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

Physical Review A

Magneto-optical force in a resonant field of elliptically polarized light waves

Прудников Олег Николаевич, А. В. Тайченачев, Anatolii M Tumaikin, Valeriy I. Yudin

Published Mar 26, 2008• 8 citations
Publisher

Abstract

In a one-dimensional model we consider the dependence of the magneto-optical force on the elliptical polarization of laser beams for different types of closed atomic transitions ${J}_{g}\ensuremath{\rightarrow}{J}_{e}$. The linear dependencies on atomic velocity and magnetic field of the magneto-optical force are found analytically. These results establish the possibility (for ${J}_{g}>0$) to capture atoms in a magneto-optical trap even at zero detuning (i.e., at the exact resonance of atoms with laser field) in certain $(ϵ\ensuremath{-}\ensuremath{\theta}\ensuremath{-}\overline{ϵ})$ field configurations as well as in an anomalous blue-detuned region. The nonlinear dependencies of the force on atomic velocity and magnetic field are studied numerically. The capture velocity and the number of trapped atoms are estimated.

DOI
10.1103/physreva.77.033420

Related papers

Magnetooptical force in the resonance field formed by elliptically polarized light waves

Прудников Олег Николаевич, A. V. Taǐchenachev, Anatolii M Tumaikin +1 more

The dependence of the magnetooptical force on the ellipticity of the polarization of light beams is studied in terms of a one-dimensional model for closed J g → J e optical transitions. A linear velocity and magnetic-field approximation is used to find analytical expressions for the magnetooptical force for a number of transitions. In the light fields formed by waves with an elliptical polarization, qualitatively new contributions are shown to appear; they have an even dependence on the detuning of the light field and do not disappear even in the case of an exact resonance. An analysis of these results demonstrates that a magnetooptical trap can stably operate at the zero detuning of the field. Numerical methods are used to investigate the nonlinear dependence of the force on the atom velocity and the magnetic field and to estimate the characteristic atom trapping rate and the number of trapped atoms.

Journal of Experimental and Theoretical Physics•May 1, 2008•1 citation

Stimulated magneto-optical force in the dressed-atom picture

Johannes Söding, Rudolf Grimm

The simulated magneto-optical force, which in the presence of a longitudinal static magnetic field is exerted on atoms resonant with the high-intensity light field of two counterpropagating, linearly polarized laser beams with an angle of \ensuremath{\sim}45\ifmmode^\circ\else\textdegree\fi{} between their directions of polarization, is described in the dressed-atom picture. This allows an easy calculation of the force on atoms at rest, illustratively explains its nonzero wavelength average, and provides an intuitive understanding of its dependence on the atomic velocity. For a simple atomic model transition (J=0\ensuremath{\leftrightarrows}J'=1) the velocity-dependent force is calculated by considering the motion along the dressed states and using the Landau-Zener model for the nonadiabatic transitions at the avoided level crossings. It is shown that for a certain relation between Larmor and optical Rabi frequency a perfectly diabatic motion takes place, leading to a disappearance of the velocity-tuned (doppleron) resonance structure.

Physical Review A•Sep 1, 1994•6 citations

Rectification of the dipole force in a monochromatic field created by elliptically polarized waves

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

The rectification of the force of induced light pressure in laser fields formed by elliptically polarized running waves in zero magnetic field is considered. Explicit analytic expressions for the induced and spontaneous forces of light pressure exerted on a stationary atom are obtained for two classes of closed optical transitions: J g = J → J e = J +1 and J g = J → J e = J ( J is half-integral), where J g and J e are the total angular momenta of the ground and excited energy levels. It is shown that the ellipticity of waves is the necessary condition for the emergence of the rectification of the induced force in a monochromatic field. The optimal parameters of the field and the maximum rectification coefficient are calculated for a number of optical transitions. The dependence of the rectified force on the velocity is investigated analytically and numerically for the simplest 1/2→1/2 transition.

Journal of Experimental and Theoretical Physics•Jul 1, 2001•3 citations

Three-dimensional Doppler, polarization-gradient, and magneto-optical forces for atoms and molecules with dark states

J. A. Devlin, Michael R. Tarbutt

We theoretically investigate the damping and trapping forces in a three-dimensional magneto-optical trap (MOT), by numerically solving the optical Bloch equations.We focus on the case where there are dark states because the atom is driven on a 'type-II' system where the angular momentum of the excited state, F¢, is less than or equal to that of the ground state, F. For these systems we find that the force in a three-dimensional light field has very different behaviour to its one dimensional counterpart.This differs from the more commonly used 'type-I' systems (F F 1 ¢ = + ) where the 1D and 3D behaviours are similar.Unlike type-I systems where, for red-detuned light, both Doppler and sub-Doppler forces damp the atomic motion towards zero velocity, in type-II systems in 3D, the Doppler force and polarization gradient force have opposite signs.As a result, the atom is driven towards a non-zero equilibrium velocity, v 0 , where the two forces cancel.We find that v 0 2 scales linearly with the intensity of the light and is fairly insensitive to the detuning from resonance.We also discover a new magneto-optical force that alters the normal MOT force at low magnetic fields and whose influence is greatest in the type-II systems.We discuss the implications of these findings for the laser cooling and magneto-optical trapping of molecules where type-II transitions are unavoidable in realising closed optical cycling transitions.

