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The entanglement of vortices in a two-dimensional Bose-Hubbard model withartificial gauge fields is investigated using the exact diagonalizationtechniques. We propose an effective Hamiltonian for the spin-spin interactionsbetween vortices responsible for this entanglement, and show that theentanglement can be detected through the quantum interference of the bosons inthe vortex centers achieved using the Raman coupling and the quantum gasmicroscope. The strong bosonic coherence between the vortex centers originatesfrom the charge-density wave order in the vortex core. It is robust against thevarying of the pinning strength for the vortices to a wide range, and thecoherent bosons can be viewed as a qubit stored in the ground state of thesystem. Our proposal provides a feasible scheme of quantum memory for storingqubits useful in quantum computation.

Detecting the entanglement of vortices in ultracold bosons with artificial gauge fields