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Localization of the three-level Λ-type atomic system interacting with two orthogonal standing-wave fields is proposed. Two equal and tunable peaks in the 2D plane are obtained by the detunings corresponding to the two orthogonal standing-wave fields when the decreasing intensities of spontaneously generated coherence (SGC) arise in the three-level Λ-type atomic system, while one circular ring with shrinking radii in the 2D plane is obtained by the adjusted phases and wave vectors of the standing-wave fields when the increasing intensities of SGC occur in the three-level Λ-type atomic system. 2D atom localization with the single ring with shrinking radii realized by the multiple parametric manipulations demonstrated the flexibility for our scheme.

Because precise position measurement of a single atom has some potential applications, such as laser cooling and trapping of neutral atoms [

More recently, the researchers proposed two-dimensional (2D) atom localization schemes [

On the other hand, the phrase of SGC is a well-known concept in quantum optics, which refers to the interference of spontaneous emission channels [

We consider a L-type system as shown in

The position-dependent Rabi frequency

where

Here,

Under the rotating-wave approximation [

The above equations are constrained by

Our goal here is to obtain the information about the atomic position from the susceptibility of the system [

where N is the atom number density in the medium and

with

where

process of the probe field. Equation (11) is the main result and reflects the position probability distribution of the atom [

The schematic our considered in

Initially, we set the detuning

The position-dependent the intensities of SGC is shown in

We next study how the detuning associating with standing-wave fields brings changes in the 2D atomic localization, i.e,

After studying the 2D atomic localization dependent the detuning associating with standing-wave fields, we further study how the phase shifts

On the basis of a three-level L-type atom model, we investigated its 2D atom localization via different parameters of the two orthogonal standing-wave fields with the decreasing or increasing intensities of SGC. Two spike- like peaks with flexible amplitudes for the atom localization are shown in the x-y plane by the decreasing intensities of SGC when the detuning corresponding to the two orthogonal standing-wave fields is varied, while the increasing intensities of SGC reduce the resolution of 2D atom localization strongly. When the phases and wave vectors corresponding to the standing-wave fields are changed, one circular ring with shrinking radii for 2D atom localization is obtained by the increasing intensities of SGC. Comparing the phases and wave vectors with the detuning corresponding to the two orthogonal standing-wave fields, a better resolution can be obtained by the phases and wave vectors corresponding to the two orthogonal standing-wave fields when SGC was manipulated. Considering the proposed three-level atom-field system to be a simple system which would be realized experimentally, such as the bichromatic EIT in cold rubidium atoms (^{87}Rb), our scheme and results may be of great interest for the researchers.

This paper is supported by the National Natural Science Foundation of China (Grant Nos. 61205205 and 6156508508), the General Program of Yunnan Provincial Research Foundation of Basic Research for application (Grant No. 2016FB009) and the Foundation for Personnel training projects of Yunnan Province, China (Grant No. KKSY201207068).

Shuncai Zhao,Qixuan Wu, (2016) Three-Level Λ-Type Atomic System Localized by the Parameters of the Two Orthogonal Standing-Wave Fields. Journal of Applied Mathematics and Physics,04,1546-1553. doi: 10.4236/jamp.2016.48164