arXiv:1608.04645•New Journal of Physics•Dec 12, 2016•72 citations

Bichromatic magneto-optical trapping for J→J,J−1 configurations

Anne Cournol, P. Pillet, Hans Lignier +1 more

A magneto-optical trap (MOT) of atoms or molecules is studied when two lasers of different detunings and polarization are used. Especially for $J\ensuremath{\rightarrow}J,J\ensuremath{-}1$ transitions, a scheme using more than one frequency per transition and different polarization is required to create a significant force. Calculations have been performed with the simplest forms of the $J\ensuremath{\rightarrow}J\ensuremath{-}1$ case (i.e., ${J}^{\ensuremath{'}\ensuremath{'}}=1\ensuremath{\rightarrow}{J}^{\ensuremath{'}}=0$) and $J\ensuremath{\rightarrow}J$ case (i.e., ${J}^{\ensuremath{'}\ensuremath{'}}=1/2\ensuremath{\rightarrow}{J}^{\ensuremath{'}}=1/2$). A one-dimensional (1D) model is presented and a complete 3D simulation using rate equations confirms the results. Even in the absence of Zeeman effect in the excited state, where no force is expected in the single laser field configuration, we show that efficient cooling and trapping forces are restored in our configuration. We study this mechanism for the ${\mathrm{C}}_{2}^{\ensuremath{-}}$ molecular anion as a typical example of the interplay between the two simple transitions $J\ensuremath{\rightarrow}J,J\ensuremath{-}1$.

arXiv:1605.06464•Physical Review A•May 24, 2016•3 citations

Nonlinear magneto-optical rotation produced by atoms near a J=1→J=0 transition

Vitalij Roščinski, Janusz Czub, W. Miklaszewski

The nonlinear magneto-optical rotation in a medium consisting of $J=1\ensuremath{\rightarrow}J=0$ atoms placed in a static magnetic field is studied. The density matrix approach and irreducible atomic basis are used to describe the state of the atomic system. The stationary propagation equations for two collinear laser beams with perpendicular circular polarizations are derived and analyzed in the case of the magnetic field perpendicular to the light propagation direction. The effect of the linear polarization rotation toward the direction parallel or perpendicular to the magnetic field vector and lossless propagation of the resulting light are predicted. The conversion of the circularly polarized beam into linearly polarized one is shown. The propagation of the leading edges of switched on cw-laser beams and their stationary propagation are analyzed numerically. The dependence of the considered effects on the light detuning and on the additional magnetic field component parallel to the light propagation direction is discussed. The destructive role of the collisional relaxation is demonstrated.

