, 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.

DOI: 10.48550/arxiv.1301.3181

Related papers

Magic wavelengths for optical cooling and trapping of potassium

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

We carry out a systematic study of the static and dynamic polarizabilities of the potassium atom using a first-principles 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. Recommended values and uncertainties are provided for the relevant electric-dipole matrix elements. Polarizabilities of the $4s$ , $4{p}_{j}$ , $5s$ , $5{p}_{j}$ , 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.We carry out a systematic study of the static and dynamic polarizabilities of the potassium atom using a first-principles 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. Recommended values and uncertainties are provided for the relevant electric-dipole matrix elements. Polarizabilities of the $4s$, $4{p}_{j}$, $5s$, $5{p}_{j}$, 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.

Physical Review AMay 6, 201329 citations

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)].

arXiv:1206.7115Physical Review AOct 10, 201254 citations

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

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

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.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.

arXiv:0709.0130Physical Review ANov 15, 200794 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

Transition properties of a potassium atom

D. K. Nandy, Yashpal Singh, Balkrishna P. Shah +1 more

We report here oscillator strengths, transition rates, branching ratios, and lifetimes due to the allowed transitions in the potassium (K) atom. We evaluate electric dipole ( $E1$ ) amplitudes using an all-order relativistic many-body perturbation method. The obtained results are compared with previously available experimental and theoretical studies. Using the $E1$ matrix elements mentioned above and estimated from the lifetimes of the $4p{\phantom{\rule{4pt}{0ex}}}^{2}\phantom{\rule{-0.16em}{0ex}}{P}_{1/2,3/2}$ states, we determine precise values of static and dynamic polarizabilities for the first five low-lying states in the considered atom. The static polarizabilities of the ground and $4p{\phantom{\rule{4pt}{0ex}}}^{2}\phantom{\rule{-0.16em}{0ex}}{P}_{1/2,3/2}$ states in the present work are more precise than the available measurements in these states. Only the present work employs relativistic theory to evaluate the polarizabilities in the $3d{\phantom{\rule{4pt}{0ex}}}^{2}\phantom{\rule{-0.16em}{0ex}}{D}_{3/2,5/2}$ states for which no experimental results are known with which to compare. We also reexamine ``magic wavelengths'' for the $4p{\phantom{\rule{4pt}{0ex}}}^{2}\phantom{\rule{-0.16em}{0ex}}{P}_{1/2}\ensuremath{\rightarrow}4s{\phantom{\rule{4pt}{0ex}}}^{2}\phantom{\rule{-0.16em}{0ex}}{S}_{1/2}$ and $4p{\phantom{\rule{4pt}{0ex}}}^{2}\phantom{\rule{-0.16em}{0ex}}{P}_{3/2}\ensuremath{\rightarrow}4s{\phantom{\rule{4pt}{0ex}}}^{2}\phantom{\rule{-0.16em}{0ex}}{S}_{1/2}$ transitions due to the linearly polarized light, which are useful to perform the state-insensitive trapping of K atoms.We report here oscillator strengths, transition rates, branching ratios, and lifetimes due to the allowed transitions in the potassium (K) atom. We evaluate electric dipole ($E1$) amplitudes using an all-order relativistic many-body perturbation method. The obtained results are compared with previously available experimental and theoretical studies. Using the $E1$ matrix elements mentioned above and estimated from the lifetimes of the $4p{\phantom{\rule{4pt}{0ex}}}^{2}\phantom{\rule{-0.16em}{0ex}}{P}_{1/2,3/2}$ states, we determine precise values of static and dynamic polarizabilities for the first five low-lying states in the considered atom. The static polarizabilities of the ground and $4p{\phantom{\rule{4pt}{0ex}}}^{2}\phantom{\rule{-0.16em}{0ex}}{P}_{1/2,3/2}$ states in the present work are more precise than the available measurements in these states. Only the present work employs relativistic theory to evaluate the polarizabilities in the $3d{\phantom{\rule{4pt}{0ex}}}^{2}\phantom{\rule{-0.16em}{0ex}}{D}_{3/2,5/2}$ states for which no experimental results are known with which to compare. We also reexamine ``magic wavelengths'' for the $4p{\phantom{\rule{4pt}{0ex}}}^{2}\phantom{\rule{-0.16em}{0ex}}{P}_{1/2}\ensuremath{\rightarrow}4s{\phantom{\rule{4pt}{0ex}}}^{2}\phantom{\rule{-0.16em}{0ex}}{S}_{1/2}$ and $4p{\phantom{\rule{4pt}{0ex}}}^{2}\phantom{\rule{-0.16em}{0ex}}{P}_{3/2}\ensuremath{\rightarrow}4s{\phantom{\rule{4pt}{0ex}}}^{2}\phantom{\rule{-0.16em}{0ex}}{S}_{1/2}$ transitions due to the linearly polarized light, which are useful to perform the state-insensitive trapping of K atoms.

