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arXiv:1807.08930

2D sub-half-wavelength atom localization in a three-level V-type atomic system

Sabir Ali, Vaishali Naik, Ayan Ray, Alok Chakrabarti

Published Jul 24, 2018• 0 citations
arXivHTMLPDF

Abstract

It is shown, using density matrix calculation, that high precision two-dimensional (2D) atom localization in V-type system can be achieved by applying an additional microwave coupling field between the excited states. In the present scheme, two lasers, probe and pump, form a V-type system by coupling the ground state to the excited states while an additional 2D standing microwave field is used to couple the excited states. The solutions of the density matrix equations reveal that the off-diagonal density matrix element $ρ_{31}$, which signify the coherence between the states connected by the probe laser, is position dependent. As the imaginary part of $ρ_{31}$ is proportional to the imaginary part of the susceptibility, the probe absorption also becomes position dependent and in this situation one can readily obtain information about the atom position from the probe absorption spectra. Perfect 2D atom localization can be achieved by carefully selecting different system parameters such as detuning, relative phase, dephasing and field strength. It is found that the atom localization is highly dependent on the probe and coupling field detuning values. In view of this, a systematic study is performed on the system parameters and different zones have been identified which give rise to different absorption shapes, e.g. "dip", "wall", "peak" as well as negative absorption or amplification. Probe absorption spectrum is also found to be dependent on relative phase between the applied fields. The dependence of the dephasing parameter on the probe absorption is investigated and found to be detrimental to atom localization. The effect of the microwave coupling strength on "wall" type absorption shape is also studied and the results are discussed. Finally, a possible practical realization of the present scheme is discussed in Conclusion section.

DOI
10.48550/arxiv.1807.08930

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It is shown, using density matrix calculation, that high precision two-dimensional (2D) atom localization in V-type system can be achieved by applying an additional microwave coupling field between the excited states. In the present scheme, two lasers, probe and pump, form a V-type system by coupling the ground state to the excited states while an additional 2D standing microwave field is used to couple the excited states. The solutions of the density matrix equations reveal that the off-diagonal density matrix element ρ31ρ_{31}ρ31​, which signify the coherence between the states connected by the probe laser, is position dependent. As the imaginary part of ρ31ρ_{31}ρ31​ is proportional to the imaginary part of the susceptibility, the probe absorption also becomes position dependent and in this situation one can readily obtain information about the atom position from the probe absorption spectra. Perfect 2D atom localization can be achieved by carefully selecting different system parameters such as detuning, relative phase, dephasing and field strength. It is found that the atom localization is highly dependent on the probe and coupling field detuning values. In view of this, a systematic study is performed on the system parameters and different zones have been identified which give rise to different absorption shapes, e.g. "dip", "wall", "peak" as well as negative absorption or amplification. Probe absorption spectrum is also found to be dependent on relative phase between the applied fields. The dependence of the dephasing parameter on the probe absorption is investigated and found to be detrimental to atom localization. The effect of the microwave coupling strength on "wall" type absorption shape is also studied and the results are discussed. Finally, a possible practical realization of the present scheme is discussed in Conclusion section.
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 of high-precision two- and three-dimensional (3D) atom localization is proposed and analyzed by using a density matrix method for a five-level atom-light coupling scheme. In this system four strong laser components (which could be standing waves) couple a pair of atomic internal states to another pair of states in all possible ways to form a closed-loop diamond-shape configuration of the atom-light interaction. By systematically solving the density matrix equations of the motion, we show that the imaginary part of the susceptibility for the weak probe field is position dependent. As a result, one can obtain information about the position of the atom by measuring the resulting absorption spectra. Focusing on the signatures of the relative phase of the applied fields stemming from the closed- loop structure of the diamond- shape subsystem, we find out that there exists a significant phase dependence of the eigenvalues required to have a maximum in the probe absorption spectra. It is found that by properly selecting the controlling parameters of the system, a nearly perfect 2D atom localization can be obtained. Finally, we numerically explore the phase control of 3D atom localization for the present scheme and show the possibility to obtain 1/2 detecting probability of finding the atom at a particular volume in 3D space within one period of standing waves.
Coherent interaction of an atom with a position-dependent standing-wave cavity field can impart position information of a moving atom through the cavity leading to subwavelength atom localization. We show that the position of the atom along the standing-wave field is determined when the probe-field absorption is measured. We find out that absorption of the weak probe field at a certain frequency leads to subwavelength localization of the atom in either of the two half-wavelength regions of the cavity field by appropriate choice of the system parameters. In addition, we demonstrate that the position information of a three-level V-shaped moving atom strongly depends on the relative phase of applied fields. By appropriate choice of the relative phase, it is shown that the scheme can be used for localizing an atom flying through the standing-wave field to the sub-half-wavelength domain.
Abstract We introduce a new approach for precise and high-resolution two-dimensional (2D) and three-dimensional (3D) atom localization in a four-level Δ∇ atomic system driven by microwave (M) and radio frequency (R) fields. In the proposed work, additional microwave and radio-frequency fields are utilized for an efficient control of the localization precision. Due to the spatially varying atom-field interaction, the probe susceptibility become position dependent and therefore, one can directly ascertain the position probability distribution of an atom by analyzing the probe spectra. The phase-sensitive property of the atomic system plays a significant role in substantially reducing the uncertainty associated with atom position measurements. We have studied the system behavior through the analysis of dressed states, which forms the basis for its physical interpretation. The increase in precision for measuring the atom’s position is a result of interference between one-photon excitation and the phase-dependent three-photon excitation arising from the closed interacting contour within the laser-driven atomic system, as demonstrated through both numerical calculations and qualitative analyses. The findings indicate that precise sub-wavelength atom localization can be attained by appropriately adjusting the system parameters. Also, the optimal adjustment of these parameters can lead to 100% probability of locating the atom at a particular position within 2D and 3D subspaces.
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.
Abstract We propose a new scheme for highly efficient three-dimensional (3D) atom localization in a coherently driven closed-loop four-level atomic system via measuring the probe absorption of the weak field. Due to the spatially dependent atom–field interaction, the absorption spectra of the weak probe laser field carry the information about the atomic position. By solving the density-matrix equations of motion and properly modulating the system parameters such as the probe detuning, the relative phase of three driving fields, and the intensity of the control and microwave fields, we can realize high-precision and high-resolution 3D atom localization. Furthermore, we can find the atom at a certain position with 100% probability under appropriate conditions, and then we employ the dressed-state analysis to explain qualitatively the reason of high-precision 3D atom localization.