  Single crystal samples of the frustrated quasi one-dimensional quantum magnet
Rb$_{2}$Cu$_{2}$Mo$_{3}$O$_{12}$ are investigated by magnetic, thermodynamic,
and electron spin resonance (ESR) measurements. Quantum phase transitions
between the gapped, magnetically ordered and fully saturated phases are
observed. Surprisingly, the former has a distinctive three-dimensional
character, while the latter is dominated by one-dimensional quantum spin
fluctuations. The entire $H$-$T$ phase diagram is mapped out and found to be
substantially anisotropic. In particular, the lower critical fields differ by
over 50\% depending on the direction of applied field, while the upper ones are
almost isotropic, as is the magnetization above saturation. The ESR spectra are
strongly dependent on field orientation and point to a helical structure with a
rigidly defined spin rotation plane.
