Parametric instability of linear systems in quantum theory

Ya.I. Granovskii, Yu. A. Dimashko

Vicky Howse, Raymond J. Spiteri

Abstract Faraday or parametric instability has been observed in various contexts in Bose–Einstein condensates. In Rabi-coupled condensates, the instability can arise without explicit modulation of external parameters. We study the dynamics of an interface in a two-component immiscible condensate near the miscible-immiscible threshold, with Rabi coupling between components. We show that a small initial perturbation leads to oscillations that grow in amplitude with increasing Rabi frequency until the interface produces droplet-like structures. We find that the interface oscillations are driven by parametric resonance with density oscillations in the bulk. This parametric instability of the interface provides a link to the walking droplet pilot wave system, which is governed by the Faraday instability. Because walking droplets simulate fundamentally quantum behaviors, and ‘vortex molecules,’ which are hosted by a Rabi-coupled condensate, simulate quark confinement, this observation suggests a mechanism-level connection between these systems and provides a possible bridge between distinct analog models of fundamental particles.

Jean Bellissard

Étienne Wamba, Jianmei Bai, Aurélien Serge Tchakoutio Nguetcho

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.

V. P. Ruban, Wenlong Wang, Christopher Ticknor +1 more

Instabilities of vortex-ring-bright coherent structures in harmonically trapped two-component three-dimensional Bose-Einstein condensates are studied numerically within the coupled Gross-Pitaevskii equations and interpreted analytically. Interestingly, the filled vortex core with a sufficiently large amount of the bright component is observed to reduce the parametric interval of stability of the vortex ring. We have identified the mechanisms of several linear instabilities and one nonlinear parametric instability in this connection. Two of the linear instabilities are qualitatively different from ones reported earlier and are associated with azimuthal modes of $m=0$ and $m=1$, i.e., deviations of the vortex from the stationary ring shape. Our nonlinear parametric resonance instability occurs between the $m=0$ and $m=2$ modes and signals the exchange of energy between them.

Hendra I. Nurdin, Naoki Yamamoto