Generating entanglement and squeezed states of nuclear spins in quantum dots

We present a scheme for achieving coherent spin squeezing of nuclear spin states in semiconductor quantum dots. The nuclear polarization dependence of the electron spin resonance generates a unitary evolution that drives nuclear spins into a collective entangled state. The polarization dependence of the resonance generates an area-preserving, twisting dynamics that squeezes and stretches the nuclear spin Wigner distribution without the need for nuclear spin flips. Our estimates of squeezing times indicate that the entanglement threshold can be reached in current experiments.