Abstract Recent observations of droplets in dipolar and binary Bose–Einstein condensate (BEC) gives motivation to study the theory of droplet formation in detail. Specifically, the authors are interested in investigating the possibility of droplet formation in a quasi‐1D geometry. Recent observations have suggested that droplets are stabilized by competition between effective mean‐field and beyond mean‐field interaction. Hence, it is possible to map the effective equation of motion to a cubic‐quartic nonlinear Schrödinger equation (CQNLSE). Two analytical solutions of the modified Gross–Pitaevskii equation or CQNLSE are obtained and they are verified numerically. Based on their stability, the parameter regime for which droplets can form is investigated. The effective potential allows for conclusions about the regions of soliton domination and self‐bound droplet formations.
Recent observations of droplets in dipolar and binary Bose-Einstein condensate (BEC) motivates us to study the theory of droplet formation in details. Precisely, we are interested in investigating the possibility of droplet formation in a quasi one dimensional geometry. The recent observation have concluded that the droplets are stabilized by the competition between effective mean-filed and beyond mean-field interaction. Hence, it is possible to map the effective equation of motion to a cubic-quartic nonlinear Schr\odinger equation (CQNLSE). We obtain two analytical solutions of the modified Gross-Pitaevskii equation or CQNLSE and based on their stability we investigate the parameter regime for which droplets can form. The effective potential allows us to conclude about the regions of soliton domination and self bound droplet formations.
We investigate beyond-mean-field corrections to the energy of an elongated homogeneous Bose gas strongly confined in two directions, with dipoles aligned along the long axis of the system. When the dipolar interaction reaches its critical strength, the mean-field approach predicts instability. However, similar to the free-space case, beyond-mean-field effects significantly alter 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 contribution to the energy in the quasi-1D region, in addition to the confinement induced shift of the mean field energy, is proportional to the third power of the density
∼n3. Therefore, it can be interpreted as an effective three-body repulsion that stabilizes the gas, preventing collapse and leading to a finite-density solution. We also show that the same effect plays a crucial role in the binding of strongly elongated dipolar droplets under harmonic confinement.