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Chinese Physics Letters

Average Dissipative and Dipole Forces on a Three-Level Atom in a Laguerre–Gaussian Beam

Zhengling Wang, Yin Jian-Ping

Published May 25, 2005• 8 citations
Publisher

Abstract

By means of the optical Bloch equations based on the atomic density matrix elements, the general expressions of the average dissipative force, dipole force and the mechanical torque acting on a Λ-configuration three-level atom in a linearly-polarized Laguerre–Gaussian beam (LGB) with an angular momentum of l ℏ are derived, and the general properties of the average dissipative and dipole force on the three-level atom in the linearly-polarized LGB are analysed. We find a resonant property (with two resonant peaks) of the dissipative force and a non-resonant property (with two pairs of non-resonant peaks) of the dipole force on the three-level atom, which are completely different from those on the two-level atom. Our study also shows that all of general expressions on the three-level atom will be simplified to those on the two-level atom in the approximation of large detuning.

DOI
10.1088/0256-307x/22/6/024

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By means of the optical Bloch equations based on the atomic density matrix elements, the general expressions of the average dissipative force, dipole force and the mechanical torque acting on a Λ-configuration three-level atom in a linearly-polarized Laguerre–Gaussian beam (LGB) with an angular momentum of l ℏ are derived, and the general properties of the average dissipative and dipole force on the three-level atom in the linearly-polarized LGB are analysed. We find a resonant property (with two resonant peaks) of the dissipative force and a non-resonant property (with two pairs of non-resonant peaks) of the dipole force on the three-level atom, which are completely different from those on the two-level atom. Our study also shows that all of general expressions on the three-level atom will be simplified to those on the two-level atom in the approximation of large detuning.
By means of the optical Bloch equations based on the atomic density matrix elements, the general expressions of the average dissipative force, dipole force and the mechanical torque acting on a A-configuration three-level atom in a linearly-polarized Laguerre-Gaussian beam (LGB) with an angular momentum of lh are derived, and the general properties of the average dissipative and dipole force on the three-level atom in the linearly-polarized LGB are analysed. We find a resonant property (with two resonant peaks) of the dissipative force and a non-resonant property (with two pairs of non-resonant peaks) of the dipole force on the three-level atom, which are completely different from those on the two-level atom. Our study also shows that all of general expressions on the three-level atom will be simplified to those on the two-level atom in the approximation of large detuning.
The general expressions of the average dissipative and dipole forces acting on a Λ-configuration three-level atom in an arbitrary light field are derived by means of the optical Bloch equations based on the atomic density matrix elements, and the general properties of the average dissipative and dipole forces on a three-level atom in the linearly-polarized high-order Bessel beams (HBBs) are analysed. We find a resonant property (with two resonant peaks) of the dissipative force and a non-resonant property (with two pairs of non-resonant peaks) of the dipole force on the three-level atom, which are completely different from those on the two-level atom. Meanwhile we find a saturation effect of the average dissipative force in the HBB, which comes from the saturation of the upper-level population. Our study shows that the general expressions of the average dissipative and dipole forces on the three-level atom will be simplified to those of the two-level atom under the approximation of large detuning. Finally, we study the axial and azimuthal Doppler cooling of atoms in 1D optical molasses composed of two counter-propagating HBBs and discuss the azimuthal influence of the HBB on the Doppler cooling limit. We also find that the Doppler limit of atoms in the molasses HBB is slightly below the conventional Doppler limit of ħΓ(2κ B ) due to the orbital angular momentum l ħ of the HBB.
We derive the general analytic expression of the effective detuning of the linearly polarized light field from the Λ -configuration three-level atomic mode.The detuning amending term resulting from the three-level atomic mode is not related with the type of light field, which is determined by the two lower level split and the ratio of the two lower level dipole matrix element to the total dipole matrix element in the three-level atomicmode.For a linearly polarized Laguerre-Gaussian laser beam, we show that there is same frequency amending for the axial, radial and azimuthal frequency detuning.We define an effective two-level atomic mode to substitute the three-level atomic mode, in which it can be more practical and convenient in consideration of the light detuning and Doppler shift from atomic transition frequency.
The nine (9) elements of the density matrix of a general three-level atom interacting with a classically described linearly polarized light are parameterized by eight (8) variables related to the populations of the atomic levels, and the coherences (interference effects) between the levels. The dynamical equations of these eight parameters (that is, the optical Bloch equations for a general three-level atom) are derived under the electric dipole as well as the rotating wave approximations, and under the assumption that the matrix elements of the atomic electric dipole are all real. The general optical Bloch equations so derived are shown to contain the well-known optical Bloch equations for three-level atoms in the , and cascade configurations as well as those for two-level atoms as special cases. Expressing the interaction of light with a three-level atom in all possible configurations as well as with a two-level atom by a single set of generalized optical Bloch equations is the main result of this work.
The leading radiation forces acting on an atom or ion subject to linearly polarized Laguerre-Gaussian (LG) light are studied. Particular emphasis is laid on the orbital angular momentum effects associated with LG light. The optical Bloch equations appropriate for the adiabatic approximation are derived and used to evaluate the forces and associated torque governing the atomic motion. The steady-state dynamics of the atom are explored for atoms subject to a single beam and multiple independent counterpropagating beams. The main features responsible for the dynamics of the atom, together with the dipole potentials characteristic of Laguerre-Gaussian light, are identified and discussed. The theory is illustrated by the numerical integration of the equation of motion for Mg+{\mathrm{Mg}}^{+}Mg+ ions in various beam configurations. This yields information on trajectories, velocity evolution, and vibrational frequencies at potential minima. Interesting effects involving a reciprocal interplay between motions in orthogonal directions are demonstrated. Such features are purely dependent on the orbital angular momentum property of the light. Their possible use in controlling atomic motion is investigated. \textcopyright{} 1996 The American Physical Society.
An effect of phase fluctuations of a driving laser field on dissipative and dipolar forces of two-level atom is considered. The phase fluctuations are treated by a phase diffusion model where phase fluctuations follow Wiener–Levy process. An exact master equation for the relevant density operator is obtained and solved in the steady state. Optical forces are calculated. The effect of phase fluctuations on angular momentum imparted by a Laguerre–Gaussian beam and an ideal Bessel beam to the atom is investigated.