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:1409.0244 · New Journal of Physics

Magneto-optical trapping forces for atoms and molecules with complex level structures

Michael R. Tarbutt

Published Jan 15, 2015• 88 citations
arXivHTMLPDF

Abstract

Laser cooling and magneto-optical trapping of molecules typically involves multiple transitions driven by several laser frequencies. We analyze how magneto-optical trapping forces depend on the angular momenta, F l and F u , and the g -factors, g l and g u , of the lower and upper states. When the polarizations must be reversed relative to cases where The correct choice of circular polarization depends on the sign of g u but not on the sign of g l . If g u is zero there is no trapping force, and the trapping force is very weak whenever g u is small compared to g l , which it usually is when the cooling transition is the to transition of a molecule. For some molecules, mixing of the excited state with a nearby excited state can greatly increase g u , leading to stronger trapping forces. A strong trapping force can also be produced by rapidly and synchronously reversing both the magnetic field and the laser polarizations. We simulate a recent experiment on magneto-optical trapping of SrF molecules, and suggest that an alternative choice of laser beam polarizations will strengthen the trapping force.

DOI
10.1088/1367-2630/17/1/015007

Related papers

Grating magneto-optical traps with complicated level structures

Daniel S. Barker, Peter K. Elgee, Ananya Sitaram +4 more

Abstract We study the forces and optical pumping within grating magneto-optical traps (MOTs) operating on transitions with non-trivial level structure. In contrast to the standard six-beam MOT configuration, rate equation modeling predicts that the asymmetric laser geometry of a grating MOT will produce spin-polarized atomic samples. Furthermore, the Landé g-factors and total angular momenta of the trapping transition strongly influence both the confinement and equilibrium position of the trap. Using the intuition gained from the rate equation model, we realize a grating MOT of fermionic 87Sr and observe that it forms closer to the center of the trap’s quadrupole magnetic field than its bosonic counterpart. We also explore the application of grating MOTs to molecule laser cooling, where the rate equations suggest that dual-frequency operation is necessary, but not sufficient, for stable confinement for type-II level structures. To test our molecule laser cooling models, we create grating MOTs using the D 1 line of 7Li and see that only two of the four possible six-beam polarization configurations operate in the grating geometry. Our results will aid the development of portable atom and molecule traps for time keeping, inertial navigation, and precision measurement.

arXiv:2305.07732•New Journal of Physics•Oct 1, 2023•22 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

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

Trapping and cooling mechanisms in blue-detuned magneto-optical traps of molecules

Qinshu Lyu, Michael R. Tarbutt

In red-detuned magneto-optical traps (MOTs) of molecules, sub-Doppler heating competes with Doppler cooling, resulting in high temperature and low density. A solution is offered by the blue-detuned MOT where sub- Doppler cooling dominates and the cloud is compressed. Several blue-detuned molecular MOTs have been implemented. A recent implementation relies on a pair of orthogonally polarized components whose frequency separation is smaller than the transition linewidth. We identify the trapping force in these MOTs. At a certain magnetic field, there is a state that is dark to the laser propagating in one direction, but not to the counterpropagating one. This Zeeman-induced dark state (ZIDS) sets up an imbalance in the photon scattering rate, leading to a restoring force. We also study the role of the moving lattices generated by the closely spaced frequency components of the light. We show that there is a velocity-dependent force that drives the molecules toward the speeds of these moving lattices, and that over a relevant range of magnetic fields this combines with the ZIDS force to transport molecules toward the center of the MOT. Here, gray molasses cooling, assisted by nonadiabatic transitions driven by the time-varying polarization of the light field, cools the molecules toward zero velocity. We study these mechanisms for model systems with simple level structures and then extend them to molecules with ground-state hyperfine structure.

arXiv:2601.21097•Physical Review Research•May 3, 2026•0 citations

Microwave-mediated magneto-optical trap for polar molecules

Dizhou Xie, Wenhao Bu, Bo Yan

Realizing a molecular magneto-optical trap has been a dream for cold molecular physicists for a long time. However, due to the complex energy levels and the small effective Lande g -factor of the excited states, the traditional magneto-optical trap (MOT) scheme does not work very well for polar molecules. One way to overcome this problem is the switching MOT, which requires very fast switching of both the magnetic field and the laser polarizations. Switching laser polarizations is relatively easy, but fast switching of the magnetic field is experimentally challenging. Here we propose an alternative approach, the microwave-mediated MOT, which requires a slight change of the current experimental setup to solve the problem. We calculate the MOT force and compare it with the traditional MOT and the switching MOT scheme. The results show that we can operate a good MOT with this simple setup.

