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

Abstract

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.

Graphical abstract

Keywords

nuclear-spin qubit / electrons−nuclei entanglement / super Bell state / Greenberger−Horne−Zeilinger state / Rydberg-mediated entanglement / quantum dense coding

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Acknowledgements

The author thanks Yan Lu for useful discussions. This work was supported by the National Natural Science Foundation of China under Grant Nos. 12074300 and 11805146, the Innovation Program for Quantum Science and Technology 2021ZD0302100, and the Fundamental Research Funds for the Central Universities.

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