Schrödinger cat state formation in small bosonic Josephson junctions at finite temperatures and dissipation

In this work, we consider the feasibility of Schrödinger cat (SC) and N00N states formation by a convenient bosonic Josephson junction system in two-mode approximation. Starting with purely quantum description of two-mode Bose–Einstein condensate we investigate the effective potential approach that provides an accurate analytical description for the system with a large number of particles. We show that in the zero temperature limit SC states result from a quantum phase transition that occurs when the nonlinear strength becomes comparable with the Josephson coupling parameter. The Wigner function approach demonstrates the growth of the SC state halves separation and formation of N00N -like states (a Fock state superposition) with the particle number increase. We examine the possibility to attain the SC state at finite temperatures and a weak dissipation leading to appearing of some critical temperature; it defines the second-order phase transition from classical activation process to the SC state formation through the quantum tunneling phenomenon. Numerical estimations demonstrate that the critical temperature is sufficiently below the temperature of atomic condensation. The results obtained may be useful for experimental observation of SC states with small condensate Josephson junctions.