Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physica Scripta

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

Himani Thakur, Zubair Iqbal Dar, Mandeep Singh, Himani Arora, Paramjit Kaur

Published May 14, 2024• 6 citations
Publisher

Abstract

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.

DOI
10.1088/1402-4896/ad4b64

Related papers

Three-dimensional atom localization with high-precision and high-resolution via a microwave field in an atomic system

Jiayu Liu, Hai-Hua Wang, Lei Wang +3 more

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.

Laser Physics•Oct 1, 2021•6 citations

High-precision three-dimensional atom localization via phase-sensitive absorption spectra in a four-level atomic system

Duo Zhang, Rong Yu, Zhaoyu Sun +2 more

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.

Journal of Physics B Atomic Molecular and Optical Physics•Nov 9, 2017•15 citations

High-precision two- and three-dimensional atom localization via spatial dependent probe absorption in a closed-loop M-type atomic system

Neeraj Singh, Ajay Wasan

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.

Journal of the Optical Society of America B•May 16, 2018•17 citations

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 +2 more

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.

Journal of Physics B Atomic Molecular and Optical Physics•May 19, 2026•0 citations

Two-dimensional sub-half-wavelength atom localization via phase control of absorption and gain

Ren-Gang Wan, Tongyi Zhang, Jun Kou

We propose a scheme for two-dimensional atom localization based on the coherent controlled absorption and gain of a weak probe field in a four-level double-\ensuremath{\Lambda} system, in which the atom interacts with two orthogonal standing-wave fields. Owing to the space-dependent atom-field interaction, the position probability distribution of the atom passing through the standing waves can be directly determined by measuring the resulting absorption and gain spectra. The phase-sensitive property of the atomic system significantly reduces the uncertainty in the position measurement of the atom. It is found that, by properly varying the parameters of the system, we can achieve sub-half-wavelength atom localization with high precision. Especially the probability of finding the atom at a particular position can be 100$%$ when a photon with certain frequency is absorbed or amplified. Numerical calculations and qualitative analyses show that the enhancement of precision in the position measurement of the atom is attributed to the interference between the one-photon excitation and the phase-dependent three-photon excitation from the closed interacting contour in the laser-driven atomic system.

Physical Review A•Apr 15, 2013•93 citations

High-precision three-dimensional atom localization in a microwave-driven atomic system

Yushan Mao, Jianchun Wu

We demonstrate the behavior of three-dimensional (3D) atom localization in a four-level Y-type atomic system driven by a microwave field. The position information of the atom can be obtained by measuring the position-dependent probe absorption when the atom interacts with three orthogonal standing-wave fields. It is found that the precision of the atom localization depends sensitively on the probe detuning and the strength of the microwave field. Remarkably, the localization precision can be significantly improved by increasing the amplitude of the microwave field, and the localization position will be changed by adjusting the relative phase between the standing-wave, microwave, and control fields.

Journal of the Optical Society of America B•May 2, 2017•16 citations
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.
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.
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.
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.
We propose a scheme for two-dimensional atom localization based on the coherent controlled absorption and gain of a weak probe field in a four-level double-\ensuremath{\Lambda} system, in which the atom interacts with two orthogonal standing-wave fields. Owing to the space-dependent atom-field interaction, the position probability distribution of the atom passing through the standing waves can be directly determined by measuring the resulting absorption and gain spectra. The phase-sensitive property of the atomic system significantly reduces the uncertainty in the position measurement of the atom. It is found that, by properly varying the parameters of the system, we can achieve sub-half-wavelength atom localization with high precision. Especially the probability of finding the atom at a particular position can be 100% when a photon with certain frequency is absorbed or amplified. Numerical calculations and qualitative analyses show that the enhancement of precision in the position measurement of the atom is attributed to the interference between the one-photon excitation and the phase-dependent three-photon excitation from the closed interacting contour in the laser-driven atomic system.
We demonstrate the behavior of three-dimensional (3D) atom localization in a four-level Y-type atomic system driven by a microwave field. The position information of the atom can be obtained by measuring the position-dependent probe absorption when the atom interacts with three orthogonal standing-wave fields. It is found that the precision of the atom localization depends sensitively on the probe detuning and the strength of the microwave field. Remarkably, the localization precision can be significantly improved by increasing the amplitude of the microwave field, and the localization position will be changed by adjusting the relative phase between the standing-wave, microwave, and control fields.