Physical Review A•Sep 17, 2004•2 citations
In a one-dimensional model we consider the dependence of the magneto-optical force on the elliptical polarization of laser beams for different types of closed atomic transitions Jg\ensuremath→Je{J}_{g}\ensuremath{\rightarrow}{J}_{e}Jg​\ensuremath→Je​. The linear dependencies on atomic velocity and magnetic field of the magneto-optical force are found analytically. These results establish the possibility (for Jg>0{J}_{g}>0Jg​>0) to capture atoms in a magneto-optical trap even at zero detuning (i.e., at the exact resonance of atoms with laser field) in certain (ϵ\ensuremath−\ensuremathθ\ensuremath−ϵ‾)(ϵ\ensuremath{-}\ensuremath{\theta}\ensuremath{-}\overline{ϵ})(ϵ\ensuremath−\ensuremathθ\ensuremath−ϵ) field configurations as well as in an anomalous blue-detuned region. The nonlinear dependencies of the force on atomic velocity and magnetic field are studied numerically. The capture velocity and the number of trapped atoms are estimated.
The dependence of the magnetooptical force on the ellipticity of the polarization of light beams is studied in terms of a one-dimensional model for closed J g → J e optical transitions. A linear velocity and magnetic-field approximation is used to find analytical expressions for the magnetooptical force for a number of transitions. In the light fields formed by waves with an elliptical polarization, qualitatively new contributions are shown to appear; they have an even dependence on the detuning of the light field and do not disappear even in the case of an exact resonance. An analysis of these results demonstrates that a magnetooptical trap can stably operate at the zero detuning of the field. Numerical methods are used to investigate the nonlinear dependence of the force on the atom velocity and the magnetic field and to estimate the characteristic atom trapping rate and the number of trapped atoms.
The simulated magneto-optical force, which in the presence of a longitudinal static magnetic field is exerted on atoms resonant with the high-intensity light field of two counterpropagating, linearly polarized laser beams with an angle of \ensuremath{\sim}45\ifmmode^\circ\else\textdegree\fi{} between their directions of polarization, is described in the dressed-atom picture. This allows an easy calculation of the force on atoms at rest, illustratively explains its nonzero wavelength average, and provides an intuitive understanding of its dependence on the atomic velocity. For a simple atomic model transition (J=0\ensuremath{\leftrightarrows}J'=1) the velocity-dependent force is calculated by considering the motion along the dressed states and using the Landau-Zener model for the nonadiabatic transitions at the avoided level crossings. It is shown that for a certain relation between Larmor and optical Rabi frequency a perfectly diabatic motion takes place, leading to a disappearance of the velocity-tuned (doppleron) resonance structure.
The rectification of the force of induced light pressure in laser fields formed by elliptically polarized running waves in zero magnetic field is considered. Explicit analytic expressions for the induced and spontaneous forces of light pressure exerted on a stationary atom are obtained for two classes of closed optical transitions: J g = J → J e = J +1 and J g = J → J e = J ( J is half-integral), where J g and J e are the total angular momenta of the ground and excited energy levels. It is shown that the ellipticity of waves is the necessary condition for the emergence of the rectification of the induced force in a monochromatic field. The optimal parameters of the field and the maximum rectification coefficient are calculated for a number of optical transitions. The dependence of the rectified force on the velocity is investigated analytically and numerically for the simplest 1/2→1/2 transition.
We theoretically investigate the damping and trapping forces in a three-dimensional magneto-optical trap (MOT), by numerically solving the optical Bloch equations.We focus on the case where there are dark states because the atom is driven on a 'type-II' system where the angular momentum of the excited state, F¢, is less than or equal to that of the ground state, F. For these systems we find that the force in a three-dimensional light field has very different behaviour to its one dimensional counterpart.This differs from the more commonly used 'type-I' systems (F F 1 ¢ = + ) where the 1D and 3D behaviours are similar.Unlike type-I systems where, for red-detuned light, both Doppler and sub-Doppler forces damp the atomic motion towards zero velocity, in type-II systems in 3D, the Doppler force and polarization gradient force have opposite signs.As a result, the atom is driven towards a non-zero equilibrium velocity, v 0 , where the two forces cancel.We find that v 0 2 scales linearly with the intensity of the light and is fairly insensitive to the detuning from resonance.We also discover a new magneto-optical force that alters the normal MOT force at low magnetic fields and whose influence is greatest in the type-II systems.We discuss the implications of these findings for the laser cooling and magneto-optical trapping of molecules where type-II transitions are unavoidable in realising closed optical cycling transitions.
A magneto-optical trap (MOT) of atoms or molecules is studied when two lasers of different detunings and polarization are used. Especially for $J\ensuremath{\rightarrow}J,J\ensuremath{-}1$ transitions, a scheme using more than one frequency per transition and different polarization is required to create a significant force. Calculations have been performed with the simplest forms of the $J\ensuremath{\rightarrow}J\ensuremath{-}1$ case (i.e., ${J}^{\ensuremath{'}\ensuremath{'}}=1\ensuremath{\rightarrow}{J}^{\ensuremath{'}}=0$) and $J\ensuremath{\rightarrow}J$ case (i.e., ${J}^{\ensuremath{'}\ensuremath{'}}=1/2\ensuremath{\rightarrow}{J}^{\ensuremath{'}}=1/2$). A one-dimensional (1D) model is presented and a complete 3D simulation using rate equations confirms the results. Even in the absence of Zeeman effect in the excited state, where no force is expected in the single laser field configuration, we show that efficient cooling and trapping forces are restored in our configuration. We study this mechanism for the ${\mathrm{C}}_{2}^{\ensuremath{-}}$ molecular anion as a typical example of the interplay between the two simple transitions $J\ensuremath{\rightarrow}J,J\ensuremath{-}1$.
The nonlinear magneto-optical rotation in a medium consisting of $J=1\ensuremath{\rightarrow}J=0$ atoms placed in a static magnetic field is studied. The density matrix approach and irreducible atomic basis are used to describe the state of the atomic system. The stationary propagation equations for two collinear laser beams with perpendicular circular polarizations are derived and analyzed in the case of the magnetic field perpendicular to the light propagation direction. The effect of the linear polarization rotation toward the direction parallel or perpendicular to the magnetic field vector and lossless propagation of the resulting light are predicted. The conversion of the circularly polarized beam into linearly polarized one is shown. The propagation of the leading edges of switched on cw-laser beams and their stationary propagation are analyzed numerically. The dependence of the considered effects on the light detuning and on the additional magnetic field component parallel to the light propagation direction is discussed. The destructive role of the collisional relaxation is demonstrated.