Controllable two- and three-dimensional atom localization via spontaneously generated coherence
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Controllable two- and three-dimensional atom localization via spontaneously generated coherence Forough Bozorgzadeha
, Mohammad Reza Ghorbani Fard, Mostafa Sahrai
Faculty of Physics, University of Tabriz, Tabriz, Iran Received: 2 September 2020 / Accepted: 9 November 2020 © Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract A scheme for two-dimensional (2D) and three-dimensional (3D) atom localization in a four-level N -type atomic system is proposed. The scheme is based on the probe absorption measurement when the atom passes through the orthogonal standing-wave fields. Using the electromagnetically induced transparency, we prove that the probe field absorption is spatially localized in sub-wavelength domain. We also show that the spatial resolution of 2D and 3D atom localization strongly depends on the probe field detuning, the quantum interference parameters induced by spontaneous emission, and the relative phase between the driving fields.
1 Introduction High-precision position measurement on atomic scale with optical techniques has been the subject of many studies due to its potential applications in laser cooling and trapping of neutral atoms, atomic nano-lithography [1], Bose–Einstein condensation [2,3], measurement of the center-of-mass wave function of moving atoms [4], and coherent patterning of matter waves [5]. In the few past decades, researchers have developed numerous optical techniques for high-precision atom localization. Earlier techniques for atom localization include the resonance fluorescence [6], coherent population trapping [7], modification of the atomic emission spectra via Autler–Townes spectroscopy [8], Ramsey interferometry [9], and electromagnetically induced transparency (EIT) [10]. Due to the wave nature of radiation, the minimal resolvable size of objects is limited to the Rayleigh diffraction limit, i.e., λ/2, where λ is the optical wavelength [11]. The position-dependent atom–field interaction is not diffraction-limited in the sub-wavelength atom localization techniques [12]. Particularly, the recently developed quantum-gas microscopes can provide a powerful tool to fully obtain the spatial information of the quantum ensembles down to the nanometer scale, for example, by implementing super-resolution quantum techniques for trapped cold atoms [13,14]. Furthermore, it is shown that single-particle-resolved fluorescence imaging significantly enriches the experimental toolbox for cold-atom systems [15]. Consequently, there is much interest in optical techniques that can go beyond the diffraction limit. Measuring the conditional position probability, i.e., the probability of finding the atom inside the pre-defined wavelength domain, refers to atom localization [16]. In fact, the max-
a e-mail: [email protected] (corresponding author)
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Eur. Phys. J. Plus
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ima in the probe absorption profiles show where the atom can be detected. The detection probability can be mea
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