Laboratoire de Physique Théorique
Toulouse - UMR 5152

We study the squeezed states of the phonon modes and the associated supercurrent in superconducting moleclular transistors with strong electron-phonon interaction. It is suggested that the phonon squeezing can be manipulated by means of continuous quantum measurement of the charge on the molecule. We use both a numerical method (to solve the master equation) and the nonequilibrium Keldysh formalism to show that the continuous measurement gives rise to the quantum Zeno effect and hence the control of the phonon squeezing.