Limitation of the Lee–Huang–Yang interaction in forming a self-bound state in Bose–Einstein condensates

The perturbative Lee–Huang–Yang (LHY) interaction proportional to n3∕2, where n is the density, creates an infinitely repulsive potential at the center of a Bose–Einstein condensate (BEC) with net attraction, which stops the collapse to form a self-bound state in a dipolar BEC and in a binary BEC. However, recent microscopic calculations of the non-perturbative beyond-mean-field (BMF) interaction indicate that the LHY interaction is valid only for very small values of gas parameter x. We show that a realistic non-perturbative BMF interaction can stop collapse and form a self-bound state only in a weakly attractive binary BEC with small x values (x⪅0.01), whereas the perturbative LHY interaction stops collapse for all attractions. We demonstrate these aspects using an analytic BMF interaction with appropriate weak-coupling LHY and strong coupling limits.