Quantum Decoherence of Dressed Central Spins in Nuclear Spin Baths

We present a physically clear, reliable and easy to implement solution to the decoherence problem of central spin induced by entanglement with the nuclear spin bath for a general class of systems. The critical feature of this class of decoherence problems is that the renormalized energy for the central spin has a dressed form in the dressed basis, which is also fluctuating together with the fluctuation of the Overhauser field when nuclear spins flip or flop in the bath. By proving that fluctuation has negligible effects on the dressed basis compared with dressed energy, we approximate dressed basis as static and treat dressed energy exactly in our model. In the renormalized basis for the bath, hyperfine mediated long range interactions are absorbed as fluctuation of the Overhauser field and contribute as single spin correlations in the total decoherence, so the central spin decoherence caused by the nuclear spin bath can be systemically solved by the cluster correlation expansion method.