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Scientific Reports

Optical absorption microscopy of localized atoms at microwave domain: two-dimensional localization based on the projection of three-dimensional localization

Bibhas Kumar Dutta, Pradipta Panchadhyayee, Indranil Bayal, Nityananda Das, P.K. Mahapatra

Published Jan 17, 2020• 13 citations
Publisher

Abstract

A new approach for achieving two - dimensional (2D) atom localization microscopy based on the projection of three - dimensional (3D) localization in the plane of the detector is described in the present work. Spatial variation of the position-dependent 2D-localization pattern in the xy-plane is obtained with the shifting of the position of the detector along the z-axis under the parallel- and cross- axis configurations of the standing-wave fields. An attempt is made to study the 2D-localization characteristics in the specific parametric conditions for which the localization structures evolve with different shapes eventually leading to 100% detection probability of the atom both in the sub-wavelength and sub-half-wavelength regimes. The scope of tuning the cross-axis configuration over a wide range adds novelty and robustness to this model. Apart from the 2D-localization, various localization patterns with eight- to single-peak structures appear as interesting outcomes through the efficient manipulation of control parameters in the study of one-dimensional (1D) atom localization. The application of the traveling-wave field or its equivalent appears to be unique in achieving high-precision localization with maximal probability (100%) in both the 1D and 2D field-configuration schemes. Proper tuning of the traveling wave accompanied by the standing wave in the 1D scheme results in the single-peak localization in the sub-half-wavelength range. As a whole, the present work seems to be very much efficient for high-precision optical lithography.

DOI
10.1038/s41598-019-57141-z

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Canadian Journal of Physics•Jul 8, 2020•5 citations
A new approach for achieving two - dimensional (2D) atom localization microscopy based on the projection of three - dimensional (3D) localization in the plane of the detector is described in the present work. Spatial variation of the position-dependent 2D-localization pattern in the xy-plane is obtained with the shifting of the position of the detector along the z-axis under the parallel- and cross- axis configurations of the standing-wave fields. An attempt is made to study the 2D-localization characteristics in the specific parametric conditions for which the localization structures evolve with different shapes eventually leading to 100% detection probability of the atom both in the sub-wavelength and sub-half-wavelength regimes. The scope of tuning the cross-axis configuration over a wide range adds novelty and robustness to this model. Apart from the 2D-localization, various localization patterns with eight- to single-peak structures appear as interesting outcomes through the efficient manipulation of control parameters in the study of one-dimensional (1D) atom localization. The application of the traveling-wave field or its equivalent appears to be unique in achieving high-precision localization with maximal probability (100%) in both the 1D and 2D field-configuration schemes. Proper tuning of the traveling wave accompanied by the standing wave in the 1D scheme results in the single-peak localization in the sub-half-wavelength range. As a whole, the present work seems to be very much efficient for high-precision optical lithography.
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.
We propose a scheme for two-dimensional (2D) atom localization based on the controllable Autler–Townes spontaneous spectrum in a three-level ladder-type atomic system. The two upper levels are driven by two orthogonal standing-wave fields, where each standing-wave field is constituted of the superposition of two standing-wave fields along the corresponding direction. It is found that, depending on the effect of the asymmetric superposition, the maximal probability of finding an atom within the sub-half-wavelength domain of the standing waves can reach unity with appropriate values of the frequency detuning of the spontaneously emitted photon and the Rabi frequencies and phase shifts associated with the standing-wave fields. Our scheme may provide a promising way to achieve high-precision and high-resolution 2D atom localization.
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 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.
We propose a scheme for high-precision two- and three-dimensional atom localization in a coherently driven closed-loop five-level M-type atomic system by using a density matrix formalism. Our system consists of not only strong and probe fields but also a microwave field to form a closed loop in the atomic system. Due to position-dependent interaction of the atom in the standing-wave field, the absorption spectra of the probe field provide the precise information about atom localization in a subspace of one wavelength. While numerically solving the density matrix equations, various kinds of localization patterns are obtained, such as parallel wave-, crater-, valley-, and bell-shape-like, in the case of two-dimensional atom localization. Further, the three-dimensional atom localization case is also discussed under different parametric conditions. High precession and high resolution of atom localization are observed for our case and the localization can be tuned to the desired subspace by properly adjusting external parameters. Moreover, maximum conditional probability distribution of the atom is also achieved, i.e., 1 in both two- and three-dimensional localization cases under appropriate conditions.
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.
The high-precision position measurement scheme of a single atom in two-dimensions and three-dimensions is investigated in a four-level tripod-type system. The atom interacts with the two orthogonal standing wave fields (OSWFs) and three OSWFs for two- and three-dimensional (2D, 3D) atom localization. The high-precision position of the atom is observed by adjusting the suitable system parameters. We achieve a high-precision single localized peak in the 2D plane and a single localized sphere smaller than the cubic optical wavelength in 3D volume space. We also see the impact of the Doppler shift on atom localization in 2D and 3D. We show that the Doppler shift dramatically deteriorates the precision of spatial information. The proposed high-precision atom localization scheme has applications in laser cooling and Bose–Einstein condensation phenomena.