Steady state of a low-density ensemble of atoms in a monochromatic field taking into account recoil effects

Prudnikov, O. N.; Il’enkov, R. Ya.; Taĭchenachev, A. V.; Tumaĭkin, A. M.; Yudin, V. I.

doi:10.1134/s1063776111050189

Cited by 29 publications

(16 citation statements)

References 14 publications

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“…[70] under weak-saturation approximation and with the help of adiabatic reduction of density matrix equations to ground state. Unfortunately that approximation gives good results not for wide range of parameters δ and I that can have an interest from the laser cooling view of point (e.g., see the work [64], where results of adiabatic approximation were compared with results of full quantum treatment). Three-dimensional quantum treatment with full account for the recoil effect and beyond the aforesaid approximations is quite difficult task that requires separate study.…”

Section: Discussionmentioning

confidence: 99%

“…We have solved the equation numerically on the basis of matrix continued fractions method. The details of the method can be found, for example, in [64] and we do not reproduce it here. Instead of that, we just present the numerical results.…”

Section: A Problem Statementmentioning

confidence: 99%

“…This treatment can be based on the density matrix formalism with full account for the recoil effect (e.g., see [9,58,64]). Moreover, as it will be seen in the next section, the quantum-treatment results noticeably differs from the semiclassical ones, based on the equation (5).…”

Section: Laser Cooling In Mot: Semiclassical Approximationmentioning

confidence: 99%

“…Here quantum treatment of atomic kinetics under the laser field (6) is based on the equation on single-atom density matrix in coordinate two-point representation that has the form (e.g., see [9,55,64]):…”

Section: A Problem Statementmentioning

confidence: 99%

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

et al. 2015

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The problem of deep laser cooling of 24 Mg atoms is theoretically studied. We propose two-stage sub-Doppler cooling strategy using electro-dipole transition 3 3 P2→3 3 D3 (λ = 383.9 nm). The first stage implies exploiting magneto-optical trap with σ + and σ − light beams, while the second one uses a lin⊥lin molasses. We focus on achieving large number of ultracold atoms (T ef f <10 µK) in a cold atomic cloud. The calculations have been done out of many widely used approximations and based on quantum treatment with taking full account of recoil effect. Steady-state average kinetic energies and linear momentum distributions of cold atoms are analyzed for various light field intensities and frequency detunings. The results of conducted quantum analysis have revealed noticeable differences from results of semiclassical approach based on the Fokker-Planck equation. At certain conditions the second cooling stage can provide sufficiently lower kinetic energies of atomic cloud as well as increased fraction of ultracold atoms than the first one. We hope that the obtained results can assist overcoming current experimental problems in deep cooling of 24 Mg atoms by means of laser fields. Cold magnesium atoms, being cooled in large number down to several µK, have certain interest, for example, in quantum metrology.

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Section: Discussionmentioning

confidence: 99%

Section: A Problem Statementmentioning

confidence: 99%

Section: Laser Cooling In Mot: Semiclassical Approximationmentioning

confidence: 99%

Section: A Problem Statementmentioning

confidence: 99%

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

et al. 2015

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“…The numerical calculations in this work were per formed using the method developed in our recent work [11] for analyzing the kinetics of cold atoms with the complete inclusion of recoil effects. This method makes it possible to study stationary distributions of atoms in both momentum and coordinate spaces for arbitrary intensity of the light field and arbitrary fre quency detuning.…”

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Anomalous spatial concentration of atoms in the field of a standing light wave

et al. 2012

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1.Laser radiation is a unique tool that makes it pos sible to efficiently control both the internal quantum state of atoms and their external degrees of freedom. The latter underlies laser cooling of atoms and ions, which is a modern field of quantum physics that is at the boundary between atomic optics and laser physics (see, e.g., [1][2][3][4][5]). Gradually increasing interest in this field is primarily due to numerous implemented diverse exciting applications of laser cooling and trap ping of atoms. Of particular interest are wide prospects of its application in fundamental quantum metrology, where laser cooled atoms are the main candidates for creating a new generation of optical frequency and time standards [6] with a very high accuracy (relative error as small as 10 -18 -10 -17 ) [7][8][9]. Laser cooling has important applications in atomic interferometry, implementation of Bose-Einstein condensation, quantum informatics, and atomic nanolithography.Various methods of laser cooling and localization of atoms (magneto optical trap, optical grating, dipole traps of various configurations, etc.) have already been developed, which make it possible to cool atoms to ultralow temperatures (to hundreds of nanokelvin). It is quite difficult to theoretically describe the kinetics of cold atoms in laser fields. For this reason, various approximations are often used. In particular, the main mechanisms of laser cooling and trapping were under stood using a two level model of atom with nondegen erate energy levels [1,2]. This model under certain conditions corresponds to real atoms with a F g = 0 F e = 1 transition. Although the two level model is con sidered to be well studied, some aspects remain unan alyzed. Indeed, even in this simplest system, addi tional simplifications are used, assuming that the stan dard deviation of atomic momenta is much higher than the momentum of a photon, i.e., បk/Δp a Ӷ 1 (the so called semiclassical approximation [2, 10]). Then, neglecting the spatial localization of atoms in the opti cal potential (at a scale of the light wavelength), an approximate Fokker-Planck equation for the momentum distribution function of atoms is consid ered rather than the exact equation for the density matrix.Concerning the spatial location of atoms in the field of a standing light wave, it is well known that atoms in weak fields are concentrated near minima of the optical potential [1,2]. In the case of red frequency detuning (when the laser frequency is lower than the frequency of an atomic transition) and blue frequency detuning, the minima of the optical potential coincide with the antinodes and nodes of the field, respectively. However, the regime of a moderate light field and red frequency detuning has not yet been analyzed from this point of view. In particular, a new effect-the anomalous concentration of atoms outside of the min ima of the optical potential and, the more so, at the maxima of the potential-is revealed in this work. This counterintuitive behavior of atoms appears to be The stationary mome...

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