The transition and coexistence of quantum droplets and solitons in quasi-1D dipolar Bose gas

In our study, we investigated bright solitons, dark solitons, and quantum droplets in quasi-one-dimensional dipolar Bose gases, and further validated the crossover and coexistence of quantum droplets and solitons using the Lieb-Liniger energy within the framework of local density approximation. Increasing the particle number N transforms the bright dipolar soliton state into a stable self-bound quantum droplet state, with further increases in N leading to a broader quantum droplet that enables the presence of dark solitons within it.