## Abstract

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.

Original language | English |
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Article number | 012013 |

Number of pages | 12 |

Journal | Journal of Physics: Conference Series |

Volume | 999 |

Issue number | 1 |

DOIs | |

State | Published - 5 Apr 2018 |

Event | 26th Annual International Laser Physics Workshop, LPHYS 2017 - Kazan, Russian Federation Duration: 17 Jul 2017 → 21 Jul 2017 |

### Bibliographical note

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.

## ASJC Scopus subject areas

- General Physics and Astronomy