Efficient two-dimensional atom localization via an external coherent magnetic field

Abstract

The primary objective of this study was to investigate the two-dimensional (2D) atom localization via a coherent magnetic field in a closed three-level atomic system. Two-dimensional (2D) atom localization in multi-level atomic systems has been studied in recent years because of its unique properties and extensive applications. However, to the best of our knowledge, no further theoretical or experimental work has been carried out to study such 2D atom localization in a closed three-level atomic system in the presence of the coherent magnetic field that motivates the current work. As for 2D atom localization, the conditional position probability distribution, i.e., the probability of finding the atom at the position in the two orthogonal standing-wave fields when the atom is found in its internal excited state. In this paper, 2D atom localization is obtained via measuring the population in the excited state, which is solved via the density-matrix equations in dipole and rotating-wave approximations. Results The precision and spatial resolution of the 2D atom localization are improved via properly adjusting the controllable parameters of the system such as the detunings and intensities of the corresponding applied fields as well as the collective phase of the probe and standing-wave fields. Due to the position-dependent atom-field interaction, the position information of the atom in the standing-wave fields can be obtained by means of the phase-sensitive excited state population. More importantly, the maximal probability of finding an atom within the sub-half-wavelength domain of the standing waves can reach 100 %. Thus, our scheme may be helpful in observing precision quantum measurement and computation for quantum information processing.