Physical Review A

Three-stage laser cooling of Sr atoms using the 5s5pP23 metastable state below Doppler temperatures

Tomoya Akatsuka, Koji Hashiguchi, Tadahiro TAKAHASHI, Noriaki Ohmae, Masao Takamoto, Hidetoshi Katori

Published Feb 25, 2021• 17 citations

Abstract

We report three-stage laser cooling of Sr atoms using the $5{s}^{2}\phantom{\rule{0.16em}{0ex}}^{1}S_{0}$ ground state and the $5s5p\phantom{\rule{0.16em}{0ex}}^{3}P_{2}$ metastable state. $^{87}\mathrm{Sr}$ atoms are precooled in a magneto-optical trap simultaneously operated on the $5{s}^{2}\phantom{\rule{0.16em}{0ex}}^{1}S_{0}$--$5s5p\phantom{\rule{0.16em}{0ex}}^{1}P_{1}$ transition at 461 nm and on the $5s5p\phantom{\rule{0.16em}{0ex}}^{3}P_{2}$--$5s5d\phantom{\rule{0.16em}{0ex}}^{3}D_{3}$ transition at 496 nm. Atoms optically pumped to the $5s5p\phantom{\rule{0.16em}{0ex}}^{3}P_{2}(F=13/2)$ state are magneto-optically trapped and cooled down to 2.5(2) $\ensuremath{\mu}\mathrm{K}$ on the $5s5p\phantom{\rule{0.16em}{0ex}}^{3}P_{2}$--$5s4d\phantom{\rule{0.16em}{0ex}}^{3}D_{3}$ transition at $2.9\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{m}$. Using this transition, we investigate one dimensional polarization gradient cooling of $^{88}\mathrm{Sr}$ atoms, which have simple energy levels without hyperfine structure, down to 0.22(18) $\ensuremath{\mu}\mathrm{K}$ or 17 times the recoil temperature. We discuss prospects for continuous generation of ultracold Sr atoms combined with a state transfer technique.

DOI: 10.1103/physreva.103.023331

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Spectroscopy of the $5s5p$ $ ^3 P_0 \rightarrow 5s5d$ $ ^3 D_1 $ transition of strontium using laser cooled atoms

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arXiv:2312.10327Dec 16, 20230 citations

Sub-Doppler cooling of bosonic strontium in a two-color magneto-optical trap

Milán János Negyedi, Shubha Deutschle, Florian Jessen +2 more

arXiv:2507.02693Physical Review AMay 12, 20261 citation

Magnetic trapping of metastable 3P2 atomic strontium

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Magneto-Optical Trapping and Cooling of Strontium Atoms down to the Photon Recoil Temperature

Hidetoshi Katori, T. Ido, Yoshitomo Isoya +1 more

Physical Review LettersFeb 8, 1999376 citations

Analyzing the optical pumping on the 5 s 4 d D 2 1 − 5 s 8 p P 1 1 transition in a magneto-optical trap of Sr atoms

Naohiro Okamoto, T. Aoki, Yoshio Torii

arXiv:2508.04109Physical Review ASep 24, 20253 citations

Quantum treatment of two-stage sub-Doppler laser cooling of magnesium atoms

Прудников Олег Николаевич, Denis V. Brazhnikov, А. В. Тайченачев +4 more

arXiv:1508.03694Physical Review ADec 15, 201517 citations

Physical Review A

Three-stage laser cooling of Sr atoms using the 5s5pP23 metastable state below Doppler temperatures

Tomoya Akatsuka, Koji Hashiguchi, Tadahiro TAKAHASHI, Noriaki Ohmae, Masao Takamoto, Hidetoshi Katori

Published Feb 25, 2021• 17 citations

Publisher

Abstract

We report three-stage laser cooling of Sr atoms using the

5{s}^{2}\phantom{\rule{0.16em}{0ex}}^{1}S_{0}

ground state and the

5s5p\phantom{\rule{0.16em}{0ex}}^{3}P_{2}

metastable state.

