arXiv:1603.07824 · Physical Review A

Magic and tune-out wavelengths for atomic francium

Umakanth Dammalapati, K. Harada, Y. Sakemi

Published Apr 8, 2016• 14 citations

Abstract

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.

DOI: 10.1103/physreva.93.043407

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arXiv:1603.07824 · Physical Review A

Magic and tune-out wavelengths for atomic francium

Umakanth Dammalapati, K. Harada, Y. Sakemi

Published Apr 8, 2016• 14 citations

arXiv HTML PDF

Abstract

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.

DOI: 10.1103/physreva.93.043407

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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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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

Magic wavelengths for the 6S-7P transition of cesium atoms

Jiandong Bai, Yang Liu, Shaofeng Fan +5 more

For the trapped pre-cooled atoms in an optical dipole trap (ODT), the magic-wavelength ODT can eliminate the differential light shift of the transition between two atomic states, so that the transition frequency between the two states is the same as that of atoms in the free space, which is of great significance for improving the experimental repetition rate and reducing the atomic decoherence in the fields of cold atom physics, quantum optics, and precision measurement. Here we calculate the dynamic polarizabilities of cesium 6S ground state and 7P excited state by using the multi-level model for the ODT with laser wavelength from 1200 to 2000 nm. The magic wavelengths of ODT are obtained for the linearly and circularly polarized laser beams at the intersection of dynamic polarizabilities of two atomic states. Furthermore, we analyze the robustness of the magic trapping conditions and the feasibility of the experimental operation near the telecom C-band wavelength.For the trapped pre-cooled atoms in an optical dipole trap (ODT), the magic-wavelength ODT can eliminate the differential light shift of the transition between two atomic states, so that the transition frequency between the two states is the same as that of atoms in the free space, which is of great significance for improving the experimental repetition rate and reducing the atomic decoherence in the fields of cold atom physics, quantum optics, and precision measurement. Here we calculate the dynamic polarizabilities of cesium 6S ground state and 7P excited state by using the multi-level model for the ODT with laser wavelength from 1200 to 2000 nm. The magic wavelengths of ODT are obtained for the linearly and circularly polarized laser beams at the intersection of dynamic polarizabilities of two atomic states. Furthermore, we analyze the robustness of the magic trapping conditions and the feasibility of the experimental operation near the telecom C-band wavelength.

Results in PhysicsAug 12, 20232 citations

Magic wavelengths for optical clock transitions in Rb 85 , Cs 133 , and Fr 223 in visible-near-infrared spectrum

Jyoti, Mandeep Kaur, Tiantian Shi +1 more

Neutral atom manipulation along with the modern laser cooling and trapping techniques have revolutionized the field of atomic physics, enabling innovation among atomic clocks as well as in the study of parity violation and the search for electron electric-dipole moment and nuclear anapole moment. The realization of highly precise and accurate atomic clocks evidently requires high signal-to-noise ratio, which is inversely proportional to Allan deviation. Keeping this in mind, we have calculated magic wavelengths $({\ensuremath{\lambda}}_{\mathrm{magic}})$ for optical clock transitions in $^{85}\mathrm{Rb}$ , $^{133}\mathrm{Cs}$ , and $^{223}\mathrm{Fr}$ atoms, viz, $5{S}_{1/2}\text{\ensuremath{-}}6{P}_{1/2,3/2}$, $6{S}_{1/2}\text{\ensuremath{-}}7{P}_{1/2,3/2}$, and $7{S}_{1/2}\text{\ensuremath{-}}8{P}_{1/2,3/2}$, respectively, particularly in the visible-near-infrared spectrum, owing to the fact that Allan deviation rapidly decreases with higher wavelengths of the electromagnetic spectrum, making them more acceptable for newer navigation systems, quantum computation devices as well as tools for high-precision experiments. In this study, we also recommend investigating near-resonant ${\ensuremath{\lambda}}_{\mathrm{magic}}$ for $^{85}\mathrm{Rb}$ [420.81(2), $418.21(4),421.390(4)$ , and 417.67 nm] and $^{133}\mathrm{Cs}$ [458.84(4) nm], utilizing dual-purpose lasers of $\ensuremath{\approx}420$ nm and $\ensuremath{\approx}459$ nm for cooling and pumping of atoms for four-level active optical clock system based on Rb and Cs frequency standards, respectively. We believe that these findings will aid in overcoming trapping challenges for atomic clocks as well as support studies for physics beyond the standard model.Neutral atom manipulation along with the modern laser cooling and trapping techniques have revolutionized the field of atomic physics, enabling innovation among atomic clocks as well as in the study of parity violation and the search for electron electric-dipole moment and nuclear anapole moment. The realization of highly precise and accurate atomic clocks evidently requires high signal-to-noise ratio, which is inversely proportional to Allan deviation. Keeping this in mind, we have calculated magic wavelengths $({\ensuremath{\lambda}}_{\mathrm{magic}})$ for optical clock transitions in $^{85}\mathrm{Rb}$, $^{133}\mathrm{Cs}$, and $^{223}\mathrm{Fr}$ atoms, viz, $5{S}_{1/2}\text{\ensuremath{-}}6{P}_{1/2,3/2}$, $6{S}_{1/2}\text{\ensuremath{-}}7{P}_{1/2,3/2}$, and $7{S}_{1/2}\text{\ensuremath{-}}8{P}_{1/2,3/2}$, respectively, particularly in the visible-near-infrared spectrum, owing to the fact that Allan deviation rapidly decreases with higher wavelengths of the electromagnetic spectrum, making them more acceptable for newer navigation systems, quantum computation devices as well as tools for high-precision experiments. In this study, we also recommend investigating near-resonant ${\ensuremath{\lambda}}_{\mathrm{magic}}$ for $^{85}\mathrm{Rb}$ [420.81(2), $418.21(4),421.390(4)$, and 417.67 nm] and $^{133}\mathrm{Cs}$ [458.84(4) nm], utilizing dual-purpose lasers of $\ensuremath{\approx}420$ nm and $\ensuremath{\approx}459$ nm for cooling and pumping of atoms for four-level active optical clock system based on Rb and Cs frequency standards, respectively. We believe that these findings will aid in overcoming trapping challenges for atomic clocks as well as support studies for physics beyond the standard model.

