Geometric phase of interacting qubits: Mean-field analysis

We consider a system consisting of a large number of interacting qubits and study the geometric phase of one of them. The many body interaction is analyzed within a mean-field approach when the reduced dynamics of a single qubit is described by a nonlinear Hartree equation. Generally, the geometric phase is highly sensitive to the type and the strength of interaction. However, we identify regimes where the geometric phase is almost independent of the qubit-qubit coupling.

Figure 1

(Color online) (a) The geometric phase $\Phi =\Phi \left(2\pi \right)$ of a qubit for the Ising-type coupling with ${\alpha }_x={\alpha }_y=0$ and ${\alpha }_z=\mu$ in Eq. (8). The qubit is initially prepared in a state given by Eq. (13) and parametrized by the angle $\theta$. (b) Plot of the curves underlined in (a). (c) GP as a function of the interaction strength $\mu$ for selected initial preparation.

Figure 2

(Color online) The geometric phase $\Phi =\Phi \left(2\pi \right)$ of a qubit evolving in the presence of decoherence. The Ising-type coupling ${\alpha }_x={\alpha }_y=0$, ${\alpha }_z=0.5$, and the initial preparation given by Eq. (13) are assumed. (a) Results for $\gamma =0.1$ and various average number of thermal photons $N$ in the environment. (b) The same as in (a) but for $N=0$ and selected values of the dissipation strength $\gamma$.