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Communications in Theoretical Physics

Spatial-dependent probe transmission based high-precision two-dimensional atomic localization

Muhammad Idrees, Humaira Kalsoom, Bakht Amin Bacha, Arif Ullah, Li‐Gang Wang

Published Feb 2, 2021• 25 citations
Publisher

Abstract

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.

DOI
10.1088/1572-9494/abe229

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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 In this study we theoretically demonstrate ultrahigh-resolution two-dimensional atomic localization within a three-level λ -type atomic medium via superposition of asymmetric and symmetric standing wave fields. Our analysis provides an understanding of the precise spatial localization of atomic positions at the atomic level, utilizing advanced theoretical approaches and principles of quantum mechanics. The dynamical behavior of a three-level atomic system is thoroughly analyzed using the density matrix formalism within the realm of quantum mechanics. A theoretical approach is constructed to describe the interaction between the system and external fields, specifically a control field and a probe field. The absorption spectrum of the probe field is thoroughly examined to clarify the spatial localization of the atom within the proposed configuration. A theoretical investigation found that symmetric and asymmetric superposition phenomena significantly influence the localized peaks within a two-dimensional spatial domain. Specifically, the emergence of one and two sharp localized peaks was observed within a one-wavelength domain. We observed notable influences of the intensity of the control field, probe field detuning and decay rates on atomic localization. Ultimately, we have achieved an unprecedented level of ultrahigh resolution and precision in localizing an atom within an area smaller than λ /35 × λ /35. These findings hold promise for potential applications in fields such as Bose–Einstein condensation, nanolithography, laser cooling, trapping of neutral atoms and the measurement of center-of-mass wave functions.
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.
Abstract We present an efficient two-dimensional atomic localization in a tripod-type four-level atomic medium using standing-wave fields. The localization behavior is significantly improved, and the maximum localization probability can be achieved under suitable conditions within the one-wavelength domain. Multiple sharp localized peaks are observed in the one-wavelength domain through examination of the absorption of the weak probe field, and theoretically, high-resolution and high-precision atomic localization can be achieved within a region smaller than λ /12 × λ /12, via the exploitation of quantum-coherence effects in laser–matter interactions. The spatial resolution of the atomic localization is extensively improved, compared to the cases with or without microwave fields studied previously. We believe that the results revealed here might have potential applications for atomic nanolithography, neutral-atom laser cooling and trapping, Bose–Einstein condensation and the center-of-mass wave-function measurements.
We propose a efficient scheme for high-precision three-dimensional (3D) atom localization via spatial interference in a generic double two-level atomic system driven by a weak probe field and three mutually perpendicular standing-wave fields. Because the spatial interference originates from the position-dependent atom-field interaction, the position information of the atom can be obtained by the measurement of the atom population. We find that the precision of 3D atom localization in volumes depends sensitively on the frequency detuning and the phase shifts associated with the standing-wave fields. Interestingly enough, we show that adjusting the frequency detuning and phase shifts can lead to a redistribution of the atoms and a significant change in the visibility of the interference pattern. As a result, the atom can be localized in volumes that are substantially smaller than a cubic optical wavelength.
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.