Dynamically stable two- and four-droplet solitons in a very strongly dipolar NaCs condensate

A strongly dipolar Bose-Einstein condensate (BEC) of Dy atoms could sustain different types of states not possible in a non-dipolar BEC. Motivated by the observation of a very strongly dipolar condensate of NaCs molecules [N. Bigagli et al., Nature 631, 289 (2024)], with dipolar interaction stronger by more than an order of magnitude compared to that of Dy atoms, we demonstrate that in a very strongly dipolar NaCs BEC, it is possible to have a two- and a four-droplet metastable soliton, axially free along the polarization $z$ direction. In this study we employ imaginary-time propagation of an improved mean-field model, including the Lee-Huang-Yang interaction. The dipolar solitons are subject to an expulsive Gaussian potential at the center and a harmonic potential $-$ both acting in the $x$-$y$ plane. The phase-coherent solitons, possessing the isolated droplets, are free to move along the $z$ axis without any relative motion between the droplets. The dynamical stability and mobility of these solitons are demonstrated by real-time propagation employing the converged imaginary-time wave function as the initial state.