Abstract
In this work, we study the stationary structures and the breathing mode behavior of a two-dimensional self-bound binary Bose droplet. We employ an analytical approach using a variational ansatz with a super-Gaussian trial order parameter and compare it with the numerical solutions of the extended Gross-Pitaevskii equation. We find that the super-Gaussian is superior to the often used Gaussian ansatz in describing the stationary and dynamical properties of the system. For sufficiently large nonrotating droplets the breathing mode is energetically favorable compared to the self-evaporating process. However, for small self-bound systems our results differ based on the ansatz. Inducing angular momentum by imprinting multiply quantized vortices at the droplet center, this preference for the breathing mode persists independent of the norm.
Highlights
For bound systems to form without external confinement, a balance between repulsive and attractive forces is required
Such Bose droplets were first discovered for dipolar bosonic systems [3,4,5,6,7,8], where the effective interatomic interactions may be adjusted such that self-bound states become stabilized by quantum fluctuations [6,9,10,11,12,13,14]
The quantum fluctuation contributions to the total energy density functional are effectively represented by the Lee-Huang-Yang (LHY) terms [17], extending the usual mean field (MF) Gross-Pitaevskii equation
Summary
For bound systems to form without external confinement, a balance between repulsive and attractive forces is required. For ultracold bosonic atoms the possibility to form self-bound droplets was proposed for binary gases with suitably tuned contact interactions [1,2], where higher-order terms in the total energy density functional may become sizable. Such Bose droplets were first discovered for dipolar bosonic systems [3,4,5,6,7,8], where the effective interatomic interactions may be adjusted such that self-bound states become stabilized by quantum fluctuations [6,9,10,11,12,13,14]. For the comparison of the variational ansatz discussed in the following, Eq (4) is solved numerically using the Fourier split-step method in imaginary and real time
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