Purity oscillations in coupled Bose-Einstein condensates

Distinct oscillations of the purity of the single-particle density matrix for many-body open quantum systems have been shown to exist [D. Dast, D. Haag, H. Cartarius, and G. Wunner, Phys. Rey. A 93, 033617 (2016)]. They are found in PT-symmetric Bose-Einstein condensates, in which the coherence of the condensate drops and is almost completely restored periodically. For this effect the presence of a gain and loss of particles turned out to be essential. We demonstrate that it can also be found in closed quantum systems whose subsystems experience a gain and loss of particles. This is shown with two different lattice setups for cold atoms, viz., a ring of six lattice sites with periodic boundary conditions and a linear chain of four lattice wells. In both cases pronounced purity oscillations are found, and it is shown that they can be made experimentally accessible via the average contrast in interference experiments. This shows that it is possible to identify this characteristic effect in closed quantum systems which have been proposed to realize PT-symmetric quantum mechanics via separation into subsystems.