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We solve the long-standing central spin problem for a general set ofinhomogeneous bath couplings and a large class of initial bath states. Wecompute the time evolution of the coherence of a central spin coupled to a spinbath by resumming all orders of the time-convolutionless master equation, thusavoiding the need to assume weak coupling to the bath. The fully quantum,non-Markovian solution is obtained in the large-bath limit and is valid up to atimescale set by the largest coupling constant. Our result captures the fulldecoherence of an electron spin qubit coupled to a nuclear spin bath in a GaAsquantum dot for experimentally relevant parameters. In addition, our solutionis quite compact and can readily be used to make quantitative predictions forthe decoherence process and to guide the design of nuclear state preparationprotocols.

Nonperturbative master equation solution of central spin dephasing dynamics