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Acta Physica Sinica

Study on atomic localization of Λ-type quasi-four level atoms based on absorption with quantum coherent control

Lei Zhang, Ge Yan, Zhang Xiang-Yang

Published Jan 1, 2015• 1 citation
Publisher

Abstract

A scheme of two-dimensional atomic localization of the Λ-type quasi-four-level atoms based on quantum-coherent-controlled absorption is proposed. Using the perturbation theory of the density matrix, the filter function is derived for the position probability distribution of atoms, which is determined by the imaginary part of the optical susceptibility. Because of the space-dependent interaction between atoms and fields, the position information is contained in the filter function, which provides an approach to explore the spacial position probability distribution of a single atom. Effect of the initial state of the atom under coherent control on the atomic localization is analyzed. It is found that the atomic localization is related to the initial atom distribution and the dipole moment between two lower levels under the coherent field control. When probing field and coupling field are under the configuration of the electromagnetically induced transparency, the position of atoms can be localized in the domain of sub wavelength; when the electromagnetically induced transparency is not satisfied, an atom can be measured in a sub wave region with the probability of 100% by changing the traveling wave amplitude in the controlling field and the detuning in the probing field.

DOI
10.7498/aps.64.134204

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A scheme of two-dimensional atomic localization of the Λ-type quasi-four-level atoms based on quantum-coherent-controlled absorption is proposed. Using the perturbation theory of the density matrix, the filter function is derived for the position probability distribution of atoms, which is determined by the imaginary part of the optical susceptibility. Because of the space-dependent interaction between atoms and fields, the position information is contained in the filter function, which provides an approach to explore the spacial position probability distribution of a single atom. Effect of the initial state of the atom under coherent control on the atomic localization is analyzed. It is found that the atomic localization is related to the initial atom distribution and the dipole moment between two lower levels under the coherent field control. When probing field and coupling field are under the configuration of the electromagnetically induced transparency, the position of atoms can be localized in the domain of sub wavelength; when the electromagnetically induced transparency is not satisfied, an atom can be measured in a sub wave region with the probability of 100% by changing the traveling wave amplitude in the controlling field and the detuning in the probing field.
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 propose a scheme for high-precision two-dimensional (2D) sub-wavelength atom localization in a tripod-type atomic system. The position information of a moving atom can be obtained by measuring the probe field absorption when the atom interacts with a weak probe field and two orthogonal standing-wave fields. It is found that sub-wavelength atom localization can be obtained under the condition of two-photon resonance. Remarkably, the localization precision can be significantly improved by changing the strength of the coherent coupling fields in the presence of superposition of coherent coupling field and standing-wave field.
We present a realistic and efficient scheme for sub-half-wavelength atom localization. This scheme is based on the phase-dependent electromagnetically induced transparency in a four-level system in the double-Λ configuration. We use a strong bichromatic field (one component of which is standing-wave field) as the driving components, and a weak bichromatic field as the probe components. By choosing the collective phase of the four applied components, the atom is localized in either of the two half-wavelength regions with 50% detecting probability when the absorption to the probe fields is detected.
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.
We study two-dimensional sub-wavelength atom localization based on the microwave coupling field controlling and spontaneously generated coherence (SGC) effect. For a five-level M-type atom, introducing a microwave coupling field between two upper levels and considering the quantum interference between two transitions from two upper levels to lower levels, the analytical expression of conditional position probability (CPP) distribution is obtained using the iterative method. The influence of the detuning of a spontaneously emitted photon, Rabi frequency of the microwave field, and the SGC effect on the CPP are discussed. The two-dimensional sub-half-wavelength atom localization with high-precision and high spatial resolution is achieved by adjusting the detuning and the Rabi frequency, where the atom can be localized in a region smaller thanλ/10×λ/10. The spatial resolution is improved significantly compared with the case without the microwave field.
By using three mutually perpendicular standing-wave fields, we propose a scheme for three-dimensional (3D) subwavelength atom localization in a five-level M-type atomic system. Based on the electromagnetically induced transparency, position probability distribution of the atom in 3D space could be determined via measuring the probe absorption which is proportional to the filter function. It is shown that patterns of 3D atom localization depends sensitively on the coupling schemes of the standing-wave fields. When the standing-wave fields couple three different transitions, the same atom localization patterns are formed in the eight subspaces of the 3D space. While all the standing-wave fields are applied on one transition, we can realize different atom localization patterns in the eight subspaces. From the view of the xy plane, various symmetric or asymmetric atom localization patterns could be formed at different z positions by adjusting the parameters of the laser fields.