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arXiv:2503.18576 · Physical Review A

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

Étienne Wamba, Jianmei Bai, Aurélien Serge Tchakoutio Nguetcho

Published Sep 29, 2025• 0 citations
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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.

DOI
10.1103/15qz-q9vm

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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.
We study the stabilization properties of dipolar Bose–Einstein condensate in a deep one-dimensional optical lattice with an additional external parametrically modulated harmonic trap potential. Through both analytical and numerical methods, we solve a dimensionless nonlocal nonlinear discrete Gross–Pitaevskii equation with both the short-range contact interaction and the long-range dipole–dipole interaction. It is shown that, the stability of dipolar condensate in modulated deep optical lattice can be controled by coupled effects of the contact interaction, the dipolar interaction and the external modulation. The system can be stabilized when the dipolar interaction, the contact interaction, the average strength of potential and the ratio of amplitude to frequency of the modulation satisfy a critical condition. In addition, the breather state, the diffused state and the attractive-interaction-induced-trapped state are predicted. The dipolar interaction and the external modulation of the lattice play important roles in stabilizing the condensate.
We study the stability of the continuous waves in the pancake shaped dipolar Bose-Einstein condensate trapped in the strong optical lattice potential with the coexisting local (the short-range s-wave) interaction and nonlocal (the dipole-dipole) interactions between the condensate atoms.The system is modeled by two two-dimensional discrete models derived from the Gross-Pitaevskii equation accounting the dipole-dipole interactions: discrete nonlinear Schrödinger equation with cubic nonlinearity and nonpolynomial Schrödinger equation.The corresponding dispersion relations are calculated analytically and the regions of the modulation instability in the parametric space are summarized into the stability diagrams.
Abstract Through a semiquantal procedure, we study the perturbed modulation of amplitude and phase of Gross-Piteavskii equation describing trapped Bose–Einstein condensates in an optical lattice potential. By introducing quantum correctional parameters, the problem is quantized and leads to the derivation of a novel dynamical instability criterion. Additional degrees of freedom carrying quantum properties play a central role on the refine of the instability bandwidth, and, combined to the strength of optical lattice potential, entail unstable modes into full stability. A set of computational tools exhibited various features that bear instability characteristics, to confirm analytically predicted results. The quantum fluctuations thus have a stabilizing effect on the dynamics of harmonically trapped Bose–Einstein condensates in an optical lattice potential.
Periodically driven quantum systems are currently explored in view of realizing novel many-body phases of matter. This approach is particularly promising in gases of ultracold atoms, where sophisticated shaking protocols can be realized and interparticle interactions are well controlled. The combination of interactions and time-periodic driving, however, often leads to uncontrollable heating and instabilities, potentially preventing practical applications of Floquet engineering in large many-body quantum systems. In this work, we experimentally identify the existence of parametric instabilities in weakly interacting Bose-Einstein condensates in strongly driven optical lattices through momentum-resolved measurements, in line with theoretical predictions. Parametric instabilities can trigger the destruction of weakly interacting Bose-Einstein condensates through the rapid growth of collective excitations, in particular in systems with weak harmonic confinement transverse to the lattice axis. Understanding the onset of parametric instabilities in driven quantum matter is crucial for determining optimal conditions for the engineering of modulation-induced many-body systems.
In past years, optical lattices have been demonstrated as an excellent platform for making, understanding, and controlling quantum matters at nonlinear and fundamental quantum levels. Shrinking experimental observations include matter-wave gap solitons created in ultracold quantum degenerate gases, such as Bose–Einstein condensates with repulsive interaction. In this paper, we theoretically and numerically study the formation of one-dimensional gap soliton molecules and clusters in ultracold coherent atom ensembles under electromagnetically induced transparency conditions and trapped by an optical lattice. In numerics, both linear stability analysis and direct perturbed simulations are combined to identify the stability and instability of the localized gap modes, stressing the wide stability region within the first finite gap. The results predicted here may be confirmed in ultracold atom experiments, providing detailed insight into the higher-order localized gap modes of ultracold bosonic atoms under the quantum coherent effect called electromagnetically induced transparency.
In this thesis we present a detailed investigation of the role played by quantum and thermal fluctuations in ultracold Bose gases. We begin with a review of several important concepts and analytical tools within a functional integration formalism. We first focus on the so-called zero-range approximation for the interaction potential, by recovering the Bogoliubov results and the Landau two-fluid model from a field-theory perspective. In deriving the beyond-mean-field equation of state, we are going to show that a crucial point concerns the proper regularization of the divergent zero-point energy. Among the alternative approaches to investigate finite-temperatures Bose gases, we apply the kinetic theory to explain some recent results on the sound propagation in two-dimensional Bose gases. We then move to consider the eventual corrections to the thermodynamics of Bose gases due to the finite-range character of the interaction potential. The coupling constants of the finite-range model are related to measurable scattering parameters through an effective-field-theory approach. The role of finite-range corrections is considered not only in three spatial dimensions but also in systems with lower dimensionalities. Our analytical predictions are in good agreement with available Monte Carlo simulations and consistent with other theoretical frames, as the Lieb-Lininger theory for one-dimensional systems. In the third chapter, the relevance of fluctuations is investigated from an alternative point of view. Indeed, for a single-component Bose gas we have actually considered their effect as deviations of thermodynamic quantities from the mean-field and zero-range picture. In the case of collapsing Bose mixtures, we are going to show that zero-temperature fluctuations play a crucial stabilizing role against the collapse instability. Because of this peculiar mechanism, ultracold mixtures can display finite-density configurations also in free space. Inspired by recent experiments, we characterize this novel self-bound state by comparison with bright solitons, following a variational scheme. We also consider the case of binary mixtures where a coherent internal coupling is turned on. In the last chapter, we move to deal with dipolar condensates. In particular, we are interested in beyond-mean-field effects leading to the formation of inhomogeneous ground states. In order to provide a reliable answer to the open issue of superfluid properties of these structures, we present our recent numerical investigation on the phase diagram of dipolar bosons.