A study on the role of the initial conditions and the nonlinear dissipation in the non-Hermitian effective Hamiltonian approach

This work examines the initial conditions dependence and the influence of nonlinear dissipation in the quantum dynamics originated by the non-Hermitian effective Hamiltonian approach. In particular, we test the performance of this theoretical approach for modeling the dynamics of the pumped-dissipative Jaynes Cummings model under different initial states such as a Fock, Gaussian and maximally mixed states, and as well as for a polaritonic light-matter state. It is demonstrated unequivocally that whereas the non-Hermitian effective Hamiltonian approach fails in to reproduce correctly the time evolution of the density matrix elements and observables of the system, the corrected version of this theoretical approach recently developed by us shows an excellent agreement with simulations based on the Lindblad master equation formalism.