^{87}\mathrm{Sr}

atoms are precooled in a magneto-optical trap simultaneously operated on the

5{s}^{2}\phantom{\rule{0.16em}{0ex}}^{1}S_{0}

5s5p\phantom{\rule{0.16em}{0ex}}^{1}P_{1}

transition at 461 nm and on the

5s5p\phantom{\rule{0.16em}{0ex}}^{3}P_{2}

5s5d\phantom{\rule{0.16em}{0ex}}^{3}D_{3}

transition at 496 nm. Atoms optically pumped to the

5s5p\phantom{\rule{0.16em}{0ex}}^{3}P_{2}(F=13/2)

state are magneto-optically trapped and cooled down to 2.5(2)

\ensuremath{\mu}\mathrm{K}

on the

5s5p\phantom{\rule{0.16em}{0ex}}^{3}P_{2}

5s4d\phantom{\rule{0.16em}{0ex}}^{3}D_{3}

transition at

2.9\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{m}

. Using this transition, we investigate one dimensional polarization gradient cooling of

^{88}\mathrm{Sr}

atoms, which have simple energy levels without hyperfine structure, down to 0.22(18)

\ensuremath{\mu}\mathrm{K}

or 17 times the recoil temperature. We discuss prospects for continuous generation of ultracold Sr atoms combined with a state transfer technique.

DOI: 10.1103/physreva.103.023331

Related papers

Spectroscopy of the $5s5p$ $ ^3 P_0 \rightarrow 5s5d$ $ ^3 D_1 $ transition of strontium using laser cooled atomsSpectroscopy of the $5s5p$ $ ^3 P_0 \rightarrow 5s5d$ $ ^3 D_1 $ transition of strontium using laser cooled atoms

Kushal Patel, Palki Gakkhar, Korak Biswas +5 more

This article presents spectroscopy results of the $5s5p{\;^3}P_0 \rightarrow 5s5d{\;^3}D_1$ transition in all isotopes of laser cooled Sr atoms and the utility of this transition for repumping application. By employing the $5s5p{\;^{3} P_{0}} \rightarrow 5s5d{\;^3}D_1 $ (483 nm) transition in combination with the excitation of $5s5p{\;^3}P_2 \rightarrow 5s6s{\;^3}S_1$ (707 nm) transition, we observe a significant increase ( $\sim$ 13 fold) in the steady state number of atoms in the magneto-optic trap (MOT). This enhancement is attributed to the efficient repumping of Sr atoms that have decayed into the dark $5s5p{\;^3}P_2$ state by returning them to the ground state $5s^2{\;^1}S_0$ without any loss into the other states. The absolute transition frequencies were measured with an absolute accuracy of 30 MHz. To support our measurements, we performed Fock-space relativistic coupled-cluster calculations of the relevant parameters in Sr. To further increase the accuracy of the calculated properties, corrections from the Breit, QED and perturbative triples were also included. The calculated branching ratio for the repumping state confirms the significantly increased population in the ${^3}P_1$ state. Thereby, leading to an increase of population of atoms trapped due to the enhanced repumping. Our calculated hyperfine-splitting energies are in excellent agreement with the measured values. Moreover, our calculated isotope shifts in the transition frequencies are in good agreement with our measured values.This article presents spectroscopy results of the $5s5p{\;^3}P_0 \rightarrow 5s5d{\;^3}D_1$ transition in all isotopes of laser cooled Sr atoms and the utility of this transition for repumping application. By employing the $5s5p{\;^{3} P_{0}} \rightarrow 5s5d{\;^3}D_1 $ (483 nm) transition in combination with the excitation of $5s5p{\;^3}P_2 \rightarrow 5s6s{\;^3}S_1$ (707 nm) transition, we observe a significant increase ($\sim$ 13 fold) in the steady state number of atoms in the magneto-optic trap (MOT). This enhancement is attributed to the efficient repumping of Sr atoms that have decayed into the dark $5s5p{\;^3}P_2$ state by returning them to the ground state $5s^2{\;^1}S_0$ without any loss into the other states. The absolute transition frequencies were measured with an absolute accuracy of 30 MHz. To support our measurements, we performed Fock-space relativistic coupled-cluster calculations of the relevant parameters in Sr. To further increase the accuracy of the calculated properties, corrections from the Breit, QED and perturbative triples were also included. The calculated branching ratio for the repumping state confirms the significantly increased population in the ${^3}P_1$ state. Thereby, leading to an increase of population of atoms trapped due to the enhanced repumping. Our calculated hyperfine-splitting energies are in excellent agreement with the measured values. Moreover, our calculated isotope shifts in the transition frequencies are in good agreement with our measured values.

