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Joint Conference of the European Frequency and Time Forum and IEEE International Frequency Control Symposium (EFTF/IFCS)

Deep laser cooling of Mg in dipole trap for frequency standard

Прудников Олег Николаевич, A. V. Taǐchenachev, Valeriy I. Yudin, Ernst Maria Rasel

Published Jul 1, 2017• 0 citations
Publisher

Abstract

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.

DOI
10.1109/fcs.2017.8088915

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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.
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 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.
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 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.
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 theory of an atom dipole trap composed of a focused, far red-detuned, trapping laser beam, and a pair of red-detuned, counterpropagating, cooling beams is developed for the simplest realistic multilevel dipole interaction scheme based on a model of a (3+5)-level atom. The description of atomic motion in the trap is based on the quantum kinetic equations for the atomic density matrix and the reduced quasiclassical kinetic equation for atomic distribution function. It is shown that when the detuning of the trapping field is much larger than the detuning of the cooling field, and with low saturation, the one-photon absorption (emission) processes responsible for the trapping potential can be well separated from the two-photon processes responsible for sub-Doppler cooling atoms in the trap. Two conditions are derived that are necessary and sufficient for stable atomic trapping. The conditions show that stable atomic trapping in the optical dipole trap can be achieved when the trapping field has no effect on the two-photon cooling process and when the cooling field does not change the structure of the trapping potential but changes only the numerical value of the trapping potential well. It is concluded that the separation of the trapping and cooling processes in a pure optical dipole trap allows one to cool trapped atoms down to a minimum temperature close to the recoil temperature, keeping simultaneously a deep potential well.