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Physical Review A

Kinetic theory of the magneto-optical trap for multilevel atoms

Jin Woo Jun, Soo Chang, Taeg Yong Kwon, Ho Seong Lee, Vladimir G. Minogin

Published Nov 1, 1999• 18 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.60.3960

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Physical Review A•Jun 1, 2001•12 citations
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.
We have derived ab initioanalytical results for the shape of the double-structure potential well for a (3+5)-level atoms in the magneto-optical trap (MOT). We show that for a case of a (3+5)-level atom and a one-dimensional ${\ensuremath{\sigma}}^{+}\ensuremath{-}{\ensuremath{\sigma}}^{\ensuremath{-}}$ laser field, the sharp bottom part of the MOT potential well results from the two-photon processes between the atomic ground-state magnetic sublevels. These nonlinear processes are, in particular, responsible for atomic temperatures below the Doppler limit which is due to the one-photon processes in the MOT. We also find that in more complicated atomic schemes, even-order multiphoton processes contribute to the sharp and narrow MOT potential well.
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.
The theory of an atom dipole trap composed of a focused, far red-detuned, trapping laser beam, and a pair of red-detuned, counterpropagating, cooling beams is developed for the simplest realistic multilevel dipole interaction scheme based on a model of a (3+5)-level atom. The description of atomic motion in the trap is based on the quantum kinetic equations for the atomic density matrix and the reduced quasiclassical kinetic equation for atomic distribution function. It is shown that when the detuning of the trapping field is much larger than the detuning of the cooling field, and with low saturation, the one-photon absorption (emission) processes responsible for the trapping potential can be well separated from the two-photon processes responsible for sub-Doppler cooling atoms in the trap. Two conditions are derived that are necessary and sufficient for stable atomic trapping. The conditions show that stable atomic trapping in the optical dipole trap can be achieved when the trapping field has no effect on the two-photon cooling process and when the cooling field does not change the structure of the trapping potential but changes only the numerical value of the trapping potential well. It is concluded that the separation of the trapping and cooling processes in a pure optical dipole trap allows one to cool trapped atoms down to a minimum temperature close to the recoil temperature, keeping simultaneously a deep potential well.
A theory of deep laser cooling of atoms by counterpropagating circular polarized laser waves in multilevel interaction schemes is developed. Using a (3+5)-level atom as an example, we show that in multilevel interaction schemes two-photon processes are responsible for creating a narrow structure near zero velocity in the ground-state atomic coherence. This structure is in turn responsible for narrow velocity structures in atomic populations and optical coherences. A Fokker-Planck-type kinetic equation is derived for a model of a (3+5)-level interaction scheme. It is found that two-photon coherent processes considerably enhance the radiation force at low velocities and the friction produced by the force at a negative detuning, and considerably decrease the diffusion coefficient. Two-photon processes in multilevel interaction schemes are identified as the basic physical mechanism responsible for deep laser cooling of atoms. The temperature of laser-cooled atoms is derived for a model (3+5)-level atom, and found to be in good agreement with the experimentally observed temperature for laser-cooled cesium atoms.
We extend the kinetic theory of the laser cooling of atoms to four multilevel atomic schemes: (3+5)-, (5+7)-, (7+9)-, and (9+11)-level atom. In all four atomic schemes the atoms are considered to be excited by two counterpropagating circularly polarized laser waves. A comparison of four multilevel atomic schemes shows that the even-order multiphoton processes are responsible for the narrow structures near zero velocity in the atomic coherences, atomic populations, dipole radiation forces, and the diffusion coefficients. The even-order multiphoton processes in a multilevel atom with a big number of magnetic sublevels are shown to produce the velocity structures, which are much narrower than that produced by the two-photon processes in a (3+5)-level atom. It is found that the multiphoton processes enhance the radiation force at low velocities and the friction produced by the force at a negative detuning. The even-order multiphoton processes caused by the laser waves are identified as the basic physical mechanism responsible for the sub-Doppler laser cooling of atoms. The temperature of laser-cooled atoms is derived for all four models and found to be lower for atomic schemes with a larger number of magnetic sublevels.