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Journal of Physics B Atomic Molecular and Optical Physics

Laser cooling with three-level cascade transitions: a study for group II atoms and ytterbium

Wictor C. Magno, Flávio C. Cruz

Published Apr 15, 2021• 3 citations
Publisher

Abstract

Abstract We analyze laser cooling of two-electron atoms with three-level cascade transitions, involving the usual 1 S 0 – 1 P 1 cooling transition coupled to either 1 S 0 or 1 D 2 states. We numerically calculate minimum temperatures for the most abundant even isotopes of group II atoms and ytterbium (which lack hyperfine structure), derive general analytical expressions from a perturbative approach, and discuss the experimental implementation of the technique. Considered as an alternative 2nd stage technique to intercombination line cooling, three-level cooling is clearly advantageous for light elements, such as Mg and Ca, while for all elements provides much higher capture ranges, increasing the transfer efficiency from the 1st stage cooling, with faster cooling times and sub-Doppler temperatures.

DOI
10.1088/1361-6455/abf8a0

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Physical Review A•Feb 25, 2021•17 citations
Abstract We analyze laser cooling of two-electron atoms with three-level cascade transitions, involving the usual 1 S 0 – 1 P 1 cooling transition coupled to either 1 S 0 or 1 D 2 states. We numerically calculate minimum temperatures for the most abundant even isotopes of group II atoms and ytterbium (which lack hyperfine structure), derive general analytical expressions from a perturbative approach, and discuss the experimental implementation of the technique. Considered as an alternative 2nd stage technique to intercombination line cooling, three-level cooling is clearly advantageous for light elements, such as Mg and Ca, while for all elements provides much higher capture ranges, increasing the transfer efficiency from the 1st stage cooling, with faster cooling times and sub-Doppler temperatures.
We employ semiclassical theoretical analysis to study laser cooling of free atoms using three-level cascade transitions, where the upper transition is much weaker than the lower one. This represents an alternate cooling scheme, particularly useful for group II atoms. We find that temperatures below the Doppler limits associated with each of these transitions are expected. The lowest temperatures arise from a remarkable increase in damping and reduced diffusion compared to two-level cooling. They are reached at the two-photon resonance, where there is a crossing between the narrow and the partially dark dressed states, and can be estimated simply by the usual Doppler limit considering the decay rate of the optical coherence between these states.
Summary form only given. We consider laser cooling of free atoms with simultaneous two-color excitation of three-level cascade transitions [1], [2], [3], [4], [5], [6] finding theoretically that temperatures below the Doppler limits associated with each one of the individual transitions are obtained. We use standard laser cooling analysis [7], [8] and the dressed state picture in order to identify different cooling regions, and determining optimum parameters for guiding further experiments. These new “sub-Doppler” limits are reached at the two-photon resonance where a significant increase of the damping coefficient and decrease of the diffusion take place. In the dressed state picture, this point corresponds to a crossing of the narrow and a (partially) dark state.Figure 1 shows a plot of temperature (normalized to the Doppler limit for cooling only on the lower transition) as function of single-photon detunings, for the 1S0-1P1-1D2 transition of Magnesium, in which the lower 1S0-1P1 transition is the usual cooling one (λ1 = 2πc/ω1 = 285 nm, λ2 = 2πc/ω2 = 881 nm, γ1 = 2π 78.8 MHz, γ2 = 2π 2.2 MHz). A minimum temperature of 38 μK is predicted. This temperature is lower than the Doppler temperature of the lower and upper transitions, TD = γ/k = 1.9 mK and 49 μK respectively. Due to the asymmetric absorption profile of the dressed atom, there is a remarkable increase in the damping coefficient (α) associated with the narrow transition, in comparison with the broad transition (two-level cooling). The cooling and damping times, inversely proportional to α, are reduced by the same amount. Since the curve for the diffusion coefficient (D) has the same shape as the curve for the absorption coefficient or the population of the intermediate state, D is also reduced with respect to the broad resonance, We analyze situations previously implemented experimentally in alkaline-Earth atoms using cascade transitions, and also discuss prospects for Aand V-type three-level systems.
The possibility of laser cooling of alkaline-earth-metal atoms and ytterbium atoms using a two-photon transition is analyzed. We consider a ${}^{1}{S}_{0}{\ensuremath{-}}^{1}{S}_{0}$ transition with excitation in near resonance with the 1P1{}^{1}{P}_{1}1P1​ level. This greatly increases the two-photon transition rate, allowing an effective transfer of momentum. The experimental implementation of this technique is discussed and we show that for calcium, for example, two-photon cooling can be used to achieve a Doppler limit of $123\ensuremath{\mu}\mathrm{K}.$ The efficiency of this cooling scheme and the main loss mechanisms are analyzed.
Doppler laser cooling of a three-level ladder system using two near-resonant laser fields is analyzed in the case of the intermediate level being metastable while the upper level is short lived. Analytical as well as numerical results, e.g., obtainable scattering rates and achievable temperatures are presented. When appropriate, comparisons with two-level single-photon Doppler laser cooling is made. These results are relevant to recent experimental Doppler laser cooling investigations addressing intercombination lines in alkaline-earth-metal atoms and quadrupole transitions in alkaline-earth-metal ions.
The laser cooling of atoms with a narrow-line optical transition, i.e., in regimes of quantum nature of laser-light interactions resulting in a significant recoil effect, is studied. It is demonstrated that a minimum laser-cooling temperature for two-level atoms in a standing wave reached for red detuning close to three recoil frequencies is vastly different from the theory used for a semiclassical description of Doppler cooling. A set of dimensionless parameters uniquely characterizing the time evolution and the steady state of different atoms with narrow-line optical transitions in the laser field is introduced. The results can be used for analysis of optimal conditions for laser cooling of atoms with narrow lines such as Ca, Sr, and Mg, which are of great interest for atomic clocks.
We report three-stage laser cooling of Sr atoms using the 5s21S05{s}^{2}\phantom{\rule{0.16em}{0ex}}^{1}S_{0}5s21S0​ ground state and the 5s5p3P25s5p\phantom{\rule{0.16em}{0ex}}^{3}P_{2}5s5p3P2​ metastable state. 87Sr^{87}\mathrm{Sr}87Sr atoms are precooled in a magneto-optical trap simultaneously operated on the 5s21S05{s}^{2}\phantom{\rule{0.16em}{0ex}}^{1}S_{0}5s21S0​--5s5p1P15s5p\phantom{\rule{0.16em}{0ex}}^{1}P_{1}5s5p1P1​ transition at 461 nm and on the 5s5p3P25s5p\phantom{\rule{0.16em}{0ex}}^{3}P_{2}5s5p3P2​--5s5d3D35s5d\phantom{\rule{0.16em}{0ex}}^{3}D_{3}5s5d3D3​ transition at 496 nm. Atoms optically pumped to the 5s5p3P2(F=13/2)5s5p\phantom{\rule{0.16em}{0ex}}^{3}P_{2}(F=13/2)5s5p3P2​(F=13/2) state are magneto-optically trapped and cooled down to 2.5(2) $\ensuremath{\mu}\mathrm{K}$ on the 5s5p3P25s5p\phantom{\rule{0.16em}{0ex}}^{3}P_{2}5s5p3P2​--5s4d3D35s4d\phantom{\rule{0.16em}{0ex}}^{3}D_{3}5s4d3D3​ transition at $2.9\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{m}$. Using this transition, we investigate one dimensional polarization gradient cooling of 88Sr^{88}\mathrm{Sr}88Sr 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.