Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:physics/0610123 · Physical Review A

Polarization-gradient laser cooling as a way to create strongly localized structures for atom lithography

Прудников Олег Николаевич, A. V. Taǐchenachev, Anatolii M Tumaikin, Valeriy I. Yudin

Published Feb 28, 2007• 14 citations
arXivHTMLPDF

Abstract

Generally, conditions for deep sub-Doppler laser cooling do not match conditions for strong atomic localization, that takes place in a deeper optical potential and leads to higher temperature. Moreover, for a given detuning in a deep optical potential the secular approximation, which is frequently used for a quantum description of laser cooling, fails. Here we investigate the atomic localization in optical potential, using a full quantum approach for atomic density matrix beyond the secular approximation. It is shown that laser cooling in a deep optical potential, created by a light field with polarization gradients, can be used as an alternative method for the formation of high contrast spatially localized structures of atoms for the purposes of atom lithography and atomic nanofabrication. Finally, we analyze possible limits for the width and contrast of localized atomic structures that can be reached in this type of light mask.

DOI
10.1103/physreva.75.023413

Related papers

Dissipative light mask generated by a nonuniformly polarized field for atomic lithography

Прудников Олег Николаевич, А. В. Тайченачев, Anatolii M Tumaikin +1 more

The localization of atoms in a deep optical potential is analyzed in the framework of the completely quantum description of the motion of the atoms using the kinetic equation for the density matrix. It is shown that the laser cooling of the neutral atoms in the deep optical potential at a relatively large detuning of the light field from resonance can be used as a method for forming spatially localized atomic structures with a high contrast for atomic lithography. This method is alternative to nondissipative light masks.

Journal of Experimental and Theoretical Physics•Jun 1, 2007•13 citations

Deep Laser Cooling of Atoms on Narrow-Line Optical Transitions in Polarized Fields: Scaling Law

R. Ya. Ilenkov, Прудников Олег Николаевич, A. V. Taǐchenachev +1 more

The theoretical description of the kinetics of neutral atoms in the polarized light fields with all the atomic levels, the coherence, the recoil effect is both important and challenging problem. The first step toward understanding mechanisms of interaction between atoms and light was called quasi-classical approach. [1,2] It lies in the fact that the equations for the density matrix can be reduced to the Fokker-Planck equation for the Wigner function in the phase space. But the semiclassical approximation is inapplicable for investigating the cooling of atoms at clock transitions, because the quasiclassical parameter (the recoil frequency) is not small (in comparison with the natural line width). Later quantum methods were developed [3], for example, the secular approach which describes cooling and localization of atoms in the optical potential. Secular approximation fails high vibrational levels and for atoms in high vibrational states.

Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)•Jun 1, 2019•0 citations

Laser cooling of trapped ions with polarization gradients

J. I. Cirac, R. Blatt, A. S. Parkins +1 more

Laser cooling of a single trapped ion with Zeeman substructure below the Doppler limit is considered theoretically. The laser field consists of two counterpropagating beams linearly polarized in different directions, and the internal atomic transition is ${\mathit{J}}_{\mathit{g}}$=1/2\ensuremath{\rightarrow}${\mathit{J}}_{\mathit{e}}$=3/2. The ion is assumed to be localized to spatial dimensions smaller than the optical wavelength (Lamb-Dicke limit) and placed at a specific position with respect to the laser beams. Under the assumption that the rate for optical pumping between the atomic ground states defines the smallest time constant in the system, analytic expressions for the final energy and the cooling rates are derived, with both a semiclassical and a full quantum treatment. The results show that laser cooling of a trapped ion using polarization gradients leads to very low energies. These energies are insensitive to the precise localization of the ion with respect to the lasers, the angle between the direction of the polarizations of the laser beams, and the detuning of the cooling laser.

Physical Review A•Aug 1, 1993•20 citations

Laser cooling limits in fields with a polarisation gradient of atoms with different recoil energies

Anastasia Kirpichnikova, Прудников Олег Николаевич, R. Ya. Ilenkov +2 more

Based on the numerical solution of the quantum kinetic equation for the atomic density matrix, which makes it possible to accurately take into account the recoil effects in the interaction of atoms with field photons, we have studied the limits of laser cooling of atoms using closed optical transitions characterised by different recoil parameters (the ratio of the recoil energy to the natural linewidth). It is shown that for optical transitions with an insufficiently small recoil parameter, the polarisation effects, which lead to the possibility of sub-Doppler laser cooling, lose their efficiency and do not ensure an attainment of the temperature below the Doppler limit. The analysis performed allows one to outline the boundaries of the sub-Doppler theory of laser cooling of atoms.

Quantum Electronics•Sep 28, 2020•12 citations

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

Прудников Олег Николаевич, R. Ya. Ilenkov, A. V. Taǐchenachev +2 more

A method has been developed for obtaining the steady-state solution of a quantum kinetic equation for the atomic density matrix in an arbitrarily polarized monochromatic field with the complete inclusion of recoil effects and degeneracy of atomic levels in the projection of the angular momentum. This method makes it possible to obtain the most general solution beyond the previously accepted approximations (semiclassical approximation, secular approximation, etc.). In particular, it has been shown that the laser cooling temperature is a function of not only the depth of the optical potential (as was previously thought), but also the mass of an atom.

