  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.