arXiv:2312.10327Dec 16, 20230 citations

Sub-Doppler cooling of bosonic strontium in a two-color magneto-optical trap

Milán János Negyedi, Shubha Deutschle, Florian Jessen +2 more

We report a two-color magneto-optical trap that continuously operates on the $\mathrm{(5s^2)\:^1S_0-(5s5p)\:^1P_1}$ and $\mathrm{(5s5p)\:^3P_2-(5s5d)\:^3D_3}$ transitions in $\mathrm{^{88}Sr}$ . Owing to the sub-Doppler cooling from the metastable $\mathrm{(5s5p)\:^3P_2}$ state, a bimodal momentum distribution is observed, with the cold part of the ensemble reaching a temperature of 105 $\mathrmμ$ K. A detailed simulation is established to explain the data. The absolute frequency of the $\mathrm{(5s5p)\:^3P_2-(5s5d)\:^3D_3}$ transition is measured to be 603 976 473 ${\pm}$ 2 MHz using a frequency comb, improving the literature value. The accompanying magnetic trap is characterized, and is shown to contribute to the sequential production of ensembles with temperatures down to 45 $\mathrmμ$ K.We report a two-color magneto-optical trap that continuously operates on the $\mathrm{(5s^2)\:^1S_0-(5s5p)\:^1P_1}$ and $\mathrm{(5s5p)\:^3P_2-(5s5d)\:^3D_3}$ transitions in $\mathrm{^{88}Sr}$. Owing to the sub-Doppler cooling from the metastable $\mathrm{(5s5p)\:^3P_2}$ state, a bimodal momentum distribution is observed, with the cold part of the ensemble reaching a temperature of 105 $\mathrmμ$K. A detailed simulation is established to explain the data. The absolute frequency of the $\mathrm{(5s5p)\:^3P_2-(5s5d)\:^3D_3}$ transition is measured to be 603 976 473 ${\pm}$ 2 MHz using a frequency comb, improving the literature value. The accompanying magnetic trap is characterized, and is shown to contribute to the sequential production of ensembles with temperatures down to 45 $\mathrmμ$K.

arXiv:2507.02693Physical Review AMay 12, 20261 citation

Magnetic trapping of metastable 3P2 atomic strontium

Sarah Nagel, Clayton E. Simien, S. Laha +3 more

We report the magnetic trapping of metastable ${}^{3}{P}_{2}$ atomic strontium. Atoms are cooled in a magneto-optical trap (MOT) operating on the dipole-allowed ${}^{1}{S}_{0}{\ensuremath{-}}^{1}{P}_{1}$ transition at 461 nm. Decay via ${}^{1}{\stackrel{\ensuremath{\rightarrow}}{{P}_{1}}}^{1}{\stackrel{\ensuremath{\rightarrow}}{{D}_{2}}}^{3}{P}_{2}$ continuously loads a magnetic trap formed by the quadrupole magnetic field of the MOT. Over ${10}^{8}$ atoms at a density of $8\ifmmode\times\else\texttimes\fi{}{10}^{9}{\mathrm{cm}}^{\ensuremath{-}3}$ and temperature of 1 mK are trapped. The atom temperature is significantly lower than what would be expected from the kinetic and potential energies of atoms as they are transferred from the MOT. This suggests the occurrence of thermalization and evaporative cooling in the magnetic trap.We report the magnetic trapping of metastable ${}^{3}{P}_{2}$ atomic strontium. Atoms are cooled in a magneto-optical trap (MOT) operating on the dipole-allowed ${}^{1}{S}_{0}{\ensuremath{-}}^{1}{P}_{1}$ transition at 461 nm. Decay via ${}^{1}{\stackrel{\ensuremath{\rightarrow}}{{P}_{1}}}^{1}{\stackrel{\ensuremath{\rightarrow}}{{D}_{2}}}^{3}{P}_{2}$ continuously loads a magnetic trap formed by the quadrupole magnetic field of the MOT. Over ${10}^{8}$ atoms at a density of $8\ifmmode\times\else\texttimes\fi{}{10}^{9}{\mathrm{cm}}^{\ensuremath{-}3}$ and temperature of 1 mK are trapped. The atom temperature is significantly lower than what would be expected from the kinetic and potential energies of atoms as they are transferred from the MOT. This suggests the occurrence of thermalization and evaporative cooling in the magnetic trap.

arXiv:physics/0212024Physical Review AJan 13, 200396 citations

Magneto-Optical Trapping and Cooling of Strontium Atoms down to the Photon Recoil Temperature

