The spiral states proposed by Shraiman and Siggia as the ground state of the doped antiferromagnet are investigated for the quantum spin liquid with a nonvanishing gap for the triplet excitations. An effective Lagrangian is derived. The dynamics of the collective modes, including the gauge field, is discussed in the single-spiral state. The normal-state properties as well as the superconductivity of this spiral state are discussed. For a parameter region of the effective Lagrangian, we find that the ground state is a laminar structure made out of the double-spiral state with staggered chirality and the single-spiral state.