arXiv:1209.5857Physical Review ANov 27, 201223 citations

Magic and tune-out wavelengths for atomic francium

Umakanth Dammalapati, K. Harada, Y. Sakemi

The frequency dependent polarizabilities of the francium atom are calculated from the available data of energy levels and transition rates. Magic wavelengths for the state insensitive optical dipole trapping are identified from the calculated light shifts of the $7s$ $^{2}{S}_{1/2}$ , $7p$ $^{2}{P}_{1/2,3/2}$ , and $8s$ $^{2}{S}_{1/2}$ levels of the $7s$ $^{2}{S}_{1/2}\ensuremath{-}7p$ $^{2}{P}_{1/2,3/2}$ and $7s$ $^{2}{S}_{1/2}\ensuremath{-}8s$ $^{2}{S}_{1/2}$ transitions, respectively. Wavelengths in the ultraviolet, visible, and near infrared region are identified that are suitable for cooling and trapping. Magic wavelengths between the 600--700 nm and 700--1000 nm regions, which are blue and red detuned with the $7s\ensuremath{-}7p$ and $7s\ensuremath{-}8s$ transitions, are feasible to implement as lasers with sufficient power are available. In addition, we calculated the tune-out wavelengths where the ac polarizability of the ground $7s$ $^{2}{S}_{1/2}$ state in francium is zero. These results are beneficial as laser cooled and trapped francium has been in use for fundamental symmetry investigations like searches for an electron permanent electric dipole moment in an atom and for atomic parity nonconservation.The frequency dependent polarizabilities of the francium atom are calculated from the available data of energy levels and transition rates. Magic wavelengths for the state insensitive optical dipole trapping are identified from the calculated light shifts of the $7s$ $^{2}{S}_{1/2}$, $7p$ $^{2}{P}_{1/2,3/2}$, and $8s$ $^{2}{S}_{1/2}$ levels of the $7s$ $^{2}{S}_{1/2}\ensuremath{-}7p$ $^{2}{P}_{1/2,3/2}$ and $7s$ $^{2}{S}_{1/2}\ensuremath{-}8s$ $^{2}{S}_{1/2}$ transitions, respectively. Wavelengths in the ultraviolet, visible, and near infrared region are identified that are suitable for cooling and trapping. Magic wavelengths between the 600--700 nm and 700--1000 nm regions, which are blue and red detuned with the $7s\ensuremath{-}7p$ and $7s\ensuremath{-}8s$ transitions, are feasible to implement as lasers with sufficient power are available. In addition, we calculated the tune-out wavelengths where the ac polarizability of the ground $7s$ $^{2}{S}_{1/2}$ state in francium is zero. These results are beneficial as laser cooled and trapped francium has been in use for fundamental symmetry investigations like searches for an electron permanent electric dipole moment in an atom and for atomic parity nonconservation.

arXiv:1603.07824Physical Review AApr 8, 201614 citations

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

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.

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)].

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.

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 report here oscillator strengths, transition rates, branching ratios, and lifetimes due to the allowed transitions in the potassium (K) atom. We evaluate electric dipole (

E1

) amplitudes using an all-order relativistic many-body perturbation method. The obtained results are compared with previously available experimental and theoretical studies. Using the

E1

matrix elements mentioned above and estimated from the lifetimes of the

4p{\phantom{\rule{4pt}{0ex}}}^{2}\phantom{\rule{-0.16em}{0ex}}{P}_{1/2,3/2}

states, we determine precise values of static and dynamic polarizabilities for the first five low-lying states in the considered atom. The static polarizabilities of the ground and

4p{\phantom{\rule{4pt}{0ex}}}^{2}\phantom{\rule{-0.16em}{0ex}}{P}_{1/2,3/2}

states in the present work are more precise than the available measurements in these states. Only the present work employs relativistic theory to evaluate the polarizabilities in the

3d{\phantom{\rule{4pt}{0ex}}}^{2}\phantom{\rule{-0.16em}{0ex}}{D}_{3/2,5/2}

states for which no experimental results are known with which to compare. We also reexamine ``magic wavelengths'' for the $4p{\phantom{\rule{4pt}{0ex}}}^{2}\phantom{\rule{-0.16em}{0ex}}{P}_{1/2}\ensuremath{\rightarrow}4s{\phantom{\rule{4pt}{0ex}}}^{2}\phantom{\rule{-0.16em}{0ex}}{S}_{1/2}$ and $4p{\phantom{\rule{4pt}{0ex}}}^{2}\phantom{\rule{-0.16em}{0ex}}{P}_{3/2}\ensuremath{\rightarrow}4s{\phantom{\rule{4pt}{0ex}}}^{2}\phantom{\rule{-0.16em}{0ex}}{S}_{1/2}$ transitions due to the linearly polarized light, which are useful to perform the state-insensitive trapping of K atoms.

7s

^{2}{S}_{1/2}

7p

^{2}{P}_{1/2,3/2}

, and

8s

^{2}{S}_{1/2}

levels of the

7s

$^{2}{S}_{1/2}\ensuremath{-}7p$

^{2}{P}_{1/2,3/2}

and

7s

$^{2}{S}_{1/2}\ensuremath{-}8s$

^{2}{S}_{1/2}

transitions, respectively. Wavelengths in the ultraviolet, visible, and near infrared region are identified that are suitable for cooling and trapping. Magic wavelengths between the 600--700 nm and 700--1000 nm regions, which are blue and red detuned with the $7s\ensuremath{-}7p$ and $7s\ensuremath{-}8s$ transitions, are feasible to implement as lasers with sufficient power are available. In addition, we calculated the tune-out wavelengths where the ac polarizability of the ground

7s

^{2}{S}_{1/2}

state in francium is zero. These results are beneficial as laser cooled and trapped francium has been in use for fundamental symmetry investigations like searches for an electron permanent electric dipole moment in an atom and for atomic parity nonconservation.