Physical Review ANov 10, 20250 citations

Determination of magic wavelengths for the 7s S1/22−7p P3/2,1/22 transitions in Fr

Sukhjit Singh Sehra, B. K. Sahoo, Bindiya Arora

Magic wavelengths (${\ensuremath{\lambda}}_{\mathrm{magic}}$) for the $7{S}_{1/2}\ensuremath{-}7{P}_{1/2,3/2}$ transitions (D lines) in Fr were reported by Dammalapati et al. [U. Dammalapati, K. Harada, and Y. Sakemi, Phys. Rev. A 93, 043407 (2016)]. These ${\ensuremath{\lambda}}_{\mathrm{magic}}$ were determined by plotting dynamic polarizabilities ($\ensuremath{\alpha}$) of the involved states with the above transitions against a desired range of wavelengths. Electric dipole (E1) matrix elements listed in [J. E. Sansonetti, J. Phys. Chem. Ref. Data 36, 497 (2007)], from the measured lifetimes of the $7{P}_{1/2,3/2}$ states and from the calculations considering core-polarization effects in the relativistic Hartree-Fock (HFR) method, were used to determine $\ensuremath{\alpha}$. However, contributions from core correlation effects and from the E1 matrix elements of the $7P\ensuremath{-}7S, 7P\ensuremath{-}8S$, and $7P\ensuremath{-}6D$ transitions to $\ensuremath{\alpha}$ of the $7P$ states were ignored. In this work, we demonstrate importance of these contributions and improve accuracies of $\ensuremath{\alpha}$ further by replacing the E1 matrix elements taken from the HFR method by the values obtained employing relativistic coupled-cluster theory. Our static $\ensuremath{\alpha}$ are found to be in excellent agreement with the other available theoretical results, whereas substituting the E1 matrix elements used by Dammalapati et al. gives very small $\ensuremath{\alpha}$ values for the $7P$ states. Owing to this, we find disagreement in ${\ensuremath{\lambda}}_{\mathrm{magic}}$ reported by Dammalapati et al. for linearly polarized light, especially at wavelengths close to the D lines and in the infrared region. As a consequence, a ${\ensuremath{\lambda}}_{\mathrm{magic}}$ reported at 797.75 nm which was seen supporting a blue detuned trap in their work is now estimated at 771.03 nm and is supporting a red detuned trap. Also, none of our results match with the earlier results for circularly polarized light. Moreover, our static values of $\ensuremath{\alpha}$ will be very useful for guiding experiments to carry out their measurements.Magic wavelengths (${\ensuremath{\lambda}}_{\mathrm{magic}}$) for the $7{S}_{1/2}\ensuremath{-}7{P}_{1/2,3/2}$ transitions (D lines) in Fr were reported by Dammalapati et al. [U. Dammalapati, K. Harada, and Y. Sakemi, Phys. Rev. A 93, 043407 (2016)]. These ${\ensuremath{\lambda}}_{\mathrm{magic}}$ were determined by plotting dynamic polarizabilities ($\ensuremath{\alpha}$) of the involved states with the above transitions against a desired range of wavelengths. Electric dipole (E1) matrix elements listed in [J. E. Sansonetti, J. Phys. Chem. Ref. Data 36, 497 (2007)], from the measured lifetimes of the $7{P}_{1/2,3/2}$ states and from the calculations considering core-polarization effects in the relativistic Hartree-Fock (HFR) method, were used to determine $\ensuremath{\alpha}$. However, contributions from core correlation effects and from the E1 matrix elements of the $7P\ensuremath{-}7S, 7P\ensuremath{-}8S$, and $7P\ensuremath{-}6D$ transitions to $\ensuremath{\alpha}$ of the $7P$ states were ignored. In this work, we demonstrate importance of these contributions and improve accuracies of $\ensuremath{\alpha}$ further by replacing the E1 matrix elements taken from the HFR method by the values obtained employing relativistic coupled-cluster theory. Our static $\ensuremath{\alpha}$ are found to be in excellent agreement with the other available theoretical results, whereas substituting the E1 matrix elements used by Dammalapati et al. gives very small $\ensuremath{\alpha}$ values for the $7P$ states. Owing to this, we find disagreement in ${\ensuremath{\lambda}}_{\mathrm{magic}}$ reported by Dammalapati et al. for linearly polarized light, especially at wavelengths close to the D lines and in the infrared region. As a consequence, a ${\ensuremath{\lambda}}_{\mathrm{magic}}$ reported at 797.75 nm which was seen supporting a blue detuned trap in their work is now estimated at 771.03 nm and is supporting a red detuned trap. Also, none of our results match with the earlier results for circularly polarized light. Moreover, our static values of $\ensuremath{\alpha}$ will be very useful for guiding experiments to carry out their measurements.

