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Journal of Applied Physics

Tunable 2D atomic localization via azimuthal quantum number in a four-level tripod-type system

Muhammad Idrees, Yuee Xie, Yuanping Chen, Hui-Jun Li, Humaira Kalsoom

Published Feb 17, 2026• 1 citation
Publisher

Abstract

In this work, we explore a tunable scheme for achieving precise two-dimensional (2D) atomic localization in a four-level tripod atomic system. The system is driven by two control fields with orbital angular momentum and a weak probe field. By varying the azimuthal quantum numbers, spatial phase shifts, and atomic decay rates, we demonstrate controlled manipulation of atomic localization with high spatial precision. The interaction of structured light fields with the atomic system generates interference patterns that result in sharp localization peaks in the 2D plane. The study investigates the effects of varying the control parameters, such as phase shifts and decay rates, on the number, spacing, and sharpness of these localization peaks. Notably, optimized parameters lead to the formation of a single, highly localized transmission peak, enabling subwavelength spatial resolution. Our results have significant implications for applications in atom lithography, precision spectroscopy, and quantum state engineering, offering a flexible method for precise control of atomic positions in quantum systems.

DOI
10.1063/5.0302871

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In this work, we explore a tunable scheme for achieving precise two-dimensional (2D) atomic localization in a four-level tripod atomic system. The system is driven by two control fields with orbital angular momentum and a weak probe field. By varying the azimuthal quantum numbers, spatial phase shifts, and atomic decay rates, we demonstrate controlled manipulation of atomic localization with high spatial precision. The interaction of structured light fields with the atomic system generates interference patterns that result in sharp localization peaks in the 2D plane. The study investigates the effects of varying the control parameters, such as phase shifts and decay rates, on the number, spacing, and sharpness of these localization peaks. Notably, optimized parameters lead to the formation of a single, highly localized transmission peak, enabling subwavelength spatial resolution. Our results have significant implications for applications in atom lithography, precision spectroscopy, and quantum state engineering, offering a flexible method for precise control of atomic positions in quantum systems.
We present a comprehensive theoretical investigation of two-dimensional (2D) Compton-azimuthal atomic localization in a three-level atomic system interacting with spatially structured light fields. The study focuses on how the azimuthal quantum numbers of the applied standing-wave fields influence the spatial probability distribution of an atom within the 2D plane. By numerically solving the governing equations of motion with realistic atomic parameters, we obtain localization maps that reveal sharp and well-defined probability peaks. The spatial localization arises from the position-dependent Rabi frequencies, which are modulated by the standing-wave interference patterns and the orbital angular momentum carried by the fields. Our results demonstrate a clear transition from multiple sharp localization peaks to a single dominant peak as ℓ1 and ℓ2 are reduced. This peak reduction significantly increases the probability of finding the atom at the remaining high-probability sites, reaching 100% localization probability in the single-peak regime. Physically, this occurs because lower azimuthal mode numbers simplify the spatial interference structure, concentrating the atomic wavefunction in a narrower spatial region. The tunability of localization via ℓ1 and ℓ2 provides a flexible control mechanism for atomic position measurement with subwavelength precision. The findings not only offer new insights into Compton-azimuthal localization mechanisms but also open potential applications in quantum metrology, atom-based nanolithography, and precision quantum control of matter–light interactions in structured optical fields.
Abstract In this article, we introduce a new theoretical approach to improve the accuracy of two-dimensional (2D) atomic localization within a tripod-type, four-level atomic system by analyzing its transmission spectrum. In this method, the atom interacts with two orthogonal standing-wave fields and a weak probe field. By examining how the weak probe field passes through the system, we can determine the atom position. Our analysis reveals the presence of both double and sharply defined single localized peaks in the transmission spectrum, which correspond to specific positions of the atom. Importantly, we achieve ultra-high-resolution atomic localization with accuracy confined to a region smaller than λ/32 × λ/32. This level of precision is a significant improvement compared to earlier methods, which had lower localization accuracy. The increased precision is due to the complex interaction between the atom and the carefully controlled standing-wave and probe fields, which allows for precise control over the atom’s position. The implications of this work are significant, especially for applications like nano-lithography, where precise atomic placement is essential, and for laser cooling technologies, where better atomic localization could lead to more effective cooling processes and improved manipulation of atomic states.
The high-precision position measurement scheme of a single atom in two-dimensions and three-dimensions is investigated in a four-level tripod-type system. The atom interacts with the two orthogonal standing wave fields (OSWFs) and three OSWFs for two- and three-dimensional (2D, 3D) atom localization. The high-precision position of the atom is observed by adjusting the suitable system parameters. We achieve a high-precision single localized peak in the 2D plane and a single localized sphere smaller than the cubic optical wavelength in 3D volume space. We also see the impact of the Doppler shift on atom localization in 2D and 3D. We show that the Doppler shift dramatically deteriorates the precision of spatial information. The proposed high-precision atom localization scheme has applications in laser cooling and Bose–Einstein condensation phenomena.
A scheme for two-dimensional (2D) subwavelength atom localization is proposed, in which the atom is in a four-level tripod configuration and driven by two orthogonal standing-wave lasers. Because of the spatial dependence of atom-field interaction, the spontaneously emitted photon carries information about the position of the atom in standing-wave fields. We exploit this fact to 2D atom localization conditioned on the measurement of spontaneously emitted photon at a particular frequency, and obtain a high precision and resolution in the position probability distribution. Moreover, an improvement by a factor of 2 in the detecting probability of an atom can be achieved by initially preparing the atom in the coherent population trapping state. Qualitatively, the high-precision, high-resolution atom localization can be attributed to the quantum interference effect between competitive multiple spontaneous decay channels.
A scheme of two-dimensional atom localization based on a coherence-controlled absorption spectrum in an N -tripod-type five-level system is proposed, in which the atom interacts with a weak probe field and three standing-wave fields. Position information of the atom can be achieved by measuring the probe absorption. It is found that the localization properties are significantly improved due to the interaction of dark resonances. It is also shown that the localization factors depend strongly on the system parameters that lead to such spatial structures of localization as chain-like, wave-like, '8'-like, spike-like, crater-like and heart-like patterns. By properly adjusting the system parameters, we can achieve a high-precision and high-resolution atom localization under certain conditions.