of potassium

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Physical Review AMay 6, 201329 citations

Laser cooling and trapping of potassium at magic wavelengths

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arXiv:1301.3181Jan 14, 20130 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.

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Using first-principles calculations, we identify ``tune-out'' optical wavelengths, ${\ensuremath{\lambda}}_{\mathrm{zero}}$, for which the ground-state frequency-dependent polarizabilities of alkali-metal atoms vanish. Our approach uses high-precision, relativistic all-order method in which all single, double, and partial triple excitations of the Dirac-Fock wave functions are included to all orders of perturbation theory. We discuss the use of tune-out wavelengths for sympathetic cooling in two-species mixtures of alkali metals with group II and other elements of interest. Special cases in which these wavelengths coincide with strong resonance transitions in a target system are identified.Using first-principles calculations, we identify ``tune-out'' optical wavelengths, ${\ensuremath{\lambda}}_{\mathrm{zero}}$, for which the ground-state frequency-dependent polarizabilities of alkali-metal atoms vanish. Our approach uses high-precision, relativistic all-order method in which all single, double, and partial triple excitations of the Dirac-Fock wave functions are included to all orders of perturbation theory. We discuss the use of tune-out wavelengths for sympathetic cooling in two-species mixtures of alkali metals with group II and other elements of interest. Special cases in which these wavelengths coincide with strong resonance transitions in a target system are identified.

arXiv:1107.2060Physical Review AOct 4, 201188 citations

Relativistic coupled-cluster calculations of the polarizabilities of atomic thallium

Yong-Bo Tang, Ningning Gao, Bing-Qiong Lou +1 more

Using the relativistic coupled-cluster method, we calculate the static dipole polarizabilities of the $6p$ , $7s$ , $7p$ , $8s$ , $8p$ , and $6d$ states and the dynamic dipole polarizabilities of the $6p$ and $7s$ states of the thallium atom. The trivalent thallium atom is computationally treated as a monovalent system, together with all linear and nonlinear terms of single- and double-cluster operators included in the correlation calculations. We observe that the dominating contributions to the static scalar polarizabilities of the $7{s}_{1/2}$ , $7{p}_{1/2}$ , $8{p}_{1/2}$ , and $8{p}_{3/2}$ states are from one or two specific transitions. The matrix elements of these specific transitions can be determined by combining the experimental values of relevant static scalar polarizabilities. A number of magic wavelengths for the $6{p}_{1/2}$ -- $7s$ and $6{p}_{3/2}$ -- $7s$ transitions in the range of 488--1300 nm and the longest tune-out wavelength of the ground state are determined. These magic wavelengths and tune-out wavelength may be useful for further thallium experiments. Experimental measurements of the magic wavelengths near 1245 nm would give estimates of the $7{s}_{1/2}$ -- $7{p}_{1/2}$ and $7{s}_{1/2}$ -- $7{p}_{3/2}$ transition matrix elements and their ratio. Furthermore, lifetimes of many excited states, as well as the Stark-induced scalar and vector dipole polarizabilities for the $6{p}_{1/2}$ -- $7{p}_{1/2}$ transition, are also evaluated and compared with available theoretical and experimental values.Using the relativistic coupled-cluster method, we calculate the static dipole polarizabilities of the $6p$, $7s$, $7p$, $8s$, $8p$, and $6d$ states and the dynamic dipole polarizabilities of the $6p$ and $7s$ states of the thallium atom. The trivalent thallium atom is computationally treated as a monovalent system, together with all linear and nonlinear terms of single- and double-cluster operators included in the correlation calculations. We observe that the dominating contributions to the static scalar polarizabilities of the $7{s}_{1/2}$, $7{p}_{1/2}$, $8{p}_{1/2}$, and $8{p}_{3/2}$ states are from one or two specific transitions. The matrix elements of these specific transitions can be determined by combining the experimental values of relevant static scalar polarizabilities. A number of magic wavelengths for the $6{p}_{1/2}$--$7s$ and $6{p}_{3/2}$--$7s$ transitions in the range of 488--1300 nm and the longest tune-out wavelength of the ground state are determined. These magic wavelengths and tune-out wavelength may be useful for further thallium experiments. Experimental measurements of the magic wavelengths near 1245 nm would give estimates of the $7{s}_{1/2}$--$7{p}_{1/2}$ and $7{s}_{1/2}$--$7{p}_{3/2}$ transition matrix elements and their ratio. Furthermore, lifetimes of many excited states, as well as the Stark-induced scalar and vector dipole polarizabilities for the $6{p}_{1/2}$--$7{p}_{1/2}$ transition, are also evaluated and compared with available theoretical and experimental values.

