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Journal of Mathematical Techniques in Modeling

Three-Dimensional Atom Localization and Microscopy in a Three-Level Λ-Type Atomic Configuration

Najm Uddin, Attaullah Khan, Afaz Uddin, Muhammad Umar Khan, Saeed Ullah

Published Oct 15, 2024• 0 citations
Publisher

Abstract

This paper introduces a method for achieving precise three-dimensional atomic microscopy within a three-level Λ-type configuration, utilizing a probe field and a standing-wave control field. The microscopy information is derived from the imaginary part of the effective susceptibility, which reveals the absorption spectrum. Applications of this approach to atomic microscopy are demonstrated for scenarios involving two atoms and interactions near boundary walls. The atomic positions are precisely controlled through parameters such as detunings (∆), field strengths (β1, p), decay rates (γa, b), and field phases (ϕ1y, ϕ1z). The theoretical findings presented in this study highlight the potential for significant advancements in applications such as laser cooling and nanolithography.

DOI
10.56868/jmtm.v1i2.39

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This paper introduces a method for achieving precise three-dimensional atomic microscopy within a three-level Λ-type configuration, utilizing a probe field and a standing-wave control field. The microscopy information is derived from the imaginary part of the effective susceptibility, which reveals the absorption spectrum. Applications of this approach to atomic microscopy are demonstrated for scenarios involving two atoms and interactions near boundary walls. The atomic positions are precisely controlled through parameters such as detunings (∆), field strengths (β1, p), decay rates (γa, b), and field phases (ϕ1y, ϕ1z). The theoretical findings presented in this study highlight the potential for significant advancements in applications such as laser cooling and nanolithography.
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Abstract In this study we explore the microscopy of atoms in three dimensions using a new technique of absorption spectrum in an atomic system with five levels of one and two atoms microscopy, Wall-like microscopy & ellipsoidal like microscopy observed. The position and probability of localized atoms are controlled and modified by tunings, the phases, strength, and direction of the applied driving fields. The current work may have potential applications in laser cooling, microscopy, and atom nano-lithography.
Abstract Herein, we propose a scheme for the realization of two-dimensional atomic localization in a λ -type three-level atomic medium such that the atom interacts with the two orthogonal standing-wave fields and a probe field. Because of the spatially dependent atom-field interaction, the information about the position of the atom can be obtained by monitoring the probe transmission spectra of the weak probe field for the first time. A single and double sharp localized peaks are observed in the one-wavelength domain. We have theoretically archived high-resolution and high-precision atomic localization within a region smaller than λ /25 × λ /25. The results may have potential applications in the field of nano-lithography and advance laser cooling technology.
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.
Abstract We investigate one-dimensional position microscopy of a three-level atom moving through a stationary wave region under the condition of electromagnetically induced transparency. The precise position information of an atom is observed on the resonance absorption and dispersion distribution spectrum of a weak probe field. Single and multiple localization peaks are observed in specific directions of the corresponding wave numbers and phase of the standing wave fields. The strength of space-independent Rabi frequency reduces the position uncertainty in the localized peaks without disturbing the probability of the atom. In a hot atomic medium the localized probability of an atom is reduced which depends upon the temperature of that medium. Our results provide useful applications in the development of laser cooling, atom nanolithography and Bose–Einstein condensation.
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.