  Using a combination of neutron scattering, calorimetry, Quantum Monte Carlo
(QMC) simulations and analytic results we uncover confinement effects in
depleted, partially magnetized quantum spin ladders. We show that introducing
non-magnetic impurities into magnetized spin ladders leads to the emergence of
a new characteristic length L in the otherwise scale-free Tomonaga-Luttinger
liquid (serving as the effective low-energy model). This results in universal
LT scaling of staggered susceptibilities. Comparison of simulation results with
experimental phase diagrams of prototypical spin ladder compounds DIMPY and
BPCB yields excellent agreement.
