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Physics Letters A

Decoherence in a two-level system coupled to a fermion environment with phase transitions

L.C. Wang, H. T. Cui, X. X. Yi

Published Oct 6, 2007• 2 citations
Publisher
DOI
10.1016/j.physleta.2007.10.001

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The decoherence induced on a single qubit by its interaction with the environment is studied. The environment is modeled as a scalar two-level boson system that can go through either first-order or continuous-excited-state quantum phase transitions, depending on the values of the control parameters. A mean-field method based on the Tamm-Damkoff approximation is worked out in order to understand the observed behavior of the decoherence. Only the continuous-excited-state phase transition produces a noticeable effect in the decoherence of the qubit. This is maximal when the system-environment coupling brings the environment to the critical point for the continuous phase transition. In this situation, the decoherence factor (or the fidelity) goes to zero with a finite-size scaling power law.
We analyze the decoherence induced on a single qubit by the interaction with a two-level boson system with critical internal dynamics.We explore how the decoherence process is affected by the presence of quantum phase transitions in the environment.We conclude that the dynamics of the qubit changes dramatically when the environment passes through a continuous excited state quantum phase transition.If the system-environment coupling energy equals the energy at which the environment has a critical behavior, the decoherence induced on the qubit is maximal and the fidelity tends to zero with finite size scaling obeying a power-law.
We describe the decoherence process induced on a two-level quantum system in direct interaction with a nonequilibrium environment. The nonequilibrium feature is represented by a nonstationary 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 different types of environments, namely, ohmic and supraohmic. These environments present different decoherence time scales than the thermal environment we used to study. As a consequence, we compute analytically and numerically the nonunitary geometric phase for the qubit in a quasicyclic evolution under the presence of these particular nonequilibrium 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.