Analytically solvable model for the entanglement via scattering-like mechanisms

We study entanglement in a composite system built out of two interacting subsystems. The long-time entanglement is shown to be quantified in terms of the S-matrix of an auxiliary single-particle scattering process. We present exact results for a system consisting of a qubit and an oscillator as well as for the case of a pair of qubits and a single oscillator. We show that entanglement can precisely be controlled by tuning the parameters of the corresponding scattering process. Within tailored parameter regimes, the extremal entanglement is achieved when time of scattering is of order of the oscillator frequency inverse.     

Geometric phase as a determinant of a qubit�C environment coupling

We investigate the qubit geometric phase and its properties in dependence on the mechanism for decoherence of a qubit weakly coupled to its environment. We consider two sources of decoherence: dephasing coupling (without exchange of energy with environment) and dissipative coupling (with exchange of energy). Reduced dynamics of the qubit is studied in terms of the rigorous Davies Markovian quantum master equation, both at zero and non–zero temperature. For pure dephasing coupling, the geometric phase varies monotonically with respect to the polar angle (in the Bloch sphere representation) parameterizing an initial state of the qubit. Moreover, it is antisymmetric about some points on the geometric phase-polar angle plane. This is in distinct contrast to the case of dissipative coupling for which the variation of the geometric phase with respect to the polar angle typically is non-monotonic, displaying local extrema and is not antisymmetric. Sensitivity of the geometric phase to details of the decoherence source can make it a tool for testing the nature of the qubit–environment interaction.