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:2507.07475

Quantum theory of magneto-optical trap

Прудников Олег Николаевич, A. V. Taǐchenachev, Valeriy I. Yudin, Lin Zhou, Mingsheng Zhan

Published Jul 10, 2025• 0 citations
arXivHTMLPDF

Abstract

We present a quantum theory of a magneto-optical trap (MOT) from first principles based on the quantum kinetic equation for the atomic density matrix with taking into account the recoil effects caused by the interaction of atoms with the laser field. An efficient method for solving the quantum kinetic equation is proposed. It is shown that the steady-state solution describing the atoms in the MOT has a significantly non-equilibrium nature and can be described within the framework of a two-temperature distribution. The momentum distribution of cold atoms in the MOT depends on the magnetic field gradient and, in general, significantly differs from the momentum distribution of atoms in the optical molasses, which is usually used as an approximation to describe the MOT. We have also shown that with an increase in the magnetic field gradient, a spatial two-component distribution of atoms in the trap is formed even for a single particle approximation when interatomic interactions are neglected.

DOI
10.48550/arxiv.2507.07475

Related papers

Kinetic theory of the magneto-optical trap for multilevel atoms

Jin Woo Jun, Soo Chang, Taeg Yong Kwon +2 more

A single-particle kinetic theory of the magneto-optical trap (MOT) for cold atoms is developed for a multilevel dipole interaction scheme. The theory analyzes the one-dimensional motion of $(3+5)$-level atoms in an inhomogeneous magnetic field and in the field of two counterpropagating circularly polarized laser waves. It is shown that in multilevel interaction schemes two-photon and generally even-order multiphoton processes are responsible for the formation of the narrow velocity and spatial structures in the radiation pressure force. The structures are located at zero velocity and near the origin of the trap. It is found that in the case of a $(3+5)$-level atom, single- and two-photon processes produce the two-component structure of the MOT potential well. Near the bottom of a conventional spatially broad potential well caused by one-photon processes, there is a much narrower well caused by two-photon processes. The double-structure MOT potential well is shown to be responsible for the two-component spatial distribution of the trapped atomic cloud. It is proposed that tight confinement of atoms near the narrow bottom of the MOT potential well can be used for the creation of a pointlike source of cold atoms for various applications in atom optics.

Physical Review A•Nov 1, 1999•18 citations

Theory of magneto-optical traps for multilevel atoms

Jin Woo Jun, Soo Chang, Taeg Yong Kwon +2 more

Since the first proposal and the first experiment on magneto-optical trapping of atoms, magneto-optical traps (MOT) became the most popular traps for cold atoms. Despite the numerous successful applications of MOT it is still unclear what ultimate parameters could be expected for atoms trapped in MOT. We develop the theory of MOT for cold atoms under the multilevel dipole interaction schemes. Theory is based on consideration of one-dimensional motion of atoms which have three ground-state sublevels (F/sub g/=1) and five upper-state sublevels (F/sub e/=2) and are in inhomogeneous magnetic field and in the field of two counter-propagating circular polarized laser waves. It is shown that in multilevel interaction schemes two-photon processes are responsible for formation of a narrow velocity and spatial structure in the radiation force. It is found that two-photon coherent process enhances considerably the friction force and the oscillation frequency at negative detuning. Single-photon and two-photon processes are shown to produce the two-component structure of the MOT potential and accordingly the two-component coordinate distribution.

Conference on Lasers and Electro-Optics Pacific Rim (CLEO-PR)•Jan 20, 2003•0 citations

Three-dimensional theory of the magneto-optical trap

Прудников Олег Николаевич, А. В. Тайченачев, Valeriy I. Yudin

The kinetics of atoms in a three-dimensional magneto-optical trap (MOT) is considered. A three-dimensional MOT model has been constructed for an atom with the optical transition J g = 0 → J e = 1 (J g, e is the total angular momentum in the ground and excited states) in the semiclassical approximation by taking into account the influence of the relative phases of light fields on the kinetics of atoms. We show that the influence of the relative phases can be neglected only in the limit of low light field intensities. Generally, the choice of relative phases can have a strong influence on the kinetics of atoms in a MOT.

Journal of Experimental and Theoretical Physics•Apr 1, 2015•8 citations

Kinetic theory of magneto-optical traps with finite-linewidth lasers

Jin Woo Jun, Ho Seong Lee

We generalize the kinetic theory of the magneto-optical trap (MOT) to investigate the finite-linewidth effect of cooling lasers. Our results confirm that the polarization-gradient cooling mechanism in the low-velocity domain of the MOT originates from a two-photon process and that the Doppler cooling mechanism in the high-velocity domain stems from a one-photon process. We find that, when we increase the linewidth of the cooling lasers, the cooling temperature increases monotonically and the atomic cloud radius initially decreases quadratically and later increases.

Physical Review A•Nov 15, 2000•0 citations

Controllable Double-Well Magneto-Optical Trap for Neutral Atoms

Yun Min, Yin Jian-Ping

We propose a novel controllable double-well magneto-optical trap (MOT) by using a square current-carrying wire and a bias magnetic field. The spatial distributions of the magnetic fields and their gradients are calculated, and the results show that the proposed trap has double magnetic wells with two centres of zero magnetic field and can be continuously evolved as a single-well trap by reducing the current in the wire or increasing the bias field, which can be used to realize a controllable double-well MOT, even to prepare one- and two-dimensional arrays of magneto-optical lattices on the surface of an atom chip. We also estimate the number (~107) and temperature (~260 μK) of trapped cold atoms in our MOT.

