Solvable model of a generic driven mixture of trapped bose–einstein condensates and properties of a many-boson floquet state at the limit of an infinite number of particles

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Abstract

A solvable model of a periodically driven trapped mixture of Bose–Einstein condensates, consisting of N1 interacting bosons of mass m1 driven by a force of amplitude fL,1 and N2 interacting bosons of mass m2 driven by a force of amplitude fL,2, is presented. The model generalizes the harmonic-interaction model for mixtures to the time-dependent domain. The resulting many-particle ground Floquet wavefunction and quasienergy, as well as the time-dependent densities and reduced density matrices, are prescribed explicitly and analyzed at the many-body and mean-field levels of theory for finite systems and at the limit of an infinite number of particles. We prove that the time-dependent densities per particle are given at the limit of an infinite number of particles by their respective mean-field quantities, and that the time-dependent reduced one-particle and two-particle density matrices per particle of the driven mixture are 100% condensed. Interestingly, the quasienergy per particle does not coincide with the mean-field value at this limit, unless the relative center-of-mass coordinate of the two Bose–Einstein condensates is not activated by the driving forces fL,1 and fL,2. As an application, we investigate the imprinting of angular momentum and its fluctuations when steering a Bose–Einstein condensate by an interacting bosonic impurity and the resulting modes of rotations. Whereas the expectation values per particle of the angular-momentum operator for the many-body and mean-field solutions coincide at the limit of an infinite number of particles, the respective fluctuations can differ substantially. The results are analyzed in terms of the transformation properties of the angular-momentum operator under translations and boosts, and as a function of the interactions between the particles. Implications are briefly discussed.

Original languageEnglish
Article number1342
Pages (from-to)1-38
Number of pages38
JournalEntropy
Volume22
Issue number12
DOIs
StatePublished - Dec 2020

Bibliographical note

Funding Information:
Funding: This research was funded by the Israel Science Foundation (Grants No. 600/15 and No. 1516/19).

Funding Information:
Acknowledgments: I thank Kaspar Sakmann for the discussions. This research was supported by the Israel Science Foundation (Grants No. 600/15 and No. 1516/19).

Publisher Copyright:
© 2020 by the authors. Licensee MDPI, Basel, Switzerland.

Keywords

  • Angular momentum
  • Coupled nonlinear Schrödinger equations
  • Driven Bose–Einstein dondensates
  • Floquet Hamiltonian
  • Harmo+nic-interaction models
  • Infinite-particle-number limit
  • Mixtures
  • Solvable models
  • Time-dependent Schrödinger equation
  • Time-dependent reduced density matrices

ASJC Scopus subject areas

  • Information Systems
  • Mathematical Physics
  • Physics and Astronomy (miscellaneous)
  • Electrical and Electronic Engineering

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