Fast nuclear-spin gates and electrons−nuclei entanglement of neutral atoms in weak magnetic fields

We present a novel class of Rydberg-mediated nuclear-spin entanglement in divalent atoms with global laser pulses.First,we show a fast nuclear-spin controlled phase gate of an arbitrary phase realizable either with two laser pulses when assisted by Stark shifts,or with three pulses.Second,we propose to create an electrons−nuclei-entangled state,which is named a super bell state(SBS)for it mimics a large Bell state incorporating three small Bell states.Third,we show a protocol to create a three-atom electrons-nuclei entangled state which contains the three-body W and Greenberger−Horne−Zeilinger(GHZ)states simultaneously.These protocols possess high intrinsic fidelities,do not require single-site Rydberg addressing,and can be executed with large Rydberg Rabi frequencies in a weak,Gauss-scale magnetic field.The latter two protocols can enable measurement-based preparation of Bell,hyperentangled,and GHZ states,and,specifically,SBS can enable quantum dense coding where one can share three classical bits of information by sending one particle.