Chinese Physics Letters•Jul 30, 2004•3 citations

Dependence of number of trapped atoms on the experimental parameters of Rb magneto-optical trap

Kaijun Jiang, Ke Li, Wang Jin +2 more

Our study indicates that the number of trapped Rb atoms in a magneto-optical trap (MOT) strongly depends on the trapping laser intensity and detuning, the repumping laser intensity and the magnetic gradient. We estimate the trapped-atom numbers changing with the trapping laser intensity and detuning, using a two-level system model. The theoretical results are in qualitative agreement with the experimental results. The experimental results also show an obvious dependence of the trapped-atom numbers on repumping laser intensity and the magnetic gradient, which the simple theory cannot account for. These studies are helpful for selecting suitable experimental parameters to achieve larger numbers of cold atoms.

Acta Physica Sinica•Jan 1, 2006•4 citations
We present a quantum theory of a magneto-optical trap (MOT) from first principles based on the quantum kinetic equation for the atomic density matrix with taking into account the recoil effects caused by the interaction of atoms with the laser field. An efficient method for solving the quantum kinetic equation is proposed. It is shown that the steady-state solution describing the atoms in the MOT has a significantly non-equilibrium nature and can be described within the framework of a two-temperature distribution. The momentum distribution of cold atoms in the MOT depends on the magnetic field gradient and, in general, significantly differs from the momentum distribution of atoms in the optical molasses, which is usually used as an approximation to describe the MOT. We have also shown that with an increase in the magnetic field gradient, a spatial two-component distribution of atoms in the trap is formed even for a single particle approximation when interatomic interactions are neglected.
A single-particle kinetic theory of the magneto-optical trap (MOT) for cold atoms is developed for a multilevel dipole interaction scheme. The theory analyzes the one-dimensional motion of (3+5)(3+5)(3+5)-level atoms in an inhomogeneous magnetic field and in the field of two counterpropagating circularly polarized laser waves. It is shown that in multilevel interaction schemes two-photon and generally even-order multiphoton processes are responsible for the formation of the narrow velocity and spatial structures in the radiation pressure force. The structures are located at zero velocity and near the origin of the trap. It is found that in the case of a (3+5)(3+5)(3+5)-level atom, single- and two-photon processes produce the two-component structure of the MOT potential well. Near the bottom of a conventional spatially broad potential well caused by one-photon processes, there is a much narrower well caused by two-photon processes. The double-structure MOT potential well is shown to be responsible for the two-component spatial distribution of the trapped atomic cloud. It is proposed that tight confinement of atoms near the narrow bottom of the MOT potential well can be used for the creation of a pointlike source of cold atoms for various applications in atom optics.
Since the first proposal and the first experiment on magneto-optical trapping of atoms, magneto-optical traps (MOT) became the most popular traps for cold atoms. Despite the numerous successful applications of MOT it is still unclear what ultimate parameters could be expected for atoms trapped in MOT. We develop the theory of MOT for cold atoms under the multilevel dipole interaction schemes. Theory is based on consideration of one-dimensional motion of atoms which have three ground-state sublevels (F/sub g/=1) and five upper-state sublevels (F/sub e/=2) and are in inhomogeneous magnetic field and in the field of two counter-propagating circular polarized laser waves. It is shown that in multilevel interaction schemes two-photon processes are responsible for formation of a narrow velocity and spatial structure in the radiation force. It is found that two-photon coherent process enhances considerably the friction force and the oscillation frequency at negative detuning. Single-photon and two-photon processes are shown to produce the two-component structure of the MOT potential and accordingly the two-component coordinate distribution.
The kinetics of atoms in a three-dimensional magneto-optical trap (MOT) is considered. A three-dimensional MOT model has been constructed for an atom with the optical transition J g = 0 → J e = 1 (J g, e is the total angular momentum in the ground and excited states) in the semiclassical approximation by taking into account the influence of the relative phases of light fields on the kinetics of atoms. We show that the influence of the relative phases can be neglected only in the limit of low light field intensities. Generally, the choice of relative phases can have a strong influence on the kinetics of atoms in a MOT.
We generalize the kinetic theory of the magneto-optical trap (MOT) to investigate the finite-linewidth effect of cooling lasers. Our results confirm that the polarization-gradient cooling mechanism in the low-velocity domain of the MOT originates from a two-photon process and that the Doppler cooling mechanism in the high-velocity domain stems from a one-photon process. We find that, when we increase the linewidth of the cooling lasers, the cooling temperature increases monotonically and the atomic cloud radius initially decreases quadratically and later increases.
We propose a novel controllable double-well magneto-optical trap (MOT) by using a square current-carrying wire and a bias magnetic field. The spatial distributions of the magnetic fields and their gradients are calculated, and the results show that the proposed trap has double magnetic wells with two centres of zero magnetic field and can be continuously evolved as a single-well trap by reducing the current in the wire or increasing the bias field, which can be used to realize a controllable double-well MOT, even to prepare one- and two-dimensional arrays of magneto-optical lattices on the surface of an atom chip. We also estimate the number (~107) and temperature (~260 μK) of trapped cold atoms in our MOT.
Our study indicates that the number of trapped Rb atoms in a magneto-optical trap (MOT) strongly depends on the trapping laser intensity and detuning, the repumping laser intensity and the magnetic gradient. We estimate the trapped-atom numbers changing with the trapping laser intensity and detuning, using a two-level system model. The theoretical results are in qualitative agreement with the experimental results. The experimental results also show an obvious dependence of the trapped-atom numbers on repumping laser intensity and the magnetic gradient, which the simple theory cannot account for. These studies are helpful for selecting suitable experimental parameters to achieve larger numbers of cold atoms.