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arXiv:2306.14184 · Laser Physics Letters

Solution of inverse problem for Gross-Pitaevskii equation with artificial neural networks

Stepan P. Pokatov, T. Yu. Ivanova, D. A. Ivanov

Published Jul 24, 2023• 3 citations
arXivHTMLPDF

Abstract

Abstract We propose an artificial neural network (ANN) design to solve the inverse problem for a 1D Gross–Pitaevskii equation (GPE). More precise, the ANN takes the squared modulus of the stationary GPE solution as an input and returns the parameters of the potential function and the factor in front of the GPE non-linear term. From the physical point of view the ANN predicts the parameters of a trap potential and the interaction constant of 1D Bose–Einstein condensate by its density distribution. Using the results of numerical solution of GPE for more than <?CDATA $30\,000$?> 30 000 sets of GPE parameters as train and validation datasets we build the ANN as a fast and accurate inverse GPE solver.

DOI
10.1088/1612-202x/ace70c

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Abstract Employing a general variational method and perturbation theory, we derived explicit solutions for the description of one-dimensional two species Bose–Einstein condensates confined by a harmonic trap potential in an optical lattice. We consider the system of two coupled Gross–Pitaevskii equations (GPE) and derive explicit expressions for the chemical potentials and wavefunctions in terms of the atom–atom interaction parameters and laser intensity. We have compared our results with the numerical solutions of the GPE and performed a quantitative analysis for the both considered methods. We underline the importance of the obtained explicit solutions to characterize the density profile or degree of miscibility of the two components.