Dissipative two-identical-particle systems: diffraction and interference

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 on 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. The decoherence process, loss of being indistinguishable, is settled gradually with time by increasing friction and temperature. In the two Gaussian slits problem within the CK approach, the single-particle probability density behaves almost similarly for all kinds of particle pairs displaying small overlapping between one-particle states. The differences among the three statistics decrease when dissipation increases. However, in the opposite limit, fermions behave completely differently from bosons which themselves behave like distinguishable particles. This last behavior is also seen when the interference pattern is considered by computing the detection probability of both particles with two detectors, one fixed and the second mobile.