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Physical Review A

Two-dimensional atom localization via probe-absorption spectrum

Rahmatullah Rahmatullah, Sajid Qamar

Published Jul 29, 2013• 91 citations
Publisher

Abstract

A scheme for two-dimensional (2D) atom localization via probe absorption in a three-level $\ensuremath{\Lambda}$-type atomic system is suggested. The required atom-field configuration is obtained when the atom interacts with a weak probe field and two orthogonal standing-wave fields where each standing-wave field is obtained from the superposition of the two standing-wave fields along the corresponding directions. We study the effect of the probe field detuning and phase shifts associated with the standing-wave fields. Two equally probable position information of the single atom are observed in the conditional position probability distribution. However, a unique position of the single atom in the 2D $xy$ plane is observed for some arbitrary choices of the phases associated with standing-wave fields and by selecting slightly different wavelengths of standing-wave fields.

DOI
10.1103/physreva.88.013846

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A scheme for two-dimensional (2D) atom localization via probe absorption in a three-level \ensuremathΛ\ensuremath{\Lambda}\ensuremathΛ-type atomic system is suggested. The required atom-field configuration is obtained when the atom interacts with a weak probe field and two orthogonal standing-wave fields where each standing-wave field is obtained from the superposition of the two standing-wave fields along the corresponding directions. We study the effect of the probe field detuning and phase shifts associated with the standing-wave fields. Two equally probable position information of the single atom are observed in the conditional position probability distribution. However, a unique position of the single atom in the 2D xyxyxy plane is observed for some arbitrary choices of the phases associated with standing-wave fields and by selecting slightly different wavelengths of standing-wave fields.
The localization of atom is studied in two-dimensional (2D) in a four-level V-type atomic system by using the Gaussian field. The atom localization is investigated through the absorption spectrum of the weak probe field inside two orthogonal standing-wave fields. We consider three hypotheses for the interaction between the atom and fields (standing-wave and Gaussian fields), each hypothesis is considered individually. We obtain the expression for the first-order approximation of the absorption of the probe field mathematically for the hypothesis (I). The Gaussian field parameter plays an important role in the precision of the atom localization. The 2D atom localization can be dependent on the detuning of the probe field (resonance and off-resonance), the Rabi frequencies and the phase shifts.
Two- and three-dimensional atom localization in a two-level atom–field system via resonance fluorescence is suggested. For the two-dimensional localization, the atom interacts with two orthogonal standing-wave fields, whereas for the three-dimensional atom localization, the atom interacts with three orthogonal standing-wave fields. The effect of the detuning and phase shifts associated with the corresponding standing-wave fields is investigated. A precision enhancement in position measurement of the single atom can be noticed via the control of the detuning and phase shifts.
A scheme for realizing two-dimensional atom localization in the sub-wavelength domain is proposed in a microwave-driven five-level hyper inverted-Y atomic system in which the atom interacts with a weak probe field, two control fields together with two orthogonal standing-wave fields. Because of the spatially dependent atom-field interaction, the information about the position of the atom can be extracted directly from the absorption and gain spectra of a weak probe field. It has been found that the probe detuning, the intensities of two control fields, and the relative phase of the driving fields can significantly improve the localization precision. Moreover, the maximal probability of finding the atom at an expected position in the sub-wavelength domain of the standing-wave field can reach unity via properly adjusting the system parameters.
A scheme of two-dimensional (2D) atom localization based on the interference of double-dark resonances is proposed, in which the N-type atom interacts with two orthogonal standing-wave fields. Because of the spatial-dependent atom–field interaction, 2D atom localization can be realized via measuring the upper state population or the probe absorption. We obtain that the maximum probability of finding an atom at a particular position in a wavelength domain (λ1×λ2) is 1/2 when the atom is localized at the intersection of the antinodes of quadrants I and III of the standing-wave plane. This scheme shows more advantages than other schemes of 2D atom localization.
Two-dimensional (2D) atom localisation of a four-level Λ-shaped atomic system with a nearly hyper-fine doublet interacting with two orthogonal standing-wave fields is investigated. The spatial information of a moving atom in xy plane is obtained by measuring the probe field absorption. The effect of quantum interference on two-dimensional atom localisation is described. The intensity of standing-waves and the detuning of the probe and standing-wave fields are found to strongly affect the two-dimensional atom localisation that lead to different spatial distribution patterns.
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.