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Journal of Physics B Atomic Molecular and Optical Physics

Excitation and quasi-transition of rogue waves in a one-dimensional quantum droplet

Li-Zheng Lv, Peng Gao, Zhan-Ying Yang, Wen‐Li Yang

Published Jun 26, 2023• 4 citations
Publisher

Abstract

Abstract We study the dynamics of rogue wave excitations and quasi-transitions in one-dimensional quantum droplets, whose homogeneous-density flat top provides an applicable background wave for nonlinear excitation. Using a quenching technique and a localized space modulation technique for the nonlinear effect coefficient, the rogue wave is excited on droplets. The excitation modes of rogue waves can be transitioned to dispersive shock waves or Kuznetsov–Ma breathers by regulating their modulation amplitude and width, and their maximal density and width can be regulated by modulation their amplitude. Meanwhile, two Gaussian modulations for droplets also bring the second-order rogue wave’s dynamics, whose maximal amplitude can approach 3.6 times that of the amplitude of droplets. Our results provide guidance for rogue wave excitation and transition on self-bound background waves and deepen our understanding of quantum droplets.

DOI
10.1088/1361-6455/ace1bd

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Abstract We study the dynamics of rogue wave excitations and quasi-transitions in one-dimensional quantum droplets, whose homogeneous-density flat top provides an applicable background wave for nonlinear excitation. Using a quenching technique and a localized space modulation technique for the nonlinear effect coefficient, the rogue wave is excited on droplets. The excitation modes of rogue waves can be transitioned to dispersive shock waves or Kuznetsov–Ma breathers by regulating their modulation amplitude and width, and their maximal density and width can be regulated by modulation their amplitude. Meanwhile, two Gaussian modulations for droplets also bring the second-order rogue wave’s dynamics, whose maximal amplitude can approach 3.6 times that of the amplitude of droplets. Our results provide guidance for rogue wave excitation and transition on self-bound background waves and deepen our understanding of quantum droplets.
Abstract Solitonic excitations of the one-dimensional quantum droplets are obtained, which smoothly connect vacuum with the flat-top droplet, akin to compactons in classical liquids. These solitons are of the kink type, necessarily residing on a constant pedestal, determined by the mean-field (MF) repulsion and beyond mean field quantum correction and having exactly one-third of the uniform condensate amplitude. Akin to the kinks, the propagating modes occur in pairs and are phase-locked with the background. The lowest chemical potential and condensate amplitude at the flat-top boundary matches with the self-trapped quantum droplet. More general excitations of analogous kind are obtained through the Möbius transform, which connect the required solutions to elliptic functions in general.
Abstract The static and dynamic properties of self-bound quantum droplets in a one-dimensional Bose-Bose mixture are discussed in the spirit of the Hartree–Fock-Bogoliubov theory. This latter enables us to provide beyond the Lee-Huang-Yang (LHY) quantum corrections to the equation of state at both zero and finite temperatures. In the uniform case our results for the ground-state energy and the critical temperature are confirmed through comparison with Quantum Monte-Carlo simulation and with available theoretical results. The density profiles are supported by numerical simulations of the generalized Gross-Pitaevskii equation which selfconsistently includes higher-order terms originating from the normal and anomalous fluctuations under the local density approximation. We show that the density exhibits a dip near its center in the flat-top plateau region for large interspecies interactions. We exemplify the impact of the beyond LHY corrections on the spatiotemporal evolution of the self-bound droplet in the presence of excitation induced by periodic density modulation. It is found that higher-order corrections may lead to the formation of a train of small droplets. We then extend our study for the case of inhomogeneous droplets in quasi one-dimensional Bose mixtures.
We study the properties of modulational instability and discrete breathers arising in a quasi-one-dimensional discrete Gross-Pitaevskii equation with Lee-Huang-Yang corrections. Conditions for modulation instability and instability regions of nonlinear plane waves are determined in parameter space. We analytically investigate the existence of different quantum droplet solutions, including intersite, onsite, front-like, flat-top, and dark localized modes, using the Page method and variational approach. Their stability is checked using linear stability analyses and numerical simulations. The analytical predictions corroborated with the numerical simulations.
We investigate the ground state and dynamics of one-dimensional spin-orbit coupled (SOC) quantum droplets within the extended Gross--Pitaevskii approach. As the SOC wave number increases, stripe droplet patterns emerge, with a flat-top background, for larger particle numbers. The surface energy decays following a power-law with respect to the interactions. At small SOC wave numbers, a transition from Gaussian to flat-top droplets occurs for either a larger number of atoms or reduced intercomponent attraction. The excitation spectrum shows that droplets for relatively small SOC wave numbers are stable, otherwise stripe droplets feature instabilities as a function of the particle number or the interactions. We also witness rich droplet dynamical features using velocity imprinting and abrupt changes in the intercomponent interaction or the SOC parameters. Characteristic responses include breathing oscillations, expansion, symmetric and asymmetric droplet fragmentation, admixtures of single and stripe droplet branches, and erratic spatial distributions suggesting the triggering of relevant instabilities. Our results reveal the controlled dynamical generation and stability properties of stripe droplets that should be detectable in current cold-atom experiments.
Quantum droplets have recently emerged as a novel liquid state of matter in a mixture of two-component ultracold Bose gases under the equilibrium condition between the competing attractive inter- and repulsive intraspecies forces. Quantum droplets represent a self-bound liquid state in purely nonlinear systems and as such there is not any management applied to their study up to now. We here introduce the nonlinear management via space-periodic Feshbach resonance technique to a binary Bose–Einstein condensate and investigate theoretically the structure, property and dynamics of the one-dimensional quantum droplets therein, three findings are made: small droplets with single hump (solitonlike), moderate droplets composed of two solitons, large droplets feature a modulated flat-top shape. Particularly, by means of linear-stability and direct perturbed simulations, we prove that the droplets have a much wider stable region than their counterparts without taking the nonlinear management. The variational approximation is adopted and validated with numerical results in terms of small droplets. The results predicted here may be realized in the frontier ultracold atoms experiments aided by Feshbach-resonance, opening up a new channel to the quantum droplets studies.
The structure and dynamics of one-dimensional binary Bose gases forming quantum droplets is studied by solving the corresponding amended Gross-Pitaevskii equation. Two physically different regimes are identified, corresponding to small droplets of an approximately Gaussian shape and large ``puddles'' with a broad flat-top plateau. Small droplets collide quasielastically, featuring the solitonlike behavior. On the other hand, large colliding droplets may merge or suffer fragmentation, depending on their relative velocity. The frequency of a breathing excited state of droplets, as predicted by the dynamical variational approximation based on the Gaussian ansatz, is found to be in good agreement with numerical results. Finally, the stability diagram for a single droplet with respect to shape excitations with a given wave number is drawn, being consistent with preservation of the Weber number for large droplets.