arXiv:1608.02073Physical Review AAug 29, 201613 citations

Laser cooling and trapping of potassium at magic wavelengths

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 are provided for a large number of electric-dipole matrix elements. Static polarizabilities of the 4s, 4p_j, 5s, 5p_j, and 3d_j states are compared with other theory and experiment where available. We use the results of the polarizability calculations to identify magic wavelengths for the 4s-np transitions for $n = 4, 5$ , 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 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 are provided for a large number of electric-dipole matrix elements. Static polarizabilities of the 4s, 4p_j, 5s, 5p_j, and 3d_j states are compared with other theory and experiment where available. We use the results of the polarizability calculations to identify magic wavelengths for the 4s-np transitions for $n = 4, 5$, 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.

arXiv:1301.3181Jan 14, 20130 citations

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}

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}

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)].

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.

^{85}\mathrm{Rb}

^{133}\mathrm{Cs}

, and

^{223}\mathrm{Fr}

atoms, viz, $5{S}_{1/2}\text{\ensuremath{-}}6{P}_{1/2,3/2}$, $6{S}_{1/2}\text{\ensuremath{-}}7{P}_{1/2,3/2}$, and $7{S}_{1/2}\text{\ensuremath{-}}8{P}_{1/2,3/2}$, respectively, particularly in the visible-near-infrared spectrum, owing to the fact that Allan deviation rapidly decreases with higher wavelengths of the electromagnetic spectrum, making them more acceptable for newer navigation systems, quantum computation devices as well as tools for high-precision experiments. In this study, we also recommend investigating near-resonant ${\ensuremath{\lambda}}_{\mathrm{magic}}$ for

^{85}\mathrm{Rb}

[420.81(2),

418.21(4),421.390(4)

, and 417.67 nm] and

^{133}\mathrm{Cs}

[458.84(4) nm], utilizing dual-purpose lasers of $\ensuremath{\approx}420$ nm and $\ensuremath{\approx}459$ nm for cooling and pumping of atoms for four-level active optical clock system based on Rb and Cs frequency standards, respectively. We believe that these findings will aid in overcoming trapping challenges for atomic clocks as well as support studies for physics beyond the standard model.

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

states and from the calculations considering core-polarization effects in the relativistic Hartree-Fock (HFR) method, were used to determine $\ensuremath{\alpha}$. However, contributions from core correlation effects and from the E1 matrix elements of the $7P\ensuremath{-}7S, 7P\ensuremath{-}8S$, and $7P\ensuremath{-}6D$ transitions to $\ensuremath{\alpha}$ of the

7P

states were ignored. In this work, we demonstrate importance of these contributions and improve accuracies of $\ensuremath{\alpha}$ further by replacing the E1 matrix elements taken from the HFR method by the values obtained employing relativistic coupled-cluster theory. Our static $\ensuremath{\alpha}$ are found to be in excellent agreement with the other available theoretical results, whereas substituting the E1 matrix elements used by Dammalapati et al. gives very small $\ensuremath{\alpha}$ values for the

7P

states. Owing to this, we find disagreement in ${\ensuremath{\lambda}}_{\mathrm{magic}}$ reported by Dammalapati et al. for linearly polarized light, especially at wavelengths close to the D lines and in the infrared region. As a consequence, a ${\ensuremath{\lambda}}_{\mathrm{magic}}$ reported at 797.75 nm which was seen supporting a blue detuned trap in their work is now estimated at 771.03 nm and is supporting a red detuned trap. Also, none of our results match with the earlier results for circularly polarized light. Moreover, our static values of $\ensuremath{\alpha}$ will be very useful for guiding experiments to carry out their measurements.

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.