  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 viewed as Bose-Einstein condensation (BEC)
of magnons. The method of dilute Bose gas enables a quantitative analysis of
quantum effects in these helimagnets and thereby three phases are found: cone,
coplanar fan and a phase-separated one. As an application, we map out the phase
diagram of a 3D helimagnet which consists of frustrated J1-J2 chains as a
function of frustration and an interchain coupling. Moreover, we also calculate
the stability of the 2-magnon bound state to investigate the possibility of the
bound-magnon BEC.
