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Bulletin of the Russian Academy of Sciences Physics

Studying the possibility of deep laser cooling of 24Mg atoms in an optical lattice: Two-level quantum model

Прудников Олег Николаевич, А. В. Тайченачев, Valeriy I. Yudin, Ernst Maria Rasel

Published Dec 1, 2017• 0 citations
Publisher

Abstract

The possible deep laser cooling of 24 Mg atoms in a deep optical lattice in the presence of an additional pumping field resonant to the narrow 3 s 3 s 1 S 0 → 3 s 3 p 3 P 1 (λ = 457 nm) optical transition is studied. Two quantum models of the laser cooling of atoms in the optical trap are compared. One is based on the direct numerical solution to the kinetic quantum equation for an atomic density matrix; it considers both optical pumping and quantum recoil effects during interaction between the atoms and field photons. The second, simplified model is based on decomposing the states of the atoms over the levels of vibration in the optical trap and analyzing the evolution of these states. The comparison allows derivation of optical field parameters (pumping field intensity and detuning) that ensure cooling of the atoms to minimal energies. The conditions for fast laser cooling in an optical trap are found.

DOI
10.3103/s1062873817120243

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The possible deep laser cooling of 24 Mg atoms in a deep optical lattice in the presence of an additional pumping field resonant to the narrow 3 s 3 s 1 S 0 → 3 s 3 p 3 P 1 (λ = 457 nm) optical transition is studied. Two quantum models of the laser cooling of atoms in the optical trap are compared. One is based on the direct numerical solution to the kinetic quantum equation for an atomic density matrix; it considers both optical pumping and quantum recoil effects during interaction between the atoms and field photons. The second, simplified model is based on decomposing the states of the atoms over the levels of vibration in the optical trap and analyzing the evolution of these states. The comparison allows derivation of optical field parameters (pumping field intensity and detuning) that ensure cooling of the atoms to minimal energies. The conditions for fast laser cooling in an optical trap are found.
We study a possibility of laser cooling of 24 Mg atoms in deep optical lattice formed by intense off-resonant laser field in a presence of cooling field resonant to narrow (3 s 3 s ) 1 S 0 → (3 s 3 p ) 3 P 1 (λ = 457 nm) optical transition. For description of laser cooling with taking into account quantum recoil effects we consider two quantum models. The first one is based on direct numerical solution of quantum kinetic equation for atom density matrix and the second one is simplified model based on decomposition of atom density matrix over vibration states in the lattice wells. We search cooling field intensity and detuning for minimum cooling energy and fast laser cooling.
We study laser cooling of 24^{24}24Mg atoms in dipole optical trap with pumping field resonant to narrow (3s3s) 1S0→ (3s3p) 3P1(3s3s)\,^1S_0 \rightarrow \, (3s3p)\,^{3}P_1(3s3s)1S0​→(3s3p)3P1​ (λ=457λ= 457λ=457 nm) optical transition. For description of laser cooling of atoms in the optical trap with taking into account quantum recoil effects we consider two quantum models. The first one is based on direct numerical solution of quantum kinetic equation for atom density matrix and the second one is simplified model based on decomposition of atom density matrix over vibration states in the dipole trap. We search pumping field intensity and detuning for minimum cooling energy and fast laser cooling.
We study deep laser cooling of24Mg atoms in dipole optical trap with pumping field resonant to narrow (3s3s)1S0→ (3s3p)3P1(λ, = 457nm) optical transition. We consider two quantum models: the first one based on direct numerical solution of quantum kinetic equation for atom density matrix and the second one is simplified model based on decomposition of atom density matrix on vibration states in dipole trap. Both models shows close results. We search pumping field intensity and detuning for minimum laser cooling energy of atoms and fast laser cooling.
Deep laser cooling of 24Mg^{24}\mathrm{Mg}24Mg 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 24Mg^{24}\mathrm{Mg}24Mg 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.
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 study laser cooling of atoms with narrow-line optical transition, i.e. in regimes when quantum nature of laser-light interactions results significant effect on atom kinetics. We demonstrate the minimum of laser cooing temperature is reached for the light field detuning close to -3 recoil frequency, i.e. is much differ from standard Doppler cooling theory is used for semiclassical description of laser cooling. We define a set of dimensionless parameters that describe the steady state solution of cold atom distribution in laser light and cooling time. The results can be used for analysis an optimal conditions of laser cooling of atoms with narrow lines Ca, Sr and Mg are of interest for optical time standards.