Hidetoshi Katori, T. Ido, Yoshitomo Isoya +1 more

We report narrow-line laser cooling and trapping of strontium atoms down to the photon recoil temperature. ${}^{88}\mathrm{Sr}$ atoms precooled by the broad $^{1}S_{0}\ensuremath{-}^{1}P_{1}$ transition at 461 nm were further cooled in a magneto-optical trap using the spin-forbidden transition $^{1}S_{0}\ensuremath{-}^{3}P_{1}$ at 689 nm. We have thus obtained an atomic sample with a density over ${10}^{12}\mathrm{cm}{}^{\ensuremath{-}3}$ and a minimum temperature of 400 nK, corresponding to a maximum phase space density of ${10}^{\ensuremath{-}2}$ which is 3 orders of magnitude larger than the value that has been obtained by magneto-optical traps to date. This scheme provides us an opportunity and system to study quantum statistical properties of degenerate fermions as well as bosons.We report narrow-line laser cooling and trapping of strontium atoms down to the photon recoil temperature. ${}^{88}\mathrm{Sr}$ atoms precooled by the broad $^{1}S_{0}\ensuremath{-}^{1}P_{1}$ transition at 461 nm were further cooled in a magneto-optical trap using the spin-forbidden transition $^{1}S_{0}\ensuremath{-}^{3}P_{1}$ at 689 nm. We have thus obtained an atomic sample with a density over ${10}^{12}\mathrm{cm}{}^{\ensuremath{-}3}$ and a minimum temperature of 400 nK, corresponding to a maximum phase space density of ${10}^{\ensuremath{-}2}$ which is 3 orders of magnitude larger than the value that has been obtained by magneto-optical traps to date. This scheme provides us an opportunity and system to study quantum statistical properties of degenerate fermions as well as bosons.

Physical Review LettersFeb 8, 1999376 citations

Analyzing the optical pumping on the 5 s 4 d D 2 1 − 5 s 8 p P 1 1 transition in a magneto-optical trap of Sr atoms

