Efficient two-dimensional atom localization in a five-level conductive chiral atomic medium via birefringence beam absorption spectrum

The present study demonstrates the atom localization in the subwavelength domain by considering a Ξ-type atomic system with nearby upper levels. When an atom passes through standing-wave couple fields, it faces a position dependent probe absorption that is the key factor for the present study. The position corresponding to a large probe absorption refers the localization position in the subwavelength domain. Our numerical calculation based on the density matrix formalism suggests that nearby levels can change the localization pattern significantly in two dimensional (2D) as well as three dimensional (3D) subwavelength domains. In the 2D case, a narrower spike-like localization pattern can be obtained by optimizing the field parameters in the presence of nearby levels. Thus, precise information of the atom’s position can be achieved. Interestingly for the 3D case, the presence of nearby levels enhances the range of probe detuning; consequently, the probability of finding the atom becomes constant in the subwavelength domain. In addition, the maximal detection probability of finding the atom at a position, i.e., unity can be obtained in both the cases, 2D and 3D, by properly adjusting the fields’ parameter in the presence of nearby levels.

Effect of nearby levels on atom localization in the Ξ atomic system via spatial dependent probe absorption

Enhancing the precision of two- and three-dimensional atom localization in an inverted-Y scheme with multiple excited levels

In this work, we propose an efficient finite difference method for the two-dimensional nonlinear time-fractional diffusion equation with weakly singular solutions. By using backward formula for the approximation of nonlinear term, and L1 scheme on uniform mesh for discretisation of temporal Caputo fractional derivative, a linear scheme is constructed and analysed. Stability and pointwise-in-time convergence of the fully discrete scheme are rigorously established. Numerical results are provided to confirm the sharpness of theoretical analysis. 

Efficient L1-ADI finite difference method for the two-dimensional nonlinear time-fractional diffusion equation

Numerical simulation of a non-linear sublimation process with temperature-dependent permeability and volumetric heat source: A phase change problem

Pointwise-in-time error estimate of an ADI scheme for two-dimensional multi-term subdiffusion equation

Error analysis of a finite difference method for the distributed order sub-diffusion equation using discrete comparison principle

Sharp error estimate of Grünwald-Letnikov scheme for a multi-term time fractional diffusion equation

We present a new scheme for three-dimensional (3D) atom localization in a three-level atomic system via measuring the absorption of a weak probe field. Owing to the space-dependent atom–field interaction, the position probability distribution of the atom can be directly determined by measuring the probe absorption. It is found that, by properly varying the parameters of the system, the probability of finding the atom in 3D space can be almost 100%. Our scheme opens a promising way to achieve high-precision and high-efficiency 3D atom localization, which provides some potential applications in laser cooling or atom nano-lithography via atom localization.

Three-dimensional atom localization via electromagnetically induced transparency in a three-level atomic system.

We present a new scheme for three-dimensional (3D) atom localization in a four-level atomic system based on the interference of double-dark resonances. Owing to the space-dependent atom-field interaction, the position probability distribution of the atom can be directly determined by measuring the probe absorption. It is found that, by properly varying the parameters of the system, the probability of finding the atom in 3D space can be 1/2. Our scheme opens a promising way to achieve high-precision and high-efficiency 3D atom localization, which provides some potential applications in the atom nanolithography via 3D atom localization.

https://iopscience.iop.org/article/10.1088/1054-660X/26/11/115501/pdf

Three-dimensional sub-half-wavelength atom localization via interacting double-dark resonances

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