Quadrupole Order in the Frustrated Pyrochlore Tb_{2+x}Ti_{2-x}O_{7+y}.

A hidden order that emerges in the frustrated pyrochlore Tb_{2+x}Ti_{2-x}O_{7+y} with T_{c}=0.53  K is studied using specific heat, magnetization, and neutron scattering experiments on a high-quality single crystal. Semiquantitative analyses based on a pseudospin-1/2 Hamiltonian for ionic non-Kramers magnetic doublets demonstrate that it is an ordered state of electric quadrupole moments. The elusive spin liquid state of the nominal Tb_{2}Ti_{2}O_{7} is most likely a U(1) quantum spin-liquid state.