Diagnostics of macroscopic quantum states of Bose-Einstein condensate in double-well potential by nonstationary Josephson effect

We propose a method of diagnostic of a degenerate ground state of Bose condensate in a double well potential. The method is based on the study of the one-particle coherent tunneling under switching the time-dependent weak Josephson coupling between the wells. We obtain a simple expression that allows to determine the phase of the condensate and the total number of the particles in the condensate from the relative number of the particles in two wells $\Delta n =n_1-n_2$ measured before the Josephson coupling is switched on and after it is switched off. The specifics of the application of the method in the cases of the external and the internal Josephson effect are discussed.