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

Abstract

We present fast Rydberg-mediated entanglement involving nuclear spins of divalent atoms with ${}^{171}$Yb as an example. First, we show a 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 a state $(|\text{cc}{⟩}_{\text{e}}\otimes |\Phi {⟩}_{\text{n}}+|\Phi {⟩}_{\text{e}}\otimes |\Psi {⟩}_{\text{n}})/\sqrt{2}$ entangled between the electrons~(e) and nuclear spins~(n) of two atoms, where $|\Phi ⟩$ and $|\Psi ⟩$ are two orthogonal Bell states and $|\text{c}{⟩}_{\text{e}}$ denotes the clock state. For want of a better term, it is called a Super Bell State for it mimics a ``large'' Bell state incorporating three ``smaller'' Bell states. Third, we show a protocol to create a three-atom state $(\sqrt{3}|\text{ccc}{⟩}_{\text{e}}\otimes |\Lambda {⟩}_{\text{n}}+|\text{W}{⟩}_{\text{e}}\otimes |\text{GHZ}{⟩}_{\text{n}})/2$, where $|\Lambda {⟩}_{\text{n}}$ is a nuclear-spin state, $|\text{W}{⟩}_{\text{e}}$ is a W state in the ground-clock state space, and $|\text{GHZ}{⟩}_{\text{n}}$ is the Greenberger-Horne-Zeilinger~(GHZ) state in the nuclear-spin state space. The four protocols possess high intrinsic fidelities, do not require single-site Rydberg addressing, and can be executed with large ${\Omega }_{\text{m}}$ in a weak, Gauss-scale magnetic field for they involve Rydberg excitation of both nuclear-spin qubit states in each atom. The latter two protocols can enable measurement-based preparation of Bell, hyperentangled, and GHZ states.

19 pages, 11 figures

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Cited by in corpus (4)

• Holonomic swap and controlled-swap gates of neutral atoms via selective Rydberg pumping
• Fast nuclear-spin entangling gates compatible with large-scale atomic arrays
• Coherence enhancement of Rydberg polaritons
• Fast measurement-based generation of large-scale Greenberger-Horne-Zeilinger state with atomic nuclear-spin qubits