# Collective excitations of a one-dimensional quantum droplet – Archive ouverte HAL

### Marek TylutkiGrigori E. AstrakharchikBoris A. Malomed 1 Dmitry S. Petrov 2 Grigori Astrakharchik 3 Boris Malomed 4 Dmitry Petrov

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

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.

• 1. Tel Aviv University [Tel Aviv]
• 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
• 3. UPC - Universitat Politècnica de Catalunya [BarcelonaTech]
• 4. Department of Interdisciplinary Studies