TY - JOUR
T1 - Solvable Model of a Generic Trapped Mixture of Interacting Bosons
T2 - 26th Annual International Laser Physics Workshop, LPHYS 2017
AU - Klaiman, S.
AU - Streltsov, A. I.
AU - Alon, O. E.
N1 - Funding Information: This research was supported by the Israel Science Foundation (Grant No. 600/15). We thank Kaspar Sakmann and Lorenz Cederbaum for discussions. OEA is grateful to the continuous hospitality of the Lewiner Institute for Theoretical Physics (LITP) at the Department of Physics, Technion. Publisher Copyright: © Published under licence by IOP Publishing Ltd.
PY - 2018/4/5
Y1 - 2018/4/5
N2 - A solvable model of a generic trapped bosonic mixture, N 1 bosons of mass m 1 and N 2 bosons of mass m 2 trapped in an harmonic potential of frequency ω and interacting by harmonic inter-particle interactions of strengths λ 1, λ 2, and λ 12, is discussed. It has recently been shown for the ground state [J. Phys. A 50, 295002 (2017)] that in the infinite-particle limit, when the interaction parameters λ 1(N 1 - 1), λ 2(N 2 - 1), λ 12 N 1, λ 12 N 2 are held fixed, each of the species is 100% condensed and its density per particle as well as the total energy per particle are given by the solution of the coupled Gross-Pitaevskii equations of the mixture. In the present work we investigate properties of the trapped generic mixture at the infinite-particle limit, and find differences between the many-body and mean-field descriptions of the mixture, despite each species being 100%. We compute analytically and analyze, both for the mixture and for each species, the center-of-mass position and momentum variances, their uncertainty product, the angular-momentum variance, as well as the overlap of the exact and Gross-Pitaevskii wavefunctions of the mixture. The results obtained in this work can be considered as a step forward in characterizing how important are many-body effects in a fully condensed trapped bosonic mixture at the infinite-particle limit.
AB - A solvable model of a generic trapped bosonic mixture, N 1 bosons of mass m 1 and N 2 bosons of mass m 2 trapped in an harmonic potential of frequency ω and interacting by harmonic inter-particle interactions of strengths λ 1, λ 2, and λ 12, is discussed. It has recently been shown for the ground state [J. Phys. A 50, 295002 (2017)] that in the infinite-particle limit, when the interaction parameters λ 1(N 1 - 1), λ 2(N 2 - 1), λ 12 N 1, λ 12 N 2 are held fixed, each of the species is 100% condensed and its density per particle as well as the total energy per particle are given by the solution of the coupled Gross-Pitaevskii equations of the mixture. In the present work we investigate properties of the trapped generic mixture at the infinite-particle limit, and find differences between the many-body and mean-field descriptions of the mixture, despite each species being 100%. We compute analytically and analyze, both for the mixture and for each species, the center-of-mass position and momentum variances, their uncertainty product, the angular-momentum variance, as well as the overlap of the exact and Gross-Pitaevskii wavefunctions of the mixture. The results obtained in this work can be considered as a step forward in characterizing how important are many-body effects in a fully condensed trapped bosonic mixture at the infinite-particle limit.
UR - http://www.scopus.com/inward/record.url?scp=85045690352&partnerID=8YFLogxK
U2 - 10.1088/1742-6596/999/1/012013
DO - 10.1088/1742-6596/999/1/012013
M3 - Article
SN - 1742-6588
VL - 999
JO - Journal of Physics: Conference Series
JF - Journal of Physics: Conference Series
IS - 1
M1 - 012013
Y2 - 17 July 2017 through 21 July 2017
ER -