Complex contact interaction for systems with short-range two-body loss

Contact interaction is a fundamental concept that appears in various areas of physics. It simplifies physical models by replacing the detailed short-range interaction with a zero-range contact potential which reproduces the same low-energy scattering parameter, i.e. the $s$-wave scattering length. In this work, we generalize this concept to a system with short-range two-body loss. We show that the short-range two-body loss can effectively be replaced by a zero-range complex contact potential with proper regularization characterized by a complex scattering length. We develop appropriate ways to regularize this potential in the Lindblad master equation and apply them to the dynamic problem of Bose-Einstein condensate with weak interaction and two-body loss.