Nonunitary geometric phases: A qubit coupled to an environment with random noise

FERNANDO C. LOMBARDO AND PAULA I. VILLAR

Paraty

Workshop; IV Quantum Information School and Workshop; 2013

CNPq-CBPF-CAPES

We describe the decoherence process induced on a two-level quantum system in direct interaction with a non-equilibrium environment. The non-equilibrium feature is represented by a non-stationary random function corresponding to the fluctuating transition frequency between two quantum states coupled to the surroundings. In this framework, we compute the decoherence factors which have a characteristic ?dip? related to the initial phases of the bath modes. We therefore study differ- ent types of environments, namely ohmic and supra-ohmic. These environments present different decoherence time-scales than the thermal environment we used to study. As a consequence, we com- pute analytically and numerically the non-unitary geometric phase for the qubit in a quasi-cyclic evolution under the presence of these particular non-equilibrium environments. We show in which cases decoherence effects could, in principle, be controlled in order to perform a measurement of the geometric phase using standard procedures.