High-precision two- and three- dimensional atom localization in a microwave and radio-frequency driven Δ∇ system

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Abstract We introduce a new approach for precise and high-resolution two-dimensional (2D) and three-dimensional (3D) atom localization in a four-level Δ∇ atomic system driven by microwave (M) and radio frequency (R) fields. In the proposed work, additional microwave and radio-frequency fields are utilized for an efficient control of the localization precision. Due to the spatially varying atom-field interaction, the probe susceptibility become position dependent and therefore, one can directly ascertain the position probability distribution of an atom by analyzing the probe spectra. The phase-sensitive property of the atomic system plays a significant role in substantially reducing the uncertainty associated with atom position measurements. We have studied the system behavior through the analysis of dressed states, which forms the basis for its physical interpretation. The increase in precision for measuring the atom’s position is a result of interference between one-photon excitation and the phase-dependent three-photon excitation arising from the closed interacting contour within the laser-driven atomic system, as demonstrated through both numerical calculations and qualitative analyses. The findings indicate that precise sub-wavelength atom localization can be attained by appropriately adjusting the system parameters. Also, the optimal adjustment of these parameters can lead to 100% probability of locating the atom at a particular position within 2D and 3D subspaces.

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