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Journal of the Optical Society of America B

Phase control of three-dimensional atom localization in a four-level atomic system in Lambda configuration

Hamid Reza Hamedi, Mohammad Reza Mehmannavaz

Published Dec 15, 2015• 21 citations
Publisher

Abstract

A scheme of phase-sensitive three-dimensional atom localization (3DAL) is presented based on absorption measurement of the weak probe field in a driven four-level Λ-type atomic system with twofold lower levels in which the atom interacts with three orthogonal standing wave fields. Because of the space-dependent coupling of the atom field in three dimensions, the position probability distribution of the passer atom through the standing wave fields can be straightforwardly assessed by gauging the resultant absorption spectra. It is found that, by appropriately tuning the system parameters, various 3D periodic isosurface patterns of localization including polyhedrons, waves, cylinders, diamonds, lattices, bowling pins, tetrahedrons, cubes, and spheres can be formed and the high-precision and high-resolution 3DAL can be manipulated. Because of the closed-loop structure in this atomic system, the probe absorption is dependent on the relative phase of applied fields. The phase dependence of 3DAL in also discussed.

DOI
10.1364/josab.33.000041

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A scheme of phase-sensitive three-dimensional atom localization (3DAL) is presented based on absorption measurement of the weak probe field in a driven four-level Λ-type atomic system with twofold lower levels in which the atom interacts with three orthogonal standing wave fields. Because of the space-dependent coupling of the atom field in three dimensions, the position probability distribution of the passer atom through the standing wave fields can be straightforwardly assessed by gauging the resultant absorption spectra. It is found that, by appropriately tuning the system parameters, various 3D periodic isosurface patterns of localization including polyhedrons, waves, cylinders, diamonds, lattices, bowling pins, tetrahedrons, cubes, and spheres can be formed and the high-precision and high-resolution 3DAL can be manipulated. Because of the closed-loop structure in this atomic system, the probe absorption is dependent on the relative phase of applied fields. The phase dependence of 3DAL in also discussed.
A scheme of high-precision two- and three-dimensional (3D) atom localization is proposed and analyzed by using a density matrix method for a five-level atom-light coupling scheme. In this system four strong laser components (which could be standing waves) couple a pair of atomic internal states to another pair of states in all possible ways to form a closed-loop diamond-shape configuration of the atom-light interaction. By systematically solving the density matrix equations of the motion, we show that the imaginary part of the susceptibility for the weak probe field is position dependent. As a result, one can obtain information about the position of the atom by measuring the resulting absorption spectra. Focusing on the signatures of the relative phase of the applied fields stemming from the closed- loop structure of the diamond- shape subsystem, we find out that there exists a significant phase dependence of the eigenvalues required to have a maximum in the probe absorption spectra. It is found that by properly selecting the controlling parameters of the system, a nearly perfect 2D atom localization can be obtained. Finally, we numerically explore the phase control of 3D atom localization for the present scheme and show the possibility to obtain 1/2 detecting probability of finding the atom at a particular volume in 3D space within one period of standing waves.
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 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.
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.
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 A new scheme for three-dimensional (3D) atom localization is proposed based on measuring the probe absorption spectra in a four-level diamond-configuration atomic system, in which the atom interacts with three orthogonal standing-wave laser fields. Due to spatial-dependent interaction between atom and fields, position information of the atom can be obtained by measuring the absorption spectra of the weak probe field. The results show that atom localization properties can be significantly improved and some interesting spatial localization structures such as double-layer lantern-like, single-layer lantern-like, gourd-like, cylinder-like, and ellipsoid-like patterns can be achieved when we adjust system parameters properly. Most importantly, we can find the atom at a particular position in 3D space with 100% probability under appropriate conditions.