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Advances in engineering research/Advances in Engineering Research

Effective Detuning of a Three-level Atom Interacted with the Laguerre-Gaussian Laser Beam

Yanli Wang, Zhengling Wang, 任乃飞, Yaru Wang, Xinzhi Hu

Published Jan 1, 2015• 0 citations
Publisher

Abstract

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.

DOI
10.2991/cmes-15.2015.2

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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.
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 show that a two-level atom moving in a Laguerre-Gaussian beam is subject to a light-induced torque, TTT, about the beam axis which is directly proportional to lll, the orbital angular momentum quantum number of the mode. The torque, which has a Lorentzian frequency response which includes an azimuthal lll-dependent Doppler shift in the detuning term, reduces in the saturation limit to the simple form $T\ensuremath{\approx}\ensuremath{\hbar}l\ensuremath{\Gamma}$, where $2\ensuremath{\Gamma}$ is the decay rate of the excited state.
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 have performed a numerical calculation for the excitation spectra arising from the interaction of a three-level atom in the lambda configuration with a strong electromagnetic field whose frequency mode is initially populated. The excitation spectra are considered for equal detunings, which refer to the cooperative two-photon resonance process, as well as for different detunings. The computed cooperative two-photon resonance spectra are compared with those derived by analytical methods. In the presence of different detunings, conditions are established under which the laser field induces sidebands at the frequency equal to that for the forbidden transition. Numerical calculations for a wide range of Rabi frequencies and detunings are presented graphically. Detailed discussion of the computed spectral intensities is given and a comparison is made between the spectra of three-level atoms in the lambda and cascade configurations.