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Journal Articles Physical Review A Year : 2020

Collective excitations of a one-dimensional quantum droplet


We calculate the excitation spectrum of a one-dimensional self-bound quantum droplet in a two-component bosonic mixture described by the Gross-Pitaevskii equation (GPE) with cubic and quadratic nonlinearities. The cubic term originates from the mean-field energy of the mixture proportional to the effective coupling constant $\delta g$, whereas the quadratic nonlinearity corresponds to the attractive beyond-mean-field contribution. The droplet properties are governed by a control parameter $\gamma\propto \delta g N^{2/3}$, where $N$ is the particle number. For large $\gamma>0$ the droplet features the flat-top shape with the discrete part of its spectrum consisting of plane-wave Bogoliubov phonons propagating through the flat-density bulk and reflected by edges of the droplet. With decreasing $\gamma$ these modes cross into the continuum, sequentially crossing the particle-emission threshold at specific critical values. A notable exception is the breathing mode which we find to be always bound. The balance point $\gamma = 0$ provides implementation of a system governed by the GPE with an unusual quadratic nonlinearity. This case is characterized by the ratio of the breathing-mode frequency to the particle-emission threshold equal to 0.8904. As $\gamma$ tends to $-\infty$ this ratio tends to 1 and the droplet transforms into the soliton solution of the integrable cubic GPE.

Dates and versions

hal-02881226 , version 1 (25-06-2020)



Marek Tylutki, Grigori E. Astrakharchik, Boris A. Malomed, Dmitry S. Petrov, Grigori E Astrakharchik, et al.. Collective excitations of a one-dimensional quantum droplet. Physical Review A, 2020, 101 (5), ⟨10.1103/PhysRevA.101.051601⟩. ⟨hal-02881226⟩
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