Quantum droplet of one-dimensional bosons with a three-body attraction

Ultracold atoms offer valuable opportunities where interparticle interactions can be controlled at will. In particular, by extinguishing the two-body interaction, one can realize unique systems governed by the three-body interaction, which is otherwise hidden behind the two-body interaction. Here we study one-dimensional bosons with a weak three-body attraction and show that they form few-body bound states as well as a many-body droplet stabilized by the quantum mechanical effect. Their binding energies relative to that of three bosons are all universal and the ground-state energy of the dilute droplet is found to grow exponentially as $E_N/E_3\to exp(8N^2/\sqrt{3}\pi )$ with increasing particle number $N\gg 1$. The realization of our system with coupled two-component bosons in an optical lattice is also discussed.

Figure 1

(a) Curve in the plane of Rabi frequency $\mathrm{\Omega }$ and detuning $\mathrm{\Delta }$ along which the effective two-body interaction energy $U_2$ vanishes. The dot marks the point at which both $U_2$ and $U_3$ vanish. (b) Effective three-body interaction energy $U_3$ as a function of $\mathrm{\Omega }$ with $\mathrm{\Delta }$ simultaneously tuned to fix $U_2=0$. The solid (dotted) curve corresponds to $\mathrm{\Delta }$ along the solid (dotted) curve in (a).