  We study high-field phase diagram and low-energy excitations of
three-dimensional quantum helimagnets. Slightly below the saturation field, the
emergence of magnetic order may be mathematically viewed as Bose-Einstein
condensation (BEC) of magnons. The method of dilute Bose gas enables an
unbiased quantitative analysis of quantum effects in three-dimensional
helimagnets and thereby three phases are found: cone, coplanar fan and an
attraction-dominant one. To investigate the last phase, we extend the usual BEC
approach so that we can handle 2-magnon bound states. In the case of 2-magnon
BEC, the transverse magnetization vanishes and long-range order occurs in the
quadrupolar channel (spin-nematic phase). As an application, we map out the
phase diagram of a 3D helimagnet which consists of frustrated J1-J2 chains
coupled by an interchain interaction J3.
