title: Polariton condensation threshold investigation through the numerical resolution of the generalized Gross-Pitaevskii equation.
abstract: We present a numerical approach for the solution of the dissipative Gross-Pitaevskii equation coupled to the reservoir equation governing the exciton-polaritons Bose-Einstein condensation. It is based on the finite difference method applied to space variables and on the fourth order Range-Kutta algorithm applied to the time variable. Numerical tests illustrate the stability and accuracy of the proposed scheme. Then results on the behavior of the condensate under large Gaussian pumping and around the threshold are presented. We determine the threshold through the particular behavior of the self-energy and characterize it by tracking the establishment time of the steady state.
authors.affiliation: Laboratoire Charles Coulomb, UMR 5221 CNRS, Université de Montpellier, Place Bataillon 34095 Montpellier, France.|Université de Carthage, Faculté des Sciences de Bizerte, Laboratoire De Physique Des Matériaux, 7021 Jarzouna-Bizerte, Tunisia.
authors.forename: Hamis
authors.initials: H
authors.lastname: Gargoubi
authors.affiliation: Laboratoire Charles Coulomb, UMR 5221 CNRS, Université de Montpellier, Place Bataillon 34095 Montpellier, France.
authors.forename: Thierry
authors.initials: T
authors.lastname: Guillet
authors.affiliation: Université de Carthage, Faculté des Sciences de Bizerte, Laboratoire De Physique Des Matériaux, 7021 Jarzouna-Bizerte, Tunisia.
authors.forename: Sihem
authors.initials: S
authors.lastname: Jaziri
authors.affiliation: Université de Carthage, Faculté des Sciences de Bizerte, Laboratoire De Physique Des Matériaux, 7021 Jarzouna-Bizerte, Tunisia.
authors.forename: Jalloul
authors.initials: J
authors.lastname: Balti
authors.affiliation: Laboratoire Charles Coulomb, UMR 5221 CNRS, Université de Montpellier, Place Bataillon 34095 Montpellier, France.
authors.forename: Brahim
authors.initials: B
authors.lastname: Guizal