Naohiro Okamoto, T. Aoki, Yoshio Torii

We explore the efficacy of optical pumping on the $5s4d\phantom{\rule{0.16em}{0ex}}^{1}D_{2}\text{\ensuremath{-}}5s8p\phantom{\rule{0.16em}{0ex}}^{1}P_{1}$ $(448\phantom{\rule{0.16em}{0ex}}\mathrm{nm})$ transition in a magneto-optical trap (MOT) of Sr atoms. The number of trapped atoms is enhanced by a factor of $12.0(6)$ relative to the case without repumping light, which is six times as large as that obtained using the pumping transition $5s4d\phantom{\rule{0.16em}{0ex}}^{1}D_{2}\text{\ensuremath{-}}5s6p\phantom{\rule{0.16em}{0ex}}^{1}P_{1}$ $(717\phantom{\rule{0.16em}{0ex}}\mathrm{nm})$ . This enhancement is limited by decay pathways that bypass the $5s4d\phantom{\rule{0.16em}{0ex}}^{1}D_{2}$ state, namely $5s5p\phantom{\rule{0.16em}{0ex}}^{1}P_{1}\ensuremath{\rightarrow}5s4d\phantom{\rule{0.16em}{0ex}}^{3}D_{1}\ensuremath{\rightarrow}5s5p\phantom{\rule{0.16em}{0ex}}^{3}P_{0}$ and $5s5p\phantom{\rule{0.16em}{0ex}}^{1}P_{1}\ensuremath{\rightarrow}5s4d\phantom{\rule{0.16em}{0ex}}^{3}D_{2}\ensuremath{\rightarrow}5s5p\phantom{\rule{0.16em}{0ex}}^{3}P_{2}$, which account for 8% of the total loss of the trapped atoms. We determine the decay rates for the $5s5p\phantom{\rule{0.16em}{0ex}}^{1}P_{1}\ensuremath{\rightarrow}5s4d\phantom{\rule{0.16em}{0ex}}^{3}D_{1}$ and $5s5p\phantom{\rule{0.16em}{0ex}}^{1}P_{1}\ensuremath{\rightarrow}5s4d\phantom{\rule{0.16em}{0ex}}^{3}D_{2}$ transitions to be $66(6)\phantom{\rule{0.16em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$ and $2.4(2)\ifmmode\times\else\texttimes\fi{}{10}^{2}\phantom{\rule{0.16em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$, respectively. Furthermore, we experimentally demonstrate, when the trap beam diameter is small, escape of atoms in the $5s4d\phantom{\rule{0.16em}{0ex}}^{1}D_{2}$ state, which has a relatively long lifetime of $400\phantom{\rule{0.16em}{0ex}}\textmu{}\mathrm{s}$, becomes a dominant loss mechanism, and that the $448\phantom{\rule{0.16em}{0ex}}\mathrm{nm}$ pumping light effectively suppresses this escape. Our findings will contribute to improved laser cooling and fluorescence imaging in cold strontium atom platforms, such as quantum computers based on optical tweezer arrays.We explore the efficacy of optical pumping on the $5s4d\phantom{\rule{0.16em}{0ex}}^{1}D_{2}\text{\ensuremath{-}}5s8p\phantom{\rule{0.16em}{0ex}}^{1}P_{1}$ $(448\phantom{\rule{0.16em}{0ex}}\mathrm{nm})$ transition in a magneto-optical trap (MOT) of Sr atoms. The number of trapped atoms is enhanced by a factor of $12.0(6)$ relative to the case without repumping light, which is six times as large as that obtained using the pumping transition $5s4d\phantom{\rule{0.16em}{0ex}}^{1}D_{2}\text{\ensuremath{-}}5s6p\phantom{\rule{0.16em}{0ex}}^{1}P_{1}$ $(717\phantom{\rule{0.16em}{0ex}}\mathrm{nm})$. This enhancement is limited by decay pathways that bypass the $5s4d\phantom{\rule{0.16em}{0ex}}^{1}D_{2}$ state, namely $5s5p\phantom{\rule{0.16em}{0ex}}^{1}P_{1}\ensuremath{\rightarrow}5s4d\phantom{\rule{0.16em}{0ex}}^{3}D_{1}\ensuremath{\rightarrow}5s5p\phantom{\rule{0.16em}{0ex}}^{3}P_{0}$ and $5s5p\phantom{\rule{0.16em}{0ex}}^{1}P_{1}\ensuremath{\rightarrow}5s4d\phantom{\rule{0.16em}{0ex}}^{3}D_{2}\ensuremath{\rightarrow}5s5p\phantom{\rule{0.16em}{0ex}}^{3}P_{2}$, which account for 8% of the total loss of the trapped atoms. We determine the decay rates for the $5s5p\phantom{\rule{0.16em}{0ex}}^{1}P_{1}\ensuremath{\rightarrow}5s4d\phantom{\rule{0.16em}{0ex}}^{3}D_{1}$ and $5s5p\phantom{\rule{0.16em}{0ex}}^{1}P_{1}\ensuremath{\rightarrow}5s4d\phantom{\rule{0.16em}{0ex}}^{3}D_{2}$ transitions to be $66(6)\phantom{\rule{0.16em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$ and $2.4(2)\ifmmode\times\else\texttimes\fi{}{10}^{2}\phantom{\rule{0.16em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$, respectively. Furthermore, we experimentally demonstrate, when the trap beam diameter is small, escape of atoms in the $5s4d\phantom{\rule{0.16em}{0ex}}^{1}D_{2}$ state, which has a relatively long lifetime of $400\phantom{\rule{0.16em}{0ex}}\textmu{}\mathrm{s}$, becomes a dominant loss mechanism, and that the $448\phantom{\rule{0.16em}{0ex}}\mathrm{nm}$ pumping light effectively suppresses this escape. Our findings will contribute to improved laser cooling and fluorescence imaging in cold strontium atom platforms, such as quantum computers based on optical tweezer arrays.