Journal of Experimental and Theoretical Physics•Jun 1, 2011•32 citations

Quantum calculations for 1D polarization gradient cooling with J{sub g}>1/2

M. R. Doery, T. H. Bergeman

Quantum calculations for magnetic field induced laser cooling have shown that cooling is less efficient for atoms near the bottom of the light shift potential wells. Inversion of population among the lowest quantum states is found when the pumping rate is less than the well depth. To see whether this occurs in lin {perpendicular} lin polarization gradient cooling, we are performing quantum density matrix calculations. Here the light shift potential matrix obtained in the weak excitation approximations is not diagonal for J{sub g} {>=} 1. We compute eigenfunctions by Fourier transform methods. The band structure is novel and puzzling. The dispersion relation (E vs. Bloch index {nu}) has 2 branches for either 2 or 3 coupled channels (coupled m{sub F} values). Degeneracies occur at {nu}=0 for 2 channels, and {nu}=1 for 3 channels. We are computing optical excitation and decay rates and the temporal evolution of the density matrix so as to obtain the velocity distribution of the cooled atoms.

Bulletin of the American Physical Society•May 1, 1993•0 citations
Generally, conditions for deep sub-Doppler laser cooling do not match conditions for strong atomic localization, that takes place in a deeper optical potential and leads to higher temperature. Moreover, for a given detuning in a deep optical potential the secular approximation, which is frequently used for a quantum description of laser cooling, fails. Here we investigate the atomic localization in optical potential, using a full quantum approach for atomic density matrix beyond the secular approximation. It is shown that laser cooling in a deep optical potential, created by a light field with polarization gradients, can be used as an alternative method for the formation of high contrast spatially localized structures of atoms for the purposes of atom lithography and atomic nanofabrication. Finally, we analyze possible limits for the width and contrast of localized atomic structures that can be reached in this type of light mask.
The localization of atoms in a deep optical potential is analyzed in the framework of the completely quantum description of the motion of the atoms using the kinetic equation for the density matrix. It is shown that the laser cooling of the neutral atoms in the deep optical potential at a relatively large detuning of the light field from resonance can be used as a method for forming spatially localized atomic structures with a high contrast for atomic lithography. This method is alternative to nondissipative light masks.
The theoretical description of the kinetics of neutral atoms in the polarized light fields with all the atomic levels, the coherence, the recoil effect is both important and challenging problem. The first step toward understanding mechanisms of interaction between atoms and light was called quasi-classical approach. [1,2] It lies in the fact that the equations for the density matrix can be reduced to the Fokker-Planck equation for the Wigner function in the phase space. But the semiclassical approximation is inapplicable for investigating the cooling of atoms at clock transitions, because the quasiclassical parameter (the recoil frequency) is not small (in comparison with the natural line width). Later quantum methods were developed [3], for example, the secular approach which describes cooling and localization of atoms in the optical potential. Secular approximation fails high vibrational levels and for atoms in high vibrational states.
Laser cooling of a single trapped ion with Zeeman substructure below the Doppler limit is considered theoretically. The laser field consists of two counterpropagating beams linearly polarized in different directions, and the internal atomic transition is Jg{\mathit{J}}_{\mathit{g}}Jg​=1/2\ensuremath{\rightarrow}Je{\mathit{J}}_{\mathit{e}}Je​=3/2. The ion is assumed to be localized to spatial dimensions smaller than the optical wavelength (Lamb-Dicke limit) and placed at a specific position with respect to the laser beams. Under the assumption that the rate for optical pumping between the atomic ground states defines the smallest time constant in the system, analytic expressions for the final energy and the cooling rates are derived, with both a semiclassical and a full quantum treatment. The results show that laser cooling of a trapped ion using polarization gradients leads to very low energies. These energies are insensitive to the precise localization of the ion with respect to the lasers, the angle between the direction of the polarizations of the laser beams, and the detuning of the cooling laser.
Based on the numerical solution of the quantum kinetic equation for the atomic density matrix, which makes it possible to accurately take into account the recoil effects in the interaction of atoms with field photons, we have studied the limits of laser cooling of atoms using closed optical transitions characterised by different recoil parameters (the ratio of the recoil energy to the natural linewidth). It is shown that for optical transitions with an insufficiently small recoil parameter, the polarisation effects, which lead to the possibility of sub-Doppler laser cooling, lose their efficiency and do not ensure an attainment of the temperature below the Doppler limit. The analysis performed allows one to outline the boundaries of the sub-Doppler theory of laser cooling of atoms.
A method has been developed for obtaining the steady-state solution of a quantum kinetic equation for the atomic density matrix in an arbitrarily polarized monochromatic field with the complete inclusion of recoil effects and degeneracy of atomic levels in the projection of the angular momentum. This method makes it possible to obtain the most general solution beyond the previously accepted approximations (semiclassical approximation, secular approximation, etc.). In particular, it has been shown that the laser cooling temperature is a function of not only the depth of the optical potential (as was previously thought), but also the mass of an atom.
Quantum calculations for magnetic field induced laser cooling have shown that cooling is less efficient for atoms near the bottom of the light shift potential wells. Inversion of population among the lowest quantum states is found when the pumping rate is less than the well depth. To see whether this occurs in lin {perpendicular} lin polarization gradient cooling, we are performing quantum density matrix calculations. Here the light shift potential matrix obtained in the weak excitation approximations is not diagonal for J{sub g} {>=} 1. We compute eigenfunctions by Fourier transform methods. The band structure is novel and puzzling. The dispersion relation (E vs. Bloch index {nu}) has 2 branches for either 2 or 3 coupled channels (coupled m{sub F} values). Degeneracies occur at {nu}=0 for 2 channels, and {nu}=1 for 3 channels. We are computing optical excitation and decay rates and the temporal evolution of the density matrix so as to obtain the velocity distribution of the cooled atoms.