Chinese Physics B•May 1, 2016•4 citations

Narrow-Line Magneto-Optical Cooling and Trapping of Strongly Magnetic Atoms

Andrew J. Berglund, James L. Hanssen, Jabez J. McClelland

Laser cooling on weak transitions is a useful technique for reaching ultracold temperatures in atoms with multiple valence electrons. However, for strongly magnetic atoms a conventional narrow-line magneto-optical trap (MOT) is destabilized by competition between optical and magnetic forces. We overcome this difficulty in Er by developing an unusual narrow-line MOT that balances optical and magnetic forces using laser light tuned to the blue side of a narrow (8 kHz) transition. The trap population is spin polarized with temperatures reaching below 2 muK. Our results constitute an alternative method for laser cooling on weak transitions, applicable to rare-earth-metal and metastable alkaline earth elements.

arXiv:0802.0857•Physical Review Letters•Mar 18, 2008•65 citations
Laser cooling and magneto-optical trapping of molecules typically involves multiple transitions driven by several laser frequencies. We analyze how magneto-optical trapping forces depend on the angular momenta, F l and F u , and the g -factors, g l and g u , of the lower and upper states. When the polarizations must be reversed relative to cases where The correct choice of circular polarization depends on the sign of g u but not on the sign of g l . If g u is zero there is no trapping force, and the trapping force is very weak whenever g u is small compared to g l , which it usually is when the cooling transition is the to transition of a molecule. For some molecules, mixing of the excited state with a nearby excited state can greatly increase g u , leading to stronger trapping forces. A strong trapping force can also be produced by rapidly and synchronously reversing both the magnetic field and the laser polarizations. We simulate a recent experiment on magneto-optical trapping of SrF molecules, and suggest that an alternative choice of laser beam polarizations will strengthen the trapping force.
Abstract We study the forces and optical pumping within grating magneto-optical traps (MOTs) operating on transitions with non-trivial level structure. In contrast to the standard six-beam MOT configuration, rate equation modeling predicts that the asymmetric laser geometry of a grating MOT will produce spin-polarized atomic samples. Furthermore, the Landé g-factors and total angular momenta of the trapping transition strongly influence both the confinement and equilibrium position of the trap. Using the intuition gained from the rate equation model, we realize a grating MOT of fermionic 87Sr and observe that it forms closer to the center of the trap’s quadrupole magnetic field than its bosonic counterpart. We also explore the application of grating MOTs to molecule laser cooling, where the rate equations suggest that dual-frequency operation is necessary, but not sufficient, for stable confinement for type-II level structures. To test our molecule laser cooling models, we create grating MOTs using the D 1 line of 7Li and see that only two of the four possible six-beam polarization configurations operate in the grating geometry. Our results will aid the development of portable atom and molecule traps for time keeping, inertial navigation, and precision measurement.
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 $J\ensuremath{\rightarrow}J,J\ensuremath{-}1$.
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.
In red-detuned magneto-optical traps (MOTs) of molecules, sub-Doppler heating competes with Doppler cooling, resulting in high temperature and low density. A solution is offered by the blue-detuned MOT where sub- Doppler cooling dominates and the cloud is compressed. Several blue-detuned molecular MOTs have been implemented. A recent implementation relies on a pair of orthogonally polarized components whose frequency separation is smaller than the transition linewidth. We identify the trapping force in these MOTs. At a certain magnetic field, there is a state that is dark to the laser propagating in one direction, but not to the counterpropagating one. This Zeeman-induced dark state (ZIDS) sets up an imbalance in the photon scattering rate, leading to a restoring force. We also study the role of the moving lattices generated by the closely spaced frequency components of the light. We show that there is a velocity-dependent force that drives the molecules toward the speeds of these moving lattices, and that over a relevant range of magnetic fields this combines with the ZIDS force to transport molecules toward the center of the MOT. Here, gray molasses cooling, assisted by nonadiabatic transitions driven by the time-varying polarization of the light field, cools the molecules toward zero velocity. We study these mechanisms for model systems with simple level structures and then extend them to molecules with ground-state hyperfine structure.
Realizing a molecular magneto-optical trap has been a dream for cold molecular physicists for a long time. However, due to the complex energy levels and the small effective Lande g -factor of the excited states, the traditional magneto-optical trap (MOT) scheme does not work very well for polar molecules. One way to overcome this problem is the switching MOT, which requires very fast switching of both the magnetic field and the laser polarizations. Switching laser polarizations is relatively easy, but fast switching of the magnetic field is experimentally challenging. Here we propose an alternative approach, the microwave-mediated MOT, which requires a slight change of the current experimental setup to solve the problem. We calculate the MOT force and compare it with the traditional MOT and the switching MOT scheme. The results show that we can operate a good MOT with this simple setup.
Laser cooling on weak transitions is a useful technique for reaching ultracold temperatures in atoms with multiple valence electrons. However, for strongly magnetic atoms a conventional narrow-line magneto-optical trap (MOT) is destabilized by competition between optical and magnetic forces. We overcome this difficulty in Er by developing an unusual narrow-line MOT that balances optical and magnetic forces using laser light tuned to the blue side of a narrow (8 kHz) transition. The trap population is spin polarized with temperatures reaching below 2 muK. Our results constitute an alternative method for laser cooling on weak transitions, applicable to rare-earth-metal and metastable alkaline earth elements.