  In our previous work it has been shown the possibility to use the
Aharonov-Anandan invariant as a tool in the analysis of disparate systems,
including Hawking and Unruh effects, as well as graphene physics and thermal
states. We show that the vacuum condensation, characterizing such systems, is
also related with geometric phases and we analyze the properties of the
geometric phase of systems represented by mixed state and undergoing a
nonunitary evolution. In particular, we consider two level atoms accelerated by
an external potential and interacting with a thermal state. We propose the
realization of Mach-Zehnder interferometers which can prove the existence of
the Unruh effect and can allow very precise measurements of temperature.
