  We present a 14N nuclear magnetic resonance study of a single crystal of
CuBr4(C5H12N)2 (BPCB) consisting of weakly coupled spin-1/2 Heisenberg
antiferromagnetic ladders. Treating ladders in the gapless phase as Luttinger
liquids, we are able to fully account for (i) the magnetic field dependence of
the nuclear spin-lattice relaxation rate 1/T_1 at 250 mK and for (ii) the phase
transition to a 3D ordered phase occuring below 110 mK due to weak interladder
exchange coupling. BPCB is thus an excellent model system where the possibility
to control Luttinger liquid parameters in a continuous manner is demonstrated
and Luttinger liquid model tested in detail over the whole fermion band.
