Dipolar Droplets at 3D-1D Crossover

We investigate beyond-mean-field corrections to the energy of a one-dimensional Bose gas confined by a box potential with dipoles aligned along the unconfined direction. When the dipolar interaction reaches its critical strength, the system becomes unstable at the mean-field level. Then, similarly to the free space case, the beyond-mean-field contribution significantly alters the ground state of the system, leading to the formation of a self-bound atomic cloud known as a quantum droplet. Our analysis demonstrates that the beyond-mean-field correction can be understood as an effective three-body repulsion stabilizing the gas, preventing its collapse and leading to a finite-density solution. The quasi-1D dipolar droplets bring into play yet another subtle quantum effect: the effective three-body interactions.