Feedback control of nuclear hyperfine fields in double quantum dot

In a coupled double quantum dot system, we present a theory for the interplay between electron and nuclear spins when the two-electron singlet state is brought into resonance with one triplet state in moderate external magnetic field. We show that the quantum interference between first order and second order hyperfine processes can lead to a feedback mechanism for manipulating the nuclear hyperfine fields. In a uniform external field, positive and negative feedback controls can be realized for the gradient of the longitudinal hyperfine field as well as the average transverse hyperfine field in the double dot. The negative feedback which suppresses fluctuations in the longitudinal nuclear field gradient can enhance the decoherence time of singlet-triplet qubit to microsecond regime. We discuss the possibility of enhancing the decoherence time of each individual spin in a cluster of dots using the negative feedback control on the transverse nuclear field.