Coherence evolution and echo effect of an electron spin, which is coupled inhomogeneously to an interacting one-dimensional finite spin bath via hyperfine-type interaction, are studied using the adaptive time-dependent density-matrix renormalization group method. It is found that the interplay of the coupling inhomogeneity and the transverse intrabath interactions results in two qualitatively different coherence evolutions, namely, a coherence-preserving evolution characterized by periodic oscillation and a complete decoherence evolution. Correspondingly, the echo effects induced by an electron-spin flip at time $\tau$ exhibit stable recoherence pulse sequence for the periodic evolution and a single peak at $\sqrt{2}\tau$ for the decoherence evolution, respectively. With the diagonal intrabath interaction included, the specific feature of the periodic regime is kept, while the $\sqrt{2}\tau$-type echo effect in the decoherence regime is significantly affected. To render the experimental verifications possible, the Hahn echo envelope as a function of $\tau$ is calculated, which eliminates the inhomogeneous broadening effect and serves for the identification of the different status of the dynamic coherence evolution, periodic versus decoherence.

• Received 13 February 2008

DOI:https://doi.org/10.1103/PhysRevB.78.054433