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Chinese Physics B

Radiation forces on a three-level atom in the high-order Bessel beams

Zhengling Wang, Yin Jian-Ping

Published Jul 1, 2008• 10 citations
Publisher

Abstract

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.

DOI
10.1088/1674-1056/17/7/021

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Acta Physica Sinica•Jan 1, 2011•1 citation
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.
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 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.
We give a general theoretical description of radiative forces on atoms in a monochromatic radiation field. The driven transition has a lower level consisting of several substates, and we consider the limit of low velocities and weak intensities. This situation comprises the schemes where cooling to temperatures below the Doppler limit is possible. After expressing the atomic dipole in terms of the polarizability tensor, we obtain an expression of the force as the sum of the radiation pressure, the dipole force, and a contribution from the gradient of the polarization. This latter contribution contains a part resulting from redistribution of photons between the plane waves that compose the field, and a part resulting from fluorescence. We express the average force and the momentum-diffusion tensor in terms of a closed evolution equation for the lower-state density matrix. We show by a scaling argument that in any case of cooling, the final temperature goes down linearly with the intensity, until the recoil limit is approached. The description is valid for a weak and monochromatic, but otherwise arbitrary field, and it allows for the presence of an external magnetic field, and of hyperfine splitting. It is applicable to cooling in one, two, or three dimensions. We give numerical results for the average force in a number of specific cases of two counterrunning plane waves.
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 radiation pressure and laser cooling of a V-type three level atom in coherent fields in a squeezed vacuum are considered. From the Hamiltonian of the atomic system, making use of Born-Markoff approximation, the optical Bloch equations are derived. Using the adiabatic approximation, the expression of the mean dissipative force are acquired. The achievable equilibrium temperature is given by the quantum regression theorem and Einstein relation. The dependence of the spontaneous radiation pressure and ultimate temperature on quantum interference, average photon number and Rabi frequency are analyzed. The result shows that temperatures lower than the Doppler limit can be achieved.