arXiv:2508.04109Physical Review ASep 24, 20253 citations

Quantum treatment of two-stage sub-Doppler laser cooling of magnesium atoms

Прудников Олег Николаевич, Denis V. Brazhnikov, А. В. Тайченачев +4 more

Deep laser cooling of $^{24}\mathrm{Mg}$ atoms has been theoretically studied. We propose a two-stage sub-Doppler cooling strategy using electrodipole transition $3\phantom{\rule{0.16em}{0ex}}{}^{3}{P}_{2}\ensuremath{\rightarrow}3\phantom{\rule{0.16em}{0ex}}{}^{3}{D}_{3}$ ($\ensuremath{\lambda}\phantom{\rule{0.16em}{0ex}}=\phantom{\rule{0.16em}{0ex}}383.8$ nm). The first stage implies exploiting magneto-optical trap with ${\ensuremath{\sigma}}^{+}$ and ${\ensuremath{\sigma}}^{\ensuremath{-}}$ light beams, while at the second stage lin $\ensuremath{\perp}$ lin molasses is used. We focus on achieving a large number of ultracold atoms (${T}_{\mathrm{eff}}<10 \ensuremath{\mu}\mathrm{K}$) in a cold-atomic cloud. The calculations have been based on quantum treatment, taking into full account the recoil effect and beyond many widely used approximations. Steady-state values of average kinetic energy and linear momentum distributions of cold atoms have been analyzed for various light-field intensities and frequency detunings. The results of conducted quantum analysis have been significantly different from the results achieved under a semiclassical approximation based on the Fokker-Planck equation. The second cooling stage allows achieving sufficiently lower kinetic energies of the atomic cloud as well as increased fraction of ultracold atoms at certain conditions compared to the first one. We hope that the obtained results can help in overcoming current experimental problems in deep cooling of $^{24}\mathrm{Mg}$ atoms by means of laser field. Cold magnesium atoms cooled in a large amount to several $\ensuremath{\mu}\mathrm{K}$ are of huge interest to, for example, quantum metrology and to other many-body cold-atoms physics.Deep laser cooling of $^{24}\mathrm{Mg}$ atoms has been theoretically studied. We propose a two-stage sub-Doppler cooling strategy using electrodipole transition $3\phantom{\rule{0.16em}{0ex}}{}^{3}{P}_{2}\ensuremath{\rightarrow}3\phantom{\rule{0.16em}{0ex}}{}^{3}{D}_{3}$ ($\ensuremath{\lambda}\phantom{\rule{0.16em}{0ex}}=\phantom{\rule{0.16em}{0ex}}383.8$ nm). The first stage implies exploiting magneto-optical trap with ${\ensuremath{\sigma}}^{+}$ and ${\ensuremath{\sigma}}^{\ensuremath{-}}$ light beams, while at the second stage lin $\ensuremath{\perp}$ lin molasses is used. We focus on achieving a large number of ultracold atoms (${T}_{\mathrm{eff}}<10 \ensuremath{\mu}\mathrm{K}$) in a cold-atomic cloud. The calculations have been based on quantum treatment, taking into full account the recoil effect and beyond many widely used approximations. Steady-state values of average kinetic energy and linear momentum distributions of cold atoms have been analyzed for various light-field intensities and frequency detunings. The results of conducted quantum analysis have been significantly different from the results achieved under a semiclassical approximation based on the Fokker-Planck equation. The second cooling stage allows achieving sufficiently lower kinetic energies of the atomic cloud as well as increased fraction of ultracold atoms at certain conditions compared to the first one. We hope that the obtained results can help in overcoming current experimental problems in deep cooling of $^{24}\mathrm{Mg}$ atoms by means of laser field. Cold magnesium atoms cooled in a large amount to several $\ensuremath{\mu}\mathrm{K}$ are of huge interest to, for example, quantum metrology and to other many-body cold-atoms physics.

arXiv:1508.03694Physical Review ADec 15, 201517 citations

We report three-stage laser cooling of Sr atoms using the

5{s}^{2}\phantom{\rule{0.16em}{0ex}}^{1}S_{0}

ground state and the

5s5p\phantom{\rule{0.16em}{0ex}}^{3}P_{2}

metastable state.

^{87}\mathrm{Sr}

atoms are precooled in a magneto-optical trap simultaneously operated on the

5{s}^{2}\phantom{\rule{0.16em}{0ex}}^{1}S_{0}

5s5p\phantom{\rule{0.16em}{0ex}}^{1}P_{1}

transition at 461 nm and on the

5s5p\phantom{\rule{0.16em}{0ex}}^{3}P_{2}

5s5d\phantom{\rule{0.16em}{0ex}}^{3}D_{3}

transition at 496 nm. Atoms optically pumped to the

5s5p\phantom{\rule{0.16em}{0ex}}^{3}P_{2}(F=13/2)

state are magneto-optically trapped and cooled down to 2.5(2)

\ensuremath{\mu}\mathrm{K}

on the

5s5p\phantom{\rule{0.16em}{0ex}}^{3}P_{2}

5s4d\phantom{\rule{0.16em}{0ex}}^{3}D_{3}

transition at

2.9\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{m}

. Using this transition, we investigate one dimensional polarization gradient cooling of

^{88}\mathrm{Sr}

atoms, which have simple energy levels without hyperfine structure, down to 0.22(18)

\ensuremath{\mu}\mathrm{K}

or 17 times the recoil temperature. We discuss prospects for continuous generation of ultracold Sr atoms combined with a state transfer technique.

