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<p>This article presents a theoretical approach for achieving sub-wavelength atomic localization in a four-level tripod-type atomic system. By analyzing the transmission spectrum, we show how the interaction of two orthogonal standing-wave fields with a weak probe field allows precise control over atomic localization. Our results reveal sharply defined one, two and four localized peaks, corresponding to specific atomic positions. We also explore how control fields, probe detuning, and decay rates influence two-dimensional atomic localization. In particular, reducing the decay rates from <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(0.05\gamma\)</EquationSource> </InlineEquation> to <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(0.01\gamma\)</EquationSource> </InlineEquation> leads to ultra-high precision, with atoms localized to regions as small as <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\lambda /32 \times \lambda /32\)</EquationSource> </InlineEquation> and a marked increase in localization probability. This enhanced precision arises from the complex interaction between the atom and the standing-wave and probe fields. These findings have important implications for advanced atomic manipulation techniques, such as nano-lithography and laser cooling, where precise control of atomic placement is crucial for improved performance and efficiency.</p>

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Sub-Wavelength Atomic Localization in a Four-Level Tripod System for Advanced Atomic Manipulation

  • 期刊论文

  • 发表日期：

    2025年11月18日

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  • Humaira Kalsoom,
  • Zareen A. Khan

摘要

This article presents a theoretical approach for achieving sub-wavelength atomic localization in a four-level tripod-type atomic system. By analyzing the transmission spectrum, we show how the interaction of two orthogonal standing-wave fields with a weak probe field allows precise control over atomic localization. Our results reveal sharply defined one, two and four localized peaks, corresponding to specific atomic positions. We also explore how control fields, probe detuning, and decay rates influence two-dimensional atomic localization. In particular, reducing the decay rates from \(0.05\gamma\) to \(0.01\gamma\) leads to ultra-high precision, with atoms localized to regions as small as \(\lambda /32 \times \lambda /32\) and a marked increase in localization probability. This enhanced precision arises from the complex interaction between the atom and the standing-wave and probe fields. These findings have important implications for advanced atomic manipulation techniques, such as nano-lithography and laser cooling, where precise control of atomic placement is crucial for improved performance and efficiency.