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Journal of Physics B Atomic Molecular and Optical Physics

Atom localization with double-cascade configuration

M. Yu. Gordeev, Ekaterina A. Efremova, Yu. Rozhdestvensky

Published Feb 22, 2016• 2 citations
Publisher

Abstract

Abstract We investigate the one-dimensional (1D) and two-dimensional (2D) atom localization of a four-level system in a double-cascade configuration. We demonstrate the possibility of 1D localization in the field of a standing wave, 2D localization in the field of two standing waves and 2D localization only in the field of running waves by using different configurations of driven waves on transitions. In addition, for each configuration we reached a high-precision atom localization in one of the states at scales much smaller than the wavelength of the incident optical radiation.

DOI
10.1088/0953-4075/49/6/065001

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Abstract We investigate the one-dimensional (1D) and two-dimensional (2D) atom localization of a four-level system in a double-cascade configuration. We demonstrate the possibility of 1D localization in the field of a standing wave, 2D localization in the field of two standing waves and 2D localization only in the field of running waves by using different configurations of driven waves on transitions. In addition, for each configuration we reached a high-precision atom localization in one of the states at scales much smaller than the wavelength of the incident optical radiation.
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.
We propose a scheme for two-dimensional (2D) atom localization in a four-level tripod system under an influence of two orthogonal standing-wave fields. Position information of the atom is retained in the atomic internal states by an additional probe field either of a standing or of a running wave. It is shown that the localization factors depend crucially on the atom-field coupling that results in such spatial structures of populations as spikes, craters, and waves. We demonstrate a high-precision localization due to measurement of population in the upper state or in any ground state.
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.
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.