Imaginary phases in two-level model with spontaneous decay

We study a two-level model coupled to the electromagnetic vacuum and to an external classic electric field with fixed frequency. The amplitude of the external electric field is supposed to vary very slowly in time. Garrison and Wright (1988 Phys. Lett. A 128 177) used the non-Hermitian Hamiltonian approach to study the adiabatic limit of this model and obtained that the probability of this two-level system to be in its upper level has an imaginary geometric phase. Using the master equation for describing the time evolution of the two-level system we obtain that the imaginary phase due to dissipative effects is time-dependent, in opposition to the Garrison and Wright result. The present results show that the non-Hermitian Hamiltonian method should not be used to discuss the nature of the imaginary phases in open systems