Pairing of Cooper Pairs in a Fully Frustrated Josephson Junction Chain

We study a one-dimensional Josephson junction chain embedded in a magnetic field. We show that when the magnetic flux per elementary loop equals half the superconducting flux quantum $\phi_0=h/2e$, a local $\nbZ_2$ symmetry arises. This symmetry is responsible for a nematic Luttinger liquid state associated to bound states of Cooper pairs. We analyze the phase diagram and we discuss some experimental possibilities to observe this exotic phase.