Spectroscopy of the

5s5p

$ ^3 P_0 \rightarrow 5s5d$ $ ^3 D_1 $ transition of strontium using laser cooled atoms

This article presents spectroscopy results of the

5s5p{\;^3}P_0 \rightarrow 5s5d{\;^3}D_1

transition in all isotopes of laser cooled Sr atoms and the utility of this transition for repumping application. By employing the $5s5p{\;^{3} P_{0}} \rightarrow 5s5d{\;^3}D_1 $ (483 nm) transition in combination with the excitation of

5s5p{\;^3}P_2 \rightarrow 5s6s{\;^3}S_1

(707 nm) transition, we observe a significant increase (

\sim

13 fold) in the steady state number of atoms in the magneto-optic trap (MOT). This enhancement is attributed to the efficient repumping of Sr atoms that have decayed into the dark

5s5p{\;^3}P_2

state by returning them to the ground state

5s^2{\;^1}S_0

without any loss into the other states. The absolute transition frequencies were measured with an absolute accuracy of 30 MHz. To support our measurements, we performed Fock-space relativistic coupled-cluster calculations of the relevant parameters in Sr. To further increase the accuracy of the calculated properties, corrections from the Breit, QED and perturbative triples were also included. The calculated branching ratio for the repumping state confirms the significantly increased population in the

{^3}P_1

state. Thereby, leading to an increase of population of atoms trapped due to the enhanced repumping. Our calculated hyperfine-splitting energies are in excellent agreement with the measured values. Moreover, our calculated isotope shifts in the transition frequencies are in good agreement with our measured values.

We report a two-color magneto-optical trap that continuously operates on the

\mathrm{(5s^2)\:^1S_0-(5s5p)\:^1P_1}

and

\mathrm{(5s5p)\:^3P_2-(5s5d)\:^3D_3}

transitions in

\mathrm{^{88}Sr}

. Owing to the sub-Doppler cooling from the metastable

\mathrm{(5s5p)\:^3P_2}

state, a bimodal momentum distribution is observed, with the cold part of the ensemble reaching a temperature of 105

\mathrmμ

K. A detailed simulation is established to explain the data. The absolute frequency of the

\mathrm{(5s5p)\:^3P_2-(5s5d)\:^3D_3}

transition is measured to be 603 976 473

{\pm}

2 MHz using a frequency comb, improving the literature value. The accompanying magnetic trap is characterized, and is shown to contribute to the sequential production of ensembles with temperatures down to 45

\mathrmμ

We report the magnetic trapping of metastable

{}^{3}{P}_{2}

atomic strontium. Atoms are cooled in a magneto-optical trap (MOT) operating on the dipole-allowed ${}^{1}{S}_{0}{\ensuremath{-}}^{1}{P}_{1}$ transition at 461 nm. Decay via ${}^{1}{\stackrel{\ensuremath{\rightarrow}}{{P}_{1}}}^{1}{\stackrel{\ensuremath{\rightarrow}}{{D}_{2}}}^{3}{P}_{2}$ continuously loads a magnetic trap formed by the quadrupole magnetic field of the MOT. Over

{10}^{8}

atoms at a density of $8\ifmmode\times\else\texttimes\fi{}{10}^{9}{\mathrm{cm}}^{\ensuremath{-}3}$ and temperature of 1 mK are trapped. The atom temperature is significantly lower than what would be expected from the kinetic and potential energies of atoms as they are transferred from the MOT. This suggests the occurrence of thermalization and evaporative cooling in the magnetic trap.

We report narrow-line laser cooling and trapping of strontium atoms down to the photon recoil temperature.

{}^{88}\mathrm{Sr}

atoms precooled by the broad $^{1}S_{0}\ensuremath{-}^{1}P_{1}$ transition at 461 nm were further cooled in a magneto-optical trap using the spin-forbidden transition $^{1}S_{0}\ensuremath{-}^{3}P_{1}$ at 689 nm. We have thus obtained an atomic sample with a density over ${10}^{12}\mathrm{cm}{}^{\ensuremath{-}3}$ and a minimum temperature of 400 nK, corresponding to a maximum phase space density of ${10}^{\ensuremath{-}2}$ which is 3 orders of magnitude larger than the value that has been obtained by magneto-optical traps to date. This scheme provides us an opportunity and system to study quantum statistical properties of degenerate fermions as well as bosons.

