  Quantum critical systems derive their finite temperature properties from the
influence of a zero temperature quantum phase transition. The paradigm is
essential for understanding unconventional high-Tc superconductors and the
non-Fermi liquid properties of heavy fermion compounds. However, the
microscopic origins of quantum phase transitions in complex materials are often
debated. Here we demonstrate experimentally, with support from numerical
renormalization group calculations, a universal crossover from quantum critical
non-Fermi liquid behavior to distinct Fermi liquid ground states in a highly
controllable quantum dot device. Our device realizes the non-Fermi liquid
two-channel Kondo state, based on a spin-1/2 impurity exchange-coupled equally
to two independent electronic reservoirs. Arbitrarily small detuning of the
exchange couplings results in conventional screening of the spin by the more
strongly coupled channel for energies below a Fermi liquid scale T*. We extract
a quadratic dependence of T* on gate voltage close to criticality and validate
an asymptotically exact description of the universal crossover between strongly
correlated non-Fermi liquid and Fermi liquid states.