Physical Review ADec 14, 201810 citations

ns

n{p}_{1∕2}

n{p}_{3∕2}

ns

and

n{p}_{1∕2}

and

n{p}_{3∕2}

atomic levels have the same ac Stark shifts, which facilitates state-insensitive optical cooling and trapping.

Using first-principles calculations, we identify magic wavelengths ${\ensuremath{\lambda}}_{\mathrm{magic}}$ for the

2s

2p

and

2s

3p

transitions in lithium. The

ns

and

np

atomic levels have the same ac Stark shifts at the corresponding magic wavelength, which facilitates state-insensitive optical cooling and trapping. Tune-out wavelengths for which the ground-state frequency-dependent polarizability vanishes are also calculated. Differences of these wavelengths between

{}^{6}

Li and

{}^{7}

Li are reported. Our approach uses high-precision, relativistic all-order methods in which all single, double, and partial triple excitations of the Dirac-Fock wave functions are included to all orders of perturbation theory. Recommended values are provided for a large number of Li electric-dipole matrix elements. Static polarizabilities for the

2s

2p

3s

3p

, and

3d

levels are compared with other theory and experiment where available. Uncertainties of all recommended values are estimated. The magic wavelengths for the uv

2s

3p

transition are of particular interest for the production of a quantum gas of lithium [Duarte et al., Phys. Rev. A 84, 061406R (2011)].

4s

4{p}_{j}

5s

5{p}_{j}

, and

3{d}_{j}

states are compared with other theoretical and experimental values when possible. We identify magic wavelengths for the $4s\ensuremath{-}np$ transitions for

n=4,5

, i.e., those wavelengths for which the two levels have the same ac Stark shifts. The magic wavelengths for the $4s\ensuremath{-}5p$ transitions are of particular interest for attaining a quantum gas of potassium at high phase-space density. We find 20 such wavelengths in the technically interesting region of

1050--1130

nm.

n = 4, 5

, i.e. those wavelengths for which the two levels have the same ac Stark shifts. These facilitate state-insensitive optical cooling and trapping. The magic wavelengths for the

4s-5p

transitions are of particular interest for attaining a quantum gas of potassium at high phase-space density. We find 20 such wavelengths in the technically interest region of 1050-1130 nm. Uncertainties of all recommended values are estimated.

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.

Using the relativistic coupled-cluster method, we calculate the static dipole polarizabilities of the

6p

7s

7p

8s

8p

, and

6d

states and the dynamic dipole polarizabilities of the

6p

and

7s

states of the thallium atom. The trivalent thallium atom is computationally treated as a monovalent system, together with all linear and nonlinear terms of single- and double-cluster operators included in the correlation calculations. We observe that the dominating contributions to the static scalar polarizabilities of the

7{s}_{1/2}

7{p}_{1/2}

8{p}_{1/2}

, and

8{p}_{3/2}

states are from one or two specific transitions. The matrix elements of these specific transitions can be determined by combining the experimental values of relevant static scalar polarizabilities. A number of magic wavelengths for the

6{p}_{1/2}

7s

and

6{p}_{3/2}

7s

transitions in the range of 488--1300 nm and the longest tune-out wavelength of the ground state are determined. These magic wavelengths and tune-out wavelength may be useful for further thallium experiments. Experimental measurements of the magic wavelengths near 1245 nm would give estimates of the

7{s}_{1/2}

7{p}_{1/2}

and

7{s}_{1/2}

7{p}_{3/2}

transition matrix elements and their ratio. Furthermore, lifetimes of many excited states, as well as the Stark-induced scalar and vector dipole polarizabilities for the

6{p}_{1/2}

7{p}_{1/2}

transition, are also evaluated and compared with available theoretical and experimental values.