Dissipative two-identical-particle systems: diffraction and interference

Abstract

Interference and diffraction of two-identical-particles are considered in the context of open quantum systems. This theoretical study is carried out within two approaches, the effective time-dependent Hamiltonian due to Caldirola-Kanai (CK) and the Caldeira-Leggett (CL) one where a master equation for the reduced density matrix is used under the presence of dissipation and temperature of the environment. Two simple but very illustrative examples are considered, diffraction by a single and two Gaussian slits by analyzing the mean square separation between particles, single-particle probability density and the simultaneous detection probability or diffraction patterns. Concerning the single Gaussian slit case, in the CK approach, the mean square separation drastically reduces with friction, reaching a constant value due to the localization effect of friction. On the contrary, in the CL approach, temperature has an opposite effect to friction and this quantity increases. Furthermore, there is a time-interval for which the joint detection probability is greater for fermions than for bosons. As has already been reported for non-dissipative systems, fermion bunching and boson anti-bunching are also observed.