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Parametric instability of ultracold Bose gases with long-range interaction and quantum fluctuations trapped in optical lattices

Etienne Wamba1,2,*, Jérémie Bai3,†, and Aurélien S. Tchakoutio Nguetcho3,4,5,‡

  • *Contact author: ettienne.wamba@ubuea.cm
  • †Contact author: baijeremie9@gmail.com
  • ‡Contact author: nguetchoserge@yahoo.fr
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Phys. Rev. A 112, 053301 – Published 3 November, 2025

DOI: https://doi.org/10.1103/15qz-q9vm

Abstract

We investigate the dynamical instabilities of a one-dimensional ultracold Bose-Bose mixture with long-range dipole-dipole interactions, trapped in deep optical lattices and subject to periodically varying contact interaction. The effect of beyond-mean-field corrections due to quantum fluctuations is considered. In the tight-binding regime, we employ Wannier functions to derive a discrete nonlinear Schrödinger equation that captures the dynamics of the system. Using linear stability analysis coupled to multiple scale expansion, we systematically study the modulational and parametric instabilities of the system in the miscible regime, identifying the conditions under which these instabilities emerge. The corresponding instability domains are found and examined. The roles of long-range interactions and quantum fluctuations are highlighted, demonstrating their significant impact on the stability and dynamics of the lattice system. Our analytical predictions are validated through direct numerical simulations, which confirm the instability diagrams through the effective onset of instabilities and reveal the intricate interplay between interaction strength, quantum fluctuation, and the long-range nature of the dipole-dipole forces. This work provides insights into the control and manipulation of ultracold quantum gases in optical lattices, which have potential applications in quantum simulation and condensed-matter physics.

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Phys. Rev. A 112, 053301– Published 3 November, 2025
  • Received 25 March 2025
  • Accepted 29 September 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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