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Journal of Physics B Atomic Molecular and Optical Physics

High-precision three-dimensional subwavelength atom localization using phase-controlled probe absorption in a closed-loop microwave-driven atomic system

Raj Kumar, Neeraj Singh, M.K. Sharma, Neeraj Panwar, malik kumar anil

Published May 19, 2026• 0 citations
Publisher

Abstract

Abstract Three-dimensional (3D) atom localization at subwavelength scales is of critical interest for advanced applications in nanolithography and laser cooling. Despite significant efforts, achieving high spatial resolution in all three dimensions remains a challenging task. In this work, we propose and analytically investigate a novel scheme for 3D subwavelength atom localization using a closed-loop five-level atomic system driven by a phase-controlled microwave field. The localization mechanism is based on the position-dependent absorption of a weak probe field in the presence of three orthogonal standing-wave coupling fields. The inclusion of a magnetically allowed microwave transition introduces a controllable relative phase ( ϕ ), enabling coherent control over the atomic spatial distribution. Our analysis demonstrates that, by judiciously tuning the system parameters—including probe detuning, relative phase, and quantum interference arising from spontaneous emission—the atom can be localized to a highly confined region with a spatial resolution as high as ∼ 0.03 λ , where λ is the optical wavelength. The results highlight the critical role of phase control and coherent field interaction in enhancing the localization precision. This technique offers a robust and versatile tool for achieving high-resolution 3D atom localization and may pave the way for practical implementations in nanoscale fabrication and quantum technologies.

DOI
10.1088/1361-6455/ae6ffb

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Abstract We propose a new scheme for highly efficient three-dimensional (3D) atom localization in a coherently driven closed-loop four-level atomic system via measuring the probe absorption of the weak field. Due to the spatially dependent atom–field interaction, the absorption spectra of the weak probe laser field carry the information about the atomic position. By solving the density-matrix equations of motion and properly modulating the system parameters such as the probe detuning, the relative phase of three driving fields, and the intensity of the control and microwave fields, we can realize high-precision and high-resolution 3D atom localization. Furthermore, we can find the atom at a certain position with 100% probability under appropriate conditions, and then we employ the dressed-state analysis to explain qualitatively the reason of high-precision 3D atom localization.
Abstract We propose a new scheme for high-precision three-dimensional (3D) atom localization by observing the spatially modulated absorption of a weak probe field operating in a partially closed-loop dependent five-level atomic system. Different spatial structures of localization patterns are presented by controlling the Rabi frequency, detuning, and field-induced collective phase-coherence with a variety of superposed standing wave field configurations. Our results highlight that 100% detection probability of atom is possible in the present model in many ways with high precision measurement of spatial absorption. It has been shown that, in the presence of standing wave fields, position information of the atom with maximum detection probability can be efficiently controlled by employing the travelling-wave field in the system. In the present work, we note that the maximum detection probability of the atom is attainable with the limit of spatial resolution better than λ/50. The efficacy of the present model is to find its application in atom nanolithography and atom-imaging having importance in quantum information processing.
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.
Abstract A scheme for three-dimensional (3D) atom localization with high-precision and high-resolution is proposed and its control is studied in a four-level atomic system driven by an additional microwave field. Because of the spatial dependent interaction between atoms and standing wave fields, the atoms can be localized in a domain with widths as small as 0.014 λ by appropriately adjusting the system parameters. The probe absorption spectrum of the atomic system gives the position information of the atoms and different evolution patterns of the localization structures in this study. The population distribution and its 3D localization structures can be easily adjusted by parameters of the microwave field, which can achieve a 100% probability of observing the atom in a specific space and the accuracy with the value of 0.014 λ . Compared with 1D or 2D localizations, 3D localization can further improve the precision of position measurement and develop its spatial resolution, which may produce a wider variety of practical applications with high precision requirement.
A scheme of phase-sensitive three-dimensional atom localization (3DAL) is presented based on absorption measurement of the weak probe field in a driven four-level Λ-type atomic system with twofold lower levels in which the atom interacts with three orthogonal standing wave fields. Because of the space-dependent coupling of the atom field in three dimensions, the position probability distribution of the passer atom through the standing wave fields can be straightforwardly assessed by gauging the resultant absorption spectra. It is found that, by appropriately tuning the system parameters, various 3D periodic isosurface patterns of localization including polyhedrons, waves, cylinders, diamonds, lattices, bowling pins, tetrahedrons, cubes, and spheres can be formed and the high-precision and high-resolution 3DAL can be manipulated. Because of the closed-loop structure in this atomic system, the probe absorption is dependent on the relative phase of applied fields. The phase dependence of 3DAL in also discussed.
We propose a scheme for high-precision two- and three-dimensional atom localization in a coherently driven closed-loop five-level M-type atomic system by using a density matrix formalism. Our system consists of not only strong and probe fields but also a microwave field to form a closed loop in the atomic system. Due to position-dependent interaction of the atom in the standing-wave field, the absorption spectra of the probe field provide the precise information about atom localization in a subspace of one wavelength. While numerically solving the density matrix equations, various kinds of localization patterns are obtained, such as parallel wave-, crater-, valley-, and bell-shape-like, in the case of two-dimensional atom localization. Further, the three-dimensional atom localization case is also discussed under different parametric conditions. High precession and high resolution of atom localization are observed for our case and the localization can be tuned to the desired subspace by properly adjusting external parameters. Moreover, maximum conditional probability distribution of the atom is also achieved, i.e., 1 in both two- and three-dimensional localization cases under appropriate conditions.