Decoherence and Loschmidt echo for qubit induced by a reservoir of coupled bosons

We study decoherence of a qubit coupling to the degenerate coupled bosons reservoir (DCBR) and the Loschmidt echo of DCBR. In the weak coupling of the qubit to the reservoir, the decoherence is significantly enhanced with increase of the coupling strength between modes, and the envelope of the decoherence function shows non-Gaussian decay (power-law). But under strong coupling conditions, the decoherence is slightly increased with increase of the coupling strength between modes, and the envelope of the decoherence function shows Gaussian decay for small coupling strength between modes. With increase of the coupling strength between modes, the envelope of the decoherence function shows irregular decay. For quite a long fixed time, change of the Loschmidt echo of DCBR with the mode coupling parameter shows stable multi- peak structure. This indicates that the decoherence will be strengthened for some value of coupling strength between modes.