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Communications in Theoretical Physics

Ultrahigh-resolution atomic localization via superposition of standing waves

Muhammad Idrees, Ahmed S. Hendy, Zareen Abdulhameed Khan

Published Oct 25, 2024• 9 citations
Publisher

Abstract

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.

DOI
10.1088/1572-9494/ad8b2f

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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 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.
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 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.
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.
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 is proposed to achieve one-dimensional localization of a two-level atom moving through a standing wave regime constructed by two classical standing-wave fields. Precise position information of the atom can be obtained by measuring resonant absorption of a weak coherent field probing the transition strongly driven by the resonant standing-wave fields. Behavior of atomic localization has been shown for symmetric superposition of the standing-wave fields arranged in two distinct configurations: (i) parallel and (ii) cross. In the cross-configuration, we have shown 100% detection probability of the atom within one wavelength range with the evolution of single localization peak in the sub-half-wavelength range due to the variation of spatial phase shift of one of the standing-wave fields. In case of nonresonant coupling of the atom with the standing-wave fields, a single localization peak in the sub-half-wavelength range can be obtained by changing the relative detuning of frequency of the probe field. For achieving high resolution single-peak localization of a two-level atom, the present scheme would be of great interest from the experimental point of view.