We explore the efficacy of optical pumping on the $5s4d\phantom{\rule{0.16em}{0ex}}^{1}D_{2}\text{\ensuremath{-}}5s8p\phantom{\rule{0.16em}{0ex}}^{1}P_{1}$

(448\phantom{\rule{0.16em}{0ex}}\mathrm{nm})

transition in a magneto-optical trap (MOT) of Sr atoms. The number of trapped atoms is enhanced by a factor of

12.0(6)

relative to the case without repumping light, which is six times as large as that obtained using the pumping transition $5s4d\phantom{\rule{0.16em}{0ex}}^{1}D_{2}\text{\ensuremath{-}}5s6p\phantom{\rule{0.16em}{0ex}}^{1}P_{1}$

(717\phantom{\rule{0.16em}{0ex}}\mathrm{nm})

. This enhancement is limited by decay pathways that bypass the

5s4d\phantom{\rule{0.16em}{0ex}}^{1}D_{2}

state, namely $5s5p\phantom{\rule{0.16em}{0ex}}^{1}P_{1}\ensuremath{\rightarrow}5s4d\phantom{\rule{0.16em}{0ex}}^{3}D_{1}\ensuremath{\rightarrow}5s5p\phantom{\rule{0.16em}{0ex}}^{3}P_{0}$ and $5s5p\phantom{\rule{0.16em}{0ex}}^{1}P_{1}\ensuremath{\rightarrow}5s4d\phantom{\rule{0.16em}{0ex}}^{3}D_{2}\ensuremath{\rightarrow}5s5p\phantom{\rule{0.16em}{0ex}}^{3}P_{2}$, which account for 8% of the total loss of the trapped atoms. We determine the decay rates for the $5s5p\phantom{\rule{0.16em}{0ex}}^{1}P_{1}\ensuremath{\rightarrow}5s4d\phantom{\rule{0.16em}{0ex}}^{3}D_{1}$ and $5s5p\phantom{\rule{0.16em}{0ex}}^{1}P_{1}\ensuremath{\rightarrow}5s4d\phantom{\rule{0.16em}{0ex}}^{3}D_{2}$ transitions to be $66(6)\phantom{\rule{0.16em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$ and $2.4(2)\ifmmode\times\else\texttimes\fi{}{10}^{2}\phantom{\rule{0.16em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$, respectively. Furthermore, we experimentally demonstrate, when the trap beam diameter is small, escape of atoms in the

5s4d\phantom{\rule{0.16em}{0ex}}^{1}D_{2}

state, which has a relatively long lifetime of $400\phantom{\rule{0.16em}{0ex}}\textmu{}\mathrm{s}$, becomes a dominant loss mechanism, and that the

448\phantom{\rule{0.16em}{0ex}}\mathrm{nm}

pumping light effectively suppresses this escape. Our findings will contribute to improved laser cooling and fluorescence imaging in cold strontium atom platforms, such as quantum computers based on optical tweezer arrays.

Deep laser cooling of

^{24}\mathrm{Mg}

atoms has been theoretically studied. We propose a two-stage sub-Doppler cooling strategy using electrodipole transition $3\phantom{\rule{0.16em}{0ex}}{}^{3}{P}_{2}\ensuremath{\rightarrow}3\phantom{\rule{0.16em}{0ex}}{}^{3}{D}_{3}$ ($\ensuremath{\lambda}\phantom{\rule{0.16em}{0ex}}=\phantom{\rule{0.16em}{0ex}}383.8$ nm). The first stage implies exploiting magneto-optical trap with ${\ensuremath{\sigma}}^{+}$ and ${\ensuremath{\sigma}}^{\ensuremath{-}}$ light beams, while at the second stage lin $\ensuremath{\perp}$ lin molasses is used. We focus on achieving a large number of ultracold atoms (${T}_{\mathrm{eff}}<10 \ensuremath{\mu}\mathrm{K}$) in a cold-atomic cloud. The calculations have been based on quantum treatment, taking into full account the recoil effect and beyond many widely used approximations. Steady-state values of average kinetic energy and linear momentum distributions of cold atoms have been analyzed for various light-field intensities and frequency detunings. The results of conducted quantum analysis have been significantly different from the results achieved under a semiclassical approximation based on the Fokker-Planck equation. The second cooling stage allows achieving sufficiently lower kinetic energies of the atomic cloud as well as increased fraction of ultracold atoms at certain conditions compared to the first one. We hope that the obtained results can help in overcoming current experimental problems in deep cooling of

^{24}\mathrm{Mg}

atoms by means of laser field. Cold magnesium atoms cooled in a large amount to several $\ensuremath{\mu}\mathrm{K}$ are of huge interest to, for example, quantum metrology and to